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OCR for page 533
Hydrodynamics of Ship Wake Surfactant Films
R. Peltzerl, J.H. Milgram2, R. Skop3, J. Kaiserl, O. Griffinl, W. Barger
([Naval Research Laboratory, USA)
Massachusetts Institute of Technology, USA)
University of Miami, USA)
ABSTRACT
When compacted at the free-surface, surface-active ma
terials have very strong wave damping properties. Careful
measurements are required to characterize these physical ef
fects. Prior to a Field Experiment in January 1989, we re
hned the spreading oil technique, developed by Adam in
1937 to characterize the physical properties of a surfactant
film, so as to provide the necessary spatial resolution to iden
tify fine structure in the surface tension gradients on the
surface generated by the passage of a ship. We present an
in-depth look at the measurements of the cross-wake surface
tension distributions that were obtained during the Field Ex
periment for a Navy ship at 25 knots. These cross-wake sur
face tension profiles, together with the film pressure-area and
elasticity data also presented, allow us for the first time to re
alistically calculate the changes in wave energy due to these
surfactants for a given radar wavelength band. To accom
plish these calculations we leave developed a computer model
which uses the time series of surface tension together with
the film pressure-area and elasticity data from the Langmuir
trough and the wind velocity and direction as input to gen
erate cross-wake profiles or two-dimensional maps of wave
energy decay for a given radar wavelength. In this paper w
describe the development of this model and present some
results of wave energy decay for a given radar wavelength
obtained with the model and compare these results to air
craft SAR intensity measurements obtained during the run. v
L, LWL
Lt
LU,P
LWW
n
n
SAW
SAO
Sow
Sw
Sal
st
Ss
NOMENCLATURE
free surface area of surfactant film
surface wave height
c wave phase speed
cg, cg (vector) group velocity of a wave
dw'/dz vertical derivative, RMS turbulent vertical velocity
D ship draft
E energy density spectrum
Ea ambient spectral level outside the wake
ES surface elasticity
F force on Wilhelmy plate exerted by liquid
gravitational acceleration
depth below the free surface
definition, h = E9k2k2
wavenumber
H
h
k
ship length, waterline length
length of the zone of ship-affected turbulence
length of Wilhelmy plate in contact with liquid
length of the white water wake
logarithmic slope of pressure-area curve
propeller revolutions per second (Figure 1)
surface tension force at the air-water interface
surface tension force at the air-oil interface
surface tension force at the oil-water interface
wave energy growth due to wind energy input
wave energy growth due to nonlinear interactions
wave energy decay due to turbulence
wave energy decay due to surfactant damping
time
friction velocity of the wind
ten meter wind speed
ship speed
wake width
downstream distance
surface tension of clean water
wind induced wave growth rate
wind induced wave growth rate
wave decay rate due to surfactant damping
wind induced wave growth rate
wave growth rate from nonlinear interactions
definition, ~ = (gk + rip k3~/2
angle between wave and wind direction
kinematic viscosity of seawater
surface film pressure
3.14159.......
density of seawater
radian wave frequency
measured surface tension
definition, ¢' = ok
t
it*
ulo
V, VS
W
Xc'
~1
i02
As
low
p
Tmeas
1.0 INTRODUCTION
One prominent feature of the wake of a surface ship
is a long narrow region of relatively calm water behind the
ship that is characterized by the absence of short wavelength
waves. This region is commonly referred to as the "dead"
water or centerline wake region. It is usually several ship
beans in width and persists for many ship lengths behind
the ship. This region of relatively low radar backscatter is
the most consistently seen wake manifestation in synthetic
aperture radar (SAR) images of ship wakes on the ocean
surface. Another feature in the SAR images of ship wakes is
533
OCR for page 534
the appearance of dark lines aligned at some narrow angle to
the ship's path that sometimes outline this centerline wake
region far behind the ship. Surface tension changes caused
by the presence of surface-active films that have been con-
centrated at the edges of the centerline wake by the passage
of the ship have been suggested as one of the physical mecha-
nisms responsible for these SAR image features. Surfactant
films strongly affect the propagation of short gravity and
capillary waves which interact with electromagnetic waves
at both radar and visible wavelengths. Surface tension and
surface elasticity are the two major physical properties of
surfactant films which contribute to short wave damping.
To investigate the physical origin of these SAR im-
age features, a small, towable, instrumented catamaran was
built and deployed by NRL scientists to measure the cross-
wake surface tension distribution after the ships passage.
This instrument package was named the Surface TEnsion
Measuring System (STEMS). The device measures surface
tension by dropping a sequence of calibrated spreading oils
along a straight line on the water surface and recording their
behavior with a video camera. Each individual oil represents
one surface tension value so that if one oil spreads and the
next one does not, then the surface tension is bracketed be-
tween the two values.
Surface elasticity cannot be measured in situ by the
spreading oil technique. Therefore, 1-liter water samples
were collected for later measurements in a Langmuir trough.
Surface elasticity is defined as the product of film area times
the slope of the pressure-area curve at the corresponding
value of the film area as measured in the trough. The sur-
face elasticity distribution can then be calculated from the
resulting pressure-area curve together with the ambient sur-
face tension distribution measured using STEMS. Coupling
the surface tension measurements made by STEMS to the
determination of the pressure-area curves has for the first
time allowed us to infer elasticity distributions for ocean
VELOCITY BLOW W-AVE Rat
//~ISR / , ~WAKED
water and to realistically calculate the changes in wave am-
plitude due to these surfactants.
In this paper we describe the STEMS device and give
examples of the results that were obtained during its deploy-
ment in an extensive Field Experiment that was conducted
in the vicinity of Santa Cruz Island, California in January,
1989 to study surfactant films. Previous to this experiment,
in situ surface tension data have never been measured to
the resolution in surface tension obtained or with such fine
spatial resolution. The NRL data from the experiment show
that these surface active films play a significant and some-
times dominant role in the formation of the two SAR image
features of ship wakes. We also present an overview of the
chemical and physical properties of surface active materi-
als and the techniques used to measure and determine their
physical properties when they adsorb at the air-water inter-
face.
2.0 BACKGROUND
2.1 Description of the Ship Wake
Irk this section we will describe the wake of a surface ship
from a perspective corresponding to the large-scale physical
phenomena that are observed both visually and by means of
remote sensing systems. A schematic of a surface ship wake
is illustrated irt Figure 1. The wake is composed of white
water, viscous wake, propeller wake, and Kelvin wake. The
white water generally originates at the bow, is reinforced at
the stern, and extends aft of the ship for a few ship lengths.
The viscous wake extends many ship lengths aft from the
stern of the ship and incorporates the flow moving in the
direction of the ship's travel due to the viscous drag, as
well as large-scale vertical flows and turbulence. Embedded
within the viscous wake is the propeller outflow or propeller
wake. Superimposed over Ellis is the classical Kelvin wave
pattern or Kelvin wale. The Kelvin wake is also the source
^.eSY~
`~\ ~/ 35°16' CUSP-CREST TANGENT LINES
l
1
1 - L = 655 V 1 5 n-05
1 WW s
it\
/ \ SHIPS HULL ~ ~
SHIP'S \REGION \ ~~~
HULL ~ \
NEAR WAKE, PRODUCTION ~
REGION
1 ~t~vvv/LwL = 53.5 [Vs/(gL`A,L)o 5]1.4o
-
Figure 1. Schematic of a surface ship wake
534
-FAR WAKE, DECAY
REGION
-
-
-
-
-
OCR for page 535
of many of the viscous wake manifestations. It is in fact the
breaking bow and stern waves from the Kelvin wave system
whirls contribute significantly to the white water regions at
the bow and stern. These wake manifestations lie upon the
ambient seaway made up of swell, wind waves, and short
gravity and capillary waves; all of which confuses the picture
even more.
It is often useful to draw an imaginary ellipse, extend-
ing several ship beans ahead of and off to each side of the
ship and a ship length or so aft of the ship, around the ship.
We call the region internal to the ellipse the near wake and
the region external to the ellipse the far wake. The near
wake can be thought of as the region where surface foam,
subsurface bubbles, and strong turbulence is generated. It is
also where the most rapid decay of these features occurs. In
the near wake, the initial region of the viscous and propeller
wakes is a region of high angular divergence (initial spread-
ing region, ISR) of foamy, turbulent, white water directly
aft of the ship's stern, generally outlined by what appears
to be a spilling-type breaking wave. There are two addi-
tional sources of highly energetic white water in the near
wake. The bow wave that is generated by the ship's mo-
tion breaks, producing white water and turbulence when the
wave steepness ah (a = wave amplitude and ~ = wavenum-
ber), is greater than ah _ 0.30 (Ramberg and Griffin 1987~.
The region adjacent to the ship's hull produces foam, bub-
bles and turbulence because of the frictional drag forces at
the surface of the hull.
The far wake is that region where the variations are
relatively slow i.e., where the foam, viscous, propeller, tur-
bulence and vertical features of the wake decay slowly and
steadily and where the surface roughness and thermal char-
acteristics gradually return to those of the surrounding am-
bient surface. Measurements have shown that thermal and
subsurface bubble wakes can persist for an hour or more after
the passage of a ship (National Defense Research Committee
1969~.
Under moderate to high wind conditions Auto > 3 m/s),
the ambient surface is sufficiently rough so that, visually, the
surface in the far wake appears smooth relative to the sur-
rounding surface. Recent high altitude photographs released
by NASA show that the centerline wake can be observed as
far back as 100 km behind a ship. Centerline wakes are vis-
ible in SAR imagery as a dark narrow line along the ships
track when the surface is sufficiently rough to yield a mea-
surable background return. Centerline wakes, in addition
to various other wake features are also visible in SEASAT
SAR imagery up to 15 km aft of flee ship (Lyden et al. 198S,
Vesecky and Stewart 1982~. Observations of the dark cen-
terline return irt many wake images show that this region is
generally significantly greater than the ship's beam in ex-
tent. The width of the dark centerline corresponds very well
with the width of the region over which there are breaking
bow and stern waves, waves from the Kelvin wave system.
The Kelvin wave system's 19°2S' boundary lines (cusp
lines) and 35°16' cusp-crest tangent lines are illustrated in
the figure. The apex of the boundary lines is always forward
of the bow (Newman 1970~. The transverse and divergent
wave crests are visible optically for many ship lengths astern
and to either side of the ship's path. Tl~e shorter, steeper di-
vergent waves tend to be emphasized in aerial photographs.
Under moderate to high wind conditions the transverse and
cusp waves appear in SAR images of the surface because
these waves modulate the existing field of ambient Bragg
waves (Lyden et al. 1988~.
The persistence of surface foam in the far wake depends
on the time it takes for the bubbles to break after they reach
the surface. The major factors that increase the stability
of a bubble at the surface are increasing salinity (Peltzer
and Griffin 1988), decreasing water temperature (Miyake
and Abe 1948), increased surface viscosity (Kitchener and
Cooper 1957), and the presence of organic surface active ma-
terials which modify the surface rheology (Adamson 1976~.
A recent photographic analysis by Peltzer (1984) developed
empirical relations for the length of the foamy white-water
region. These empirical relations are shown in the figure
and indicate that the length of the white water region is a
function of the Froude number.
2.2 Surface-Active Materials
The surface-active (surfactant) materials that are found
in all natural water bodies are chemicals which are by-
products of plant and animal life. The term surfactant
means that the long-chain (10 to 1000's) carbon polar-
organic chemicals which constitute these materials have a
natural affinity for the free surface of the water in which they
reside. Typically the molecules have an acid, alcohol, ketone
or other water-soluble radical on one end, which makes that
end of the molecule hydrophilic. The opposite end is very
similiar to a pure hydrocarbon, which is insoluble in water
and is hydrophobic. Because of the polar nature of these
substances, when they reach the water surface they find a
preferred state in which the hydrophobic end of the molecule
removes itself (sticks out) from the water, and this reduces
the Gibbs free energy of the water-surfactant system. The
lower free energy of the system requires energy to be put
back into the system to force the surfactants back into the
bulk water. Wind stress is the primary mechanism to do
this.
As the surfactants adsorb on the surface, they reduce
the surface tension and increase the two-dimensional elastic
modulus of the surface. A small increase in the surface con-
centration of the materials at the interface can lead to sig-
niDcant capillary and small surface-gravity wave (< 20 cm)
damping because the film viscously retards the very-small-
scale velocity held just under the interface. When these
areas become large enough they alter the appearance of the
sea surface being observed by remote sensing instruments.
In light to moderate winds Auto < 3 m/see) these surfactant
films are highly persistent. The films can reduce the radar
cross-section of the surface by as much as 15 dB depending
on the concentration and elastic properties of the film and
the radar wavelength.
Films can become concentrated enough to attenuate
surface waves when they are compacted by horizontal con-
vergences due to current field variations at the ocean surface.
The currents which are most likely to compact the surfactant
films within a ship's wake are the transverse currents gen-
erated by flow around the hull or currents associated with
the breaking bow and stern waves. Surfactant material can
also be rapidly transported to the water surface by adsorp-
tion at the air/water interface of rising bubbles generated
by air entrainment around the ship's hull, in the breaking
bow and stern waves and, in the wake flow. As these bub-
bles burst when they reach the air/water interface, the ma-
terial is merged with that already adsorbed on the water
535
OCR for page 536
surface (Skop, Brown and Lindsley, 1989~. These bubbles
are also concentrated by the horizontal convergences in the
wake flow behind the ship; this is an additional mechanism
which should enhance surfactant concentrations in the sur-
face convergence zones.
Measurements and observations of the wakes of large
ships (Kaiser et al., 1988) show the most persistent wake
feature to be a pair of bands of compacted surfactant mate-
rial aligned with the ship track along the edges of the tur-
bulent wake. The bands are typically one to several meters
wide and show a pronounced depression in surface tension.
The surface tension in the core of the wake generally has the
same value as the ambient water. Photographs suggest that
the surfactant material is being organized into these bands
by rising bubbles generated in the breaking bow wave which
scour the surfactants from the water column. Bubbles are
additionally important because they have been observed to
persist for an hour or more in a ship's wake. Since these bub-
bles presumably transport surfactants to the surface during
this time, they may contribute substantially to the long per-
sistence of the dark centerline wake signature.
Remote sensing of these ship-generated surfactant
bands with a SAR depends on the interaction of the electro-
magnetic waves with the Bragg-resonant short waves in the
region of the bands. The viscous properties of the surfac-
tant films in these bands attenuate the short waves and also
block their formation or reformation by wind. The damping
of these short waves reduces the Bragg scattering in the films
compared to that of the surrounding clean water and the film
bands appear dark in SAR images. Laboratory experiments
(Garrett 1967) have shown that surface-active materials at-
tenuate capillary waves through viscous damping at the sur-
face. Full-scale experiments (Huhnerfuss et al. 1981) have
demonstrated that slicks of surface-active materials attenu-
ate Bragg waves in the X- and L- SAR wavelength bands by
40 to GO percent. Since the magnitude of the backscattered
radiation from the surface is proportional to the amplitude
squared of the Bragg scatterers, this attenuation results in
a significant reduction of the backscattered radiation.
An example of the reduced return from these ship-
generated slick bands is shown in Figure 2a (Ochadlick, et
al. 1990~. The measurements were made near the Chesa-
peake Light Tower by the NADC SAR during the SAXON
88 experiment. Note the remarkable similarity between the
ship wakes and ambient features (mesoscale circulation pat-
terns highlighted by surfactant film bands) in the SAR image
and the similar features in the photographic image (Figure
2b) of the Mediterranean Sea taken from the Space Shuttle
Challenger by Scully-Power in 1984 (Scully Power, 1986~.
The photograph was taken into the sunglint pattern which
is produced on the water surface by those wave facets which
are oriented with respect to the surface to produce specular
reflections of the SU1I. In this case, the long persistent ship
wakes appear as bright, double bands with a darker area
between the bands. Both of these images are approximately
10 km wide and 42 km long. These concentrated films af-
fect the wake surface because they influence the transfer of
energy and momentum from the wind to the wave field and
inhibit wave formation (Barger et al. 19744.
a) L-Band SAR Image
by Pholographic Image
. ~..S
40 km
Figure 2. Airborne SAR and photographic images of ship-generated surfactant bands
536
OCR for page 537
3.0 SURFACTANT MEASUREMENTS
3.1 Surface Tension Measurement by
Spreading Oils
Several techniques have been proposed to measure the
mechanical properties of ocean surfactant films in situ (e.g.,
capillary wave damping, laser second-harmonic generation,
and spreading oils), but only the use of spreading oils has
been successful thus far. Adam (1937) was the first to use
a series of buoyant calibrated oils to determine the surface
tension of sea water in situ. More recently this technique
has been described by Garrett and Duce (1980~. When sev-
eral oils are dropped onto the surface of the sea where a film
of surface-active material may or may not be present, some
will spread while others will not, and therefore the surface
tension of the sea at the test point can be bracketed between
the calibrated values of any two oils in the set. Figure 3 il-
lustrates (a) a spreading oil and (b) a non-spreading oil on
the water surface. The straight white lines are toothpicks
that were used to apply the oils to the surface. The reso-
lution of the surface tension measurements depends on the
differences in the calibrated values of the test oils. The oils
must also be dispensed rapidly and close together to identify
fine structure in the surface tension gradients. For the Field
Experiment we refined this technique to provide the neces-
sary spatial resolution and prepared a set of twenty three
spreading oils to cover the surface tension range from 44 to
73 mN/m. The preparation and calibration of these oils and
the principle by which these oils work is described below.
a) Spreading Oil
b) Non-SpreadIng Oil
Figure 3. Video image of the spreading oil distribution
The spreading oils were made from a pure non-
spreading paraffin oil into which precisely controlled trace
quantities of a pure surface-active compound, dodecanol,
were dissolved. Different batches of commercially available
paraffin oil already contain traces of surface-active compo-
nents, so each set of spreading oils must be calibrated - they
cannot be made reliably by following the recipe employed for
an earlier set. Calibrations were carried out using the Lang-
muir trough facility of the NRL Chemistry Division and can
be more easily discussed in terms in terms of film pressures.
Film pressure (II) is defined as the difference in surface ten-
sion calculated by subtracting the surface tension of water
covered by a film (Tmeas) from the surface tension of clean
water Gil, or II = ct-TmeaS
The surface tension (and therefore the film pressure)
was varied in the Langmuir trough instrument by compress-
ing or expanding a monolayer film of oleyl alcohol surround-
ing the oil to be calibrated. The plateau film pressure (at
which the oil drop had expanded to a thin disc that could be
varied in diameter by expanding or compressing the mono-
layer while still maintaining a constant film pressure) was
the assigned equilibrium spreading pressure (ESP) of the
oil. For oil drops of approximately 20 mg the diameter was
approximately 3 cm at the ESP.
The principle by which these oils work is illustrated in
Figure 4. SAW is the surface tension at the air-water in-
terface, SAO is tile surface tension at the air-oil interface,
and Sow is the oil water interracial tension. Since SAO and
Sow are reduced by adding a surface-active compound to
the paraffin oil, a series of oils with varying spreading charac-
teristics can be prepared. If SAW > (SAOCOSA + SOWCOSB)
the oil will spread. Organic surface-active films on water
will reduce SAW. AS the oil becomes thinner by spreading,
both cosA and cosB approach the value of 1 and the force
balance required for continued spreading becomes SAW >
(SAO + SOW). When the colorless oil spreads to a thickness
in the 500 to 700 nanometer range, interference colors can
be observed visually from a distance. To make a measure-
ment, oils with progressively higher concentrations of dode-
canol are dropped onto the surface until one is observed to
spread.
SAW
SAO
Sow
~` AIR
OIL )
-
>/ WATER
Figure 4. Balance of forces acting on an oil drop
The resolution of the measurement in surface tension
depends on the ambient surface tension. Table 1 gives the
spreading pressures for tile twenty three oils used in the Field
Experiment. The resolution is nominally the difference in
pressure between adjacent oils, which is tabulated in Column
Three of Table 1. Note that at high surface tensions (near
s37
OCR for page 538
the clean water values) the resolution is nearly 0.16 mN/m,
but reduces to several mN/m at very low surface tensions.
The spreading pressures were intentionally graduated this
way to optimize the resolution of the measurement to the
physical processes involved.
Oil Number Surface Tension Difference
2
3
4
5
6
7
8
9
10
73.03
72.87
72.72
72.56
72.40
72.26
72.08
71.92
71.76
71.63
.16
.15
.16
.16
.14
.18
.16
.16
.13
.28
The measurement in the Langmuir trough consists of
determining the pressure-area relationship for flee surfac-
tant, from which its elastic properties are calculated. This
procedure is described in detail by Barger and Means (1985)
and outlined here. The surfactant material in the sample ad-
sorbs to the surface in a few hours and forms a thin film. The
free surface area (A) containing the film is decreased slowly
by moving a barrier along the surface as the surface ten-
sion (Tmeas) is measured with a Wilhelmy plate (Barger and
Means 1985). The V\7ilhelmy plate technique uses a flame-
cleaned thin platinum plate which is over the filmed water
surface. It is carefully and slowly brought into contact with
the film and a meniscus forms which then exerts a down-
ward force F on the plate equal to 2TmeaSL1Vp, where Lop is
the length of the plate in contact with the liquid (bonyancy
and plate-effects are ignored here). The surface tension is
Amens = F/2Lu,p. In the actual procedure the force is mea-
sured with a strain gauge and the system carefully calibrated
against known liquids. This procedure generates the func-
tion VIA). The measured surface tension TmeaS is related
to the underlying clean water surface tension (~) and the
pressure (II) exerted by the surfactant film by the relation
11 71.35 .34
12 71.01 .17Tmeas = LY-II. (1)
13 70.84 .31The elasticity of the film is defined as
14 70.53 .53
,5 70.00 .67E9 =-AdA. (2)
16
17
18
19
20
21
22
23
69.33
68.71
66.62
64.63
61.99
60.82
53.4()
44.55
TABLE 1. SPREADING OILS
3.2 Determination of Film Elasticity
The important property of a surfactant film which gov-
erns the wave damping is its elasticity (Es). However, we
did not measure this in situ, but determined it indirectly as
follows.
We collected samples of water during the Field Experi-
ment and then transported them back to NRL for measure-
ment in the Chemistry Division's Langmnir trough. The
bottles were chemically cleaned, one liter reagent bottles
containing a residual amount of triple-distilled water. The
bottles were drained, flushed several times with the sea wa-
ter to be sampled from a depth of 0.25 to 0.5 meters, and
then filled. This was done by lowering the bottles over the
side of the host research vessel R/V Garnet Banks. The sam-
ples were then treated with lo Al of a sodium azide solution
to kill any life in the sample, thus "freezing" the chemical
composition of the surfactants. The bottle was then sealed
and stored in a cool, dark place until measurements were
made in the Langmnir trough.
.62 Theme hv t.~.kin~ t.h~ n~.tive. Of the logarithmic slope of the
2.09
1.99
2.64
1.17
_ ^^ ~ ~ _, ~ wade ~ -O · O · O ~ ~
Il(A) curve measured in the Langmnir trough we obtain the
function Es(A). From the measured II(A) relation we then
obtain
ES = Es(~)'
7.42
8.85 hi, i,
(3)
cinch hate F7~tAN and 1[(AN are single valued over the range
of values of II encountered in the Field Experiment (0 to 30
mN/m)
In order to determine the elasticity Es by this method
we make the assumption that the surfactant material ad-
sorbing at the water sample in the laboratory has the same
physical properties as that which had adsorbed on the sea
surface. Treating the samples with sodium azide solution
is intended to help insure this process. Very recent tests by
W. Barger (private communication, 1990) suggest that sam-
ples collected and measured within one hour give the same
results as samples stored for months. Hundreds of film sam-
ples collected by various techniques, including screens and
rotating glass drums which sample a layer on the order of
microns near the surface, have shown remarkably similar
pressure-area relations (Barger and Means, 1985; Barger et
al., 1988). In addition, surface chemists define the reciprocal
of the elasticity as the coefficient of compressibility. Com-
pressibility measurements for fifty two film samples from
Atlantic surface, bulk and deep water and Chesapeake Bay
water are reported in Barger and Means (1985) and also
show remarkable similaries in behavior.
However, there is the possibility that mechanical and
chemical reactions occur on the ocean surface which may al-
ter the mechanical properties of the surfactant film. The two
most likely possibilities are photo-chemical reactions due to
the ultraviolet component of the solar spectrum and working
of the film due to the continual compaction and expansion
538
OCR for page 539
caused by the passage of surface waves. Furthermore, in
calm conditions the surface constituents may not have the
same relative concentrations as those in the sampled water
column. Presently there is little or no evidence to address
these issues, so we are reasonably confident in the relation-
ship given by equation (3) to determine the elasticity of films
on the the ocean surface.
3.3 STEMS (Surface TEnsion Measuring
Systems Description
3.3.1 Deployment and Operation
STEMS is a catamaran which is towed from the host
vessel (R/V Garnet Banks, an ex-Navy YTB class tug) from
a boom (6 m long) off the forward port side of the vessel.
A photograph of STEMS is shown in Figure 5. It is 2 m
wide, 3 m long, and weighs 135 kg (300 lbs). Figure 6 shows
the towing configuration employed in the Field Experiment.
STEMS needs to be outside of any disturbance created by
the host vessel, so it has a movable rudder to control its
distance away from the towing vessel. In all cases it must
sample an undisturbed water surface. Maximum tow speed
depends on sea conditions and wind, but generally a tow
speed of 0.5 m/see (1 kt) was found to give relaible perfor-
mance of STEMS. During the operation we positioned the
R/V Garnet Banks either north or south of the wake pro-
duced by the passing target ship, about 100 to 200 meters
off-track before the scheduled start of the individual test
runs. As the target approached, we moved up on its track
and towed STEMS across the wake, intending to follow the
serpentine pattern shown in Figure 7. Our tow speed was
about 0.5 m/see, so that in the time allocated for each run
(approximately 50 minutes) we could only make three to
four wake crossings. If the sea became too rough, turbu-
lence and splashing within STEMS made observation of the
spreading oil behavior difficult to impossible.
The device measures the surface tension in situ by drop-
ping any twenty two of the twenty three calibrated spreading
oils on the water surface from twenty two individually regu-
lated channels. The spreading behavior of the oils (whether
they do or don't spread) is recorded with a video camera
system. Each oil represents one surface tension value, so if
one oil spreads and the next one does not, the in situ surface
tension is bracketed between the values of the two spreading
oils. In some cases a drop of oil will neither spread nor not
spread, but it will oscillate instead. Presumably its spread-
ing pressure is almost exactly the value of the surfactant film
and the oscillation occurs because the ambient surface ten-
sion oscillates about a mean value due to alternate surface
compactions and expansions induced by the passage of sur-
face waves. The dropping of each individual oil is controlled
from the ship and a permanent video record of its spreading
behavior is obtained for later analysis. In addition to being
recorded on VHS video tapes, the STEMS data were mon-
itored in real time with the operator annotating the videos
with verbal comments on the audio track. A second video
system was placed on a mast above the bridge to monitor
STEMS and to record the general environmental conditions
encountered. In addition, an audio cassette record was made
from the bridge describing various facets of the operation,
the environmental conditions, when STEMS entered a slick,
and other pertinent test information.
Surface TEnsion Illeasurement system (STEINS)
Figure 5. Photograph of the STEMS
~30m ~
0.5 m/se ~ R/V GARNET BANKS | =
(1 at) ~ ~
\1 em BOOM
\ TOWING/UMBIUCAL CABLE
15m \
\/\= SURFACE TENSION MEASUREMENT
_13 m1-
SYSTEM (STEMS)
Figure 6. STEMS towing configuration
~ - -TTARR&aCEK - - - 1~
1
/^
video,:
t
RN GARNET BANKS
if
20C m
_
__ ~WAKEN 100 m
CENTERLINE I
it)- SIIIOKE FLARE
Figure 7. STEMS wake crossing pattern
3.3.2 Data Resolution and Quality
One reading of surface tension was typically obtained
every one to two seconds when the winds were under 5.5
m/see, and less frequently for higher wind speeds. This
gave a cross-wake resolution of 0.5 to 1.0 m in the lighter-
wind runs. The down-wake resolution was highly variable
539
OCR for page 540
but averaged 50 m. The resolution in surface tension varied
from 0.16 mN/m to a few mN/m based on the differences
in spreading pressures of the oils (see Table 1~. Through
the first nine days of the Field Experiment (Jan. 23rd to
Jan. 30th), the oil number in the table corresponded di-
rectly to the channel number on the STEMS. Channels 5
and ~ did not work throughout the entire test and channel
22 worked only on the final two days of the Field Experi-
ment (Jan. 31st and Feb 1st). Oil 23 was used on the final
day of the test (Feb. 1st) in place of oil 1. It was unfortu-
nate that oils 22 and 23 were not working or available during
most of the Field Experiment because we could not estab-
lish the maximum value of the surface tension decrease in
certain regions of both the ship generated and ambient sur-
factant bands. If we assume that the physical properties of
the compacted surfactant material in the bands were similar
throughout the Field Experiment, we know that the maxi-
mum surface tension decrease in the bands varied between
our measured value of 11.3 mN/m and some value greater
than 27.2 mN/m. There were regions where oils 21, 22 and
23 did not spread when they were used on the final day (Feb.
1st) of the Field Experiment and in addition, oils 21 and 22
did not spread during portions of the measurements on Jan.
31st. All of the film pressure - area curves we have exam-
ined so far (1/26, 1/28, 1/29) have similar characteristics,
which suggests that the physical properties of the surfactant
films are indeed similar on a day to day basis. Furthermore,
measurements of surface film pressures of surface-active or-
ganic matter generated by marine phytoplankton typically
range between 20 mN/m and 30 mN/m (Frew et al., 1990~.
Considering all of the above, we can confidently assume that
the maximum surface film pressure in the film bands varied
somewhere between 11.3 ~nN/m and 30 mN/m.
3.4 Results of the Surface Tension Measure-
ments
The STEMS data processing consists of playing back
the video tapes several times and recording the spreading
behavior of each oil. In this manner the dividing line be-
tween spread and non-spread is determined as a function of
time on the video. Readings are made each second. The
time series of surface tension is then input to a computer to-
gether with the film pressure-area and elasticity data from
the Langmuir trough. Also, wave damping coefficients (as a
function of elasticity for a given surface wavelength) can be
calculated. Finally cross-wake profiles or two-dimensional
maps of surface tension, film pressure, elasticity and wave
damping can be generated for a given surface wavelength.
We include here for each of the wake crossings, the measured
surface tension profiles across the wake. The corresponding
film pressure profiles can be calculated using equation (1)
with cat taken as the surface tension measured in the clean
water well outside of the wake. The film pressure directly
relates our field measurements to the laboratory-determined
elasticity. The wake widths were determined by multiplying
the speed of the towed STEMS platform by the total time
it took the STEMS to cross the wake.
Surface tension measurements were obtained during the
25 knot run along three wake crossings centered at 3735 m,
11978 m and 21316 meters aft of the ship. These surface
tension distributions are shown in Figure 8. All crossings
are plotted so that the water south of the wake (0.0 m) is at
the left of the figure. The wake edges are defined as the lo
. .
cation of the edge of the outermost foam bands in the video
record made by the STEMS as it crossed the wake and/or
the region corresponding directly to the sudden decrease (or
increase) in surface tension measured by the STEMS as it en-
tered (or exited) these outermost surfactant bands. Regions
of decreased surface tension relative to the ambient value are
caused by increased film pressure of a compacted surfactant
in those regions. Each of the three crossings has two edge
bands of compacted film as well as one or more additional
bands between the edge bands. From this data alone it is
not clear whether these inner bands persist, but rather move
around, or appear and disappear. The two outermost bands
were visible to the eye as slicks, whereas this was not gen-
erally true for the inner bands. Since the surface is already
smooth in the centerline region of the turbulent wake, the
visibility of these inner bands will be limited. In addition,
the surfactant films will not allow the wind waves to regrow
in these regions and will limit the regrowth throughout the
entire centerline wake region. The outer bands are visible
because of the contrast between the ambient surface where
small waves are present and the smooth surface where the
small waves have been damped by the compacted surfactant
material. The surface tension in the core of the wake has
the same value as the ambient (away from the wake).
As was discussed in Section 3.3.2, we were not able to
measure the minimum surface tension value in certain re-
gions of the crossings. For the crossings shown in Figure 8 we
have assigned an arbitrary value of 60.0 mN/m to those re-
gions where oil 21 did not spread. This value is only slightly
less than the measured value of 60.82 mN/m associated with
oil 21 which did not spread.
4.0 MODEL DEVELOPMENT, CALCU-
LATIONS AND COMPARISONS WITH
MEASUREMENTS
4.1 The Energy Balance Equation
To examine the short wave field in the wake of a sur-
face ship, we have developed a model based on the spectral
energy balance equation
)
ot + cg( k ) - VE( k ) = SW( ~ ) + Snl( A' )
-St( k )-Ss( k ),
(4)
where E is the energy density spectrum, k is the circular
wave number vector, t is time and cg( k ) is the group ve-
locity vector for the spectral component and the S's are the
energy source terms for the spectral component at the wave
number k.
SW and Snl represent the rates of energy input to the
waves from, respectively, the wind and wave-wave nonlinear
interactions. St is the rate of energy dissipation due to the
interactions of the waves with turbulence. Ss is the direct
rate of energy dissipation due to viscosity which can be in-
fluenced by the effect of surface film elasticity on the free
surface boundary layer.
The energy balance in the form of equation (4) neglects
wave scattering by turbulence and wave diffraction by mean
flows. These effects are insignificant compared to the other
540
OCR for page 541
_ 78
F 73
0
._
68-
:
~ 63
In
58
78
E 73
~ 63
In
58
78 ~
73 ~
0
In 68
In
58
a) Distance Aft, 3575 m (21.8L), Wake Width, 117 m (6.93B)
I ~MAIMS \AI;~ _ I
I Isaac ''IUtil -|
Edge Band ~1
~ Inner Band.
is/ \*
~Edge Band
b) Distance Aft, 11978 m (69.8L), Wake Width, 144 m (8.56B)
~ ~Wake Width .~
Edge Bandy
~Edge Band
c) Distance Aft, 21316 m (124.2L), Wake Width, 165 m (9.83B)
,_ -Wake Width ~- 1
Edge Band
Inner Bands
~ Edge Band |
_ _!
. . . . . . . .
15 65 115 165 215 265
Cross-Wake Distance, (m)
Figure 8. Measured cross-wake surface tension distributions
source terms except in the first few ship lengths of the wake
(near field region), when estimated from the scattering the-
ory of Phillips (1958) and the analysis of diffraction by ship
wake flows by Skop et al. (1990~.
At the present time little is known about relationships
between the four source terms on the right hand side of
equation (4) and oceanic conditions, either in or out of ship
wakes, for the short waves associated with radar backscat-
tering. For this reason, we cannot make a precise compar-
ison between radar measurements and the predicted wave
energy distribution. Instead, we shall compare radar mea-
surements with predictions frown equation (4) using plausible
formulations for the source terms based on what is currently
known about them. The resulting qualitative agreement
between radar measurements and the calculated wave en-
ergy distribution, including its sensitivity to variations in
the source term formulations, will indicate the important
hydrodynamic effects leading to the short wave calming in
ship wakes. Taking this approach, we now explain the for-
mulations we have used for the source terms.
-1
4.1.1 Wind Energy Input to Short Waves
Wind induced growth of short waves was determined by
Plant (1982) on the basis of available experimental data. He
expressed the growth rate, ,Bw(a), of a spectral component
with circular frequency ~ as:
§1,, = (0.04 ~ 0.02)a(u*/c)2cos8. (5)
Here it* is the friction velocity of the wind, c is the phase ve-
locity of the wave component and ~ is the angle between the
wind and the direction of wave propagation. Since the data
used by Plant includes damping from viscosity, the growth
due to wind alone should be slightly larger than his esti-
mate. Therefore, we will use 0.05 for the numerical coeffi-
cient which is slightly above the median, but still in Plant's
range. Under typical conditions, u* is related to the ten
meter wind speed ulo by:
Ilm = Ulo/30.
541
(6)
OCR for page 542
Useful information on wind energy input in addition to
equation (5) is provided by the studies of Mitsuyasu and
Honda (1982~. They found that when the water surface was
calmed, interestingly achieved with a surfactant, the friction
velocity was reduced to less than u~o/30. Changing from a
naturally wind roughened surface to a nearly calm surface
reduced the friction velocity by roughly 14 percent. If the
formulation of equation (5) applies, this reduces the spectral
growth by thirty percent.
To account for the reduction in growth rate when the
waves are calmed, rather than using Su, = 'dwE' we approx-
imate Sw as:
Sw = (41 + p2 E )E, (7)
where Ea is the ambient spectral level outside the wake, and
31 + p2 = 0.05~(u*/c)2cos8. (8)
For our subsequent "base case" calculations, we shall take
p2 = pi/2. This corresponds to a 33 percent reduction in
the energy growth rate from the wind if the waves were
completely calmed.
The short waves which are attenuated in the ship wakes
have wavenumbers and frequencies several times that of the
spectral peak. On the other hand, the available data used
by Plant in developing equation (5) are based on wave fre-
quencies close to the spectral peak. The validity of the for-
mulation for frequencies much higher than the spectral peak
is unknown. However, it is the best information presently
available and that is why we have used it, modified by the
reduction due to surface smoothness. We shall include the
base case of p2 = 0 in our subsequent calculations to demon-
strate the effect of neglecting the reduction in growth rate
due to smoothness.
4.1.2 Nonlinear Energy Transfer to
Short Waves
The present state of the art in estimating nonlinear en-
ergy transfer is the resonant interaction theory of Hassel-
mann (1962~. This is a perturbation based theory that in-
cludes Taylor series expansions about the mean free surface
elevation. As a result, when short waves have lengths that
are small in comparison to the long wave amplitudes, the
range of use of the series covers many short wavelengths.
The validity of the existing theory for this situation is un-
certain and is an area of active fundamental research at
this time. Nevertheless, with nothing more certain or bet-
ter available at this time, we have applied a computer code
based on the Hasselmann theory to the range of frequen-
cies from very small to those responsible for L-band radar
backscattering. Heretofore, application of the Hasselmann
theory has not included these short, high-frequency waves.
Figure 9 shows the computed nonlinear energy transfer
rate to waves propagating in the wind direction as a func-
tion of wave frequency for a Jonswap spectrum correspond-
ing to a wind speed of 6.2 m/s (12 knots at a height of 10
meters). The figure also shows the wind energy input rate
as a function of the theory according to Plant (1982~. For
the frequency range corresponding to L-band scattering, the
nonlinear energy transfer rate is roughly 20 percent of the
wind energy input rate.
0.20
O. ~ ~
N
E
in 0 15 '
$
L`J
o
- 0.13
z 0.10
z 0.08
0.05
U.
0.03
. ~
ooooo FROM NONLINEAR INTERACTIONS
~ o 0 0 FROM WIND STRESS
1.00 1.50 2.00 2.50
FREQUENCY ( Hz )
Figure 9. Computed energy transfer to short waves from the
wind and nonlinear interactions
Although knowledge of nonlinear energy input to waves
much shorter than the spectral peak wavelength in equilib-
rium conditions is scanty, even less is known about it for
the non-equilibrium condition of attenuated and regrowing
short waves in a ship wake. To deal with this uncertainty
here, we will take two steps:
1. Set the nonlinear energy input to 20 percent of the wind
energy input for our "base case" calculations,
Snot = HE (9a)
= 0.20(,l], +,(12-). (9b)
En
2. Perform calculations with other values of fly to deter-
mine both the effect of the uncertainty and the order-
of-magnitude of the influence of the nonlinear energy
transfer on the short wave energy distribution through
the wake.
4.1.3 Short Wave Energy Dissipation Due
to Turbulence
The primary mechanism for wave energy dissipation by
turbulence in non-breaking wave conditions is thought to be
downward convection of wave energy by the vertical velocity
components of the turbulence. Kitaigorodskii and Lumley
(1983) derived a mathematical relationship, based on this
concept, between the dissipation rate and the correlation
between the vertical turbulence velocity and the square of
the fluid velocity due to the waves. However, as far as we
know, this correlation has never been measured either in or
out of a ship wake. Thus, we are directed to an alternative
approach for estimating the downward convection of wave
energy by turbulence.
Olmez and Milgram (1989) measured the dissipation of
short waves due to turbulence generated by a submerged
oscillating grid in a laboratory tank. Using the concept of
the downward convection of wave energy, they developed the
following order-of-magnitude formula for St:
542
OCR for page 543
St = ((2 WE = 0.4(dw'/dz)E, (10)
where dw'/dz is the rate of increase of the RMS vertical
turbulence velocity near the water surface. w' is presumed
to be zero at the surface.
To use equation lO, the RMS vertical turbulence ve-
locity, flu', must be estimated. Kitaigorodskii et al., (1983)
have estimated this velocity component from measurements
made in Lake Oratorio. Their shallowest measurement loca-
tion was 0.3 meters beneath the surface where both w' and
the RMS horizontal velocity, u,, were roughly u~o/120. To
is the wind speed at a height of ten meters. The turbulent
velocity was estimated by subtracting the vertical wave ve-
locity, inferred from the measured wave elevation, from the
measured total velocity. We note nearly all errors in the
estimate of wave velocity will lead to over estimates of w'.
Brumley and Jirka (1987) studied the influence of a free
surface on otherwise homogeneous turbulence. Parameters
of the horizontal turbulence velocity were altered slightly
whereas parameters of the vertical velocity were strongly
altered in a layer having a depth about equal to the integral
length scale of the horizontal turbulence. The vertical RMS
velocity and integral length scale were nearly zero at the free
surface and increased to values comparable to those of the
horizontal turbulence at the bottom of the layer.
The functional form of w' versus depth is uncertain.
The Brumley and Jirka data show a linear dependence for
the upper 2 percent changing to a (depth)~/3 dependence
over the lower 95 percent. McDougal (1979) measured the
effect of a rigid lid on otherwise homogeneous turbulence.
His results were similar to those of Brumley and Jirka, ex-
cept the increase of w' with depth was nearly linear over a
depth equal to the integral length scale of the horizontal tur-
bulence. Hunt and Graham (1978) have shown theoretically
and numerically that the form of w' versus depth depends
on details of the turbulence spectrum.
For our purposes here, we will make the approximation
that w, increases linearly from zero at the surface to u~o/120
at a depth ET (which we shall take to be 0.3 meters),
dw,/dz _ u~o/~120H), (11)
outside the wake.
The only wake turbulence measurements available to
us are those taken in model tests and provided to us by W.
Lindenmuth (private communication, 1990~. Very strong
turbulence just behind the ship model decayed such that at
a distance of ten ship beams aft of the stern, u' was approxi-
mately 0.02V in the near surface region, where V is the ship
speed. The depth of the zone of influence of the free surface
on the vertical turbulence velocity was about one-eighth of
the ship draft (D/8~. Further aft, the turbulent velocities
became too small to reliably measure with the laser doppler
anemometer being used. We need to couple Lindenmuth's
measurements with our measurements of wake widths and
known features of turbulent wakes in general.
Under the assumption of self-similar velocity profiles
and eddy viscosities, a round drag wake grows asymptot-
ically as W ~ x/3, where W is the width and x is the
downstream distance. A wake with zero net axial momen-
tum grows as W ~ X]/5 (Birkhoff and Zarantonello 1957~.
Because of the low Froude numbers of wakes further aft than
one ship length, they are expected to behave globally in the
same fashion as round wakes. If all of the hull drag were
due to skin friction, this drag would be exactly balanced by
the propeller thrust and the wake as a whole would have
zero axial momentum. Because of the energy radiated by
the ship-generated waves, the wake has net momentum flux
directed aft with a magnitude equal to the wave drag. How-
ever, for the ship parameters and speeds of interest here,
the skin friction drag is larger than the wave drag so we ex-
pect the far wake behavior to be more like a zero-momentum
wake than a drag wake or a jet. This expectation is justi-
fied by the measured widths of the zone of wake-modified
surface tensions. Figure JO shows these measured widths
(corresponding to Figure 8) as well as the following equa-
tion which fits the data well:
W(~) = 22.9(x + 0.4B)~/5, (12)
where W,x, and the ship beam B are measured in meters.
For the ship that generated the data for Figures 8 and to
the beam B = 16.75 meters.
~ 175
cY
Al
~ ~
~ 125
I _
C) _
3 75
111
25-t ~
/
_ - ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 '- '
0 5000 10000 15000 20000
DISTANCE BEHIND SHIP (METERS)
Figure to. Measured and theoretical wake widths
For a self-similar zero-momentum wake, all velocities
behave asymptotically as X-4/5, SO with u, = 0.02V ten
ship beams aft of the ship, we model u' over the entire wake
as:
( ) (a + 0 4B) (13)
TheII, dw,/dz is approximated as
dw, do = 0.02- 10.4B 4/5
/ (D/8)(s+04B)
, (14)
inside the wake. Equation 14 neglects the variation in tur-
bulence across the wake. Also, this equation is used in our
model only when the turbulence gradient exceeds the ambi-
ent level given by equation (ll). Setting the two expressions
equal yields the length Lo of tl~e zone of ship-affected tur-
bulence as:
L 418B(H V )5/4 - 0 4B (15)
4.1.4 Dissipation of Energy Due to the
Presence of a Surfactant Film
The damping of surface waves in clean water is well
known to have a l/e time of 1/(2uk2) where I' is the kine-
matic viscosity and k is the wavenumber (Lamb 1945). The
l/e times are about 4500 seconds for 30 cm waves responsi
543
OCR for page 544
ble for L-band Bragg scattering, 32 seconds for 5 cm waves
associated with C-band scattering and 5 seconds for 2 cm
waves associated with X-band scattering. These decay rates
are typically small in comparison to growth rates (equation
5) due to modest winds.
What is less well known, is that elastic surface films
can dramatically increase the viscous damping rates of short
waves. In the absence of a surface film, the requirement of
zero shear on the surface leads to a very weak surface bound-
ary layer with similarly weak damping. In the presence of
an elastic film, however, a much stronger boundary layer
with increased damping can be necessary to provide a shear
stress equal to the gradient of the surface tension.
A thorough study of the wave damping due to a lami-
nar boundary layer beneath an elastic surface film was con-
ducted by Dorrestein (19513. His results can be written as:
Ss = psE (16a)
where
with
_ [ ~ I]
[ ( ~ ) ( ~ ) ]
(gk + ~k3)l/2 ~ = Ilk h = ash kit · (16C)
Here g = 980 cm/s2 is the gravitational acceleration,
p = 1.02 gm/cm3 is the density of seawater, ~ = 0.01 cm2/s
is the kinematic viscosity of seawater, cr = 73 mN/m is the
nominal surface tension at the air/seawater interface, Es (in
mN/m) is the film elasticity and ~ is the wavenumber of the
wave.
Figure 11 illustrates the rate of decay of capillary-
gravity waves on the free surface due to the presence of a
surfactant film based on the studies of Dorrestein. The wave-
length range in the figure covers the Ka- to L-Band range in
SAR operating frequencies. Plotted are a family of curves
showing the ratio of the wave energy after one wavelength of
propagation in the surfact ant film band to the energy at the
beginning of the cycle for surfaces films with different physi-
cal or elastic properties. In addition, the two limiting cases,
a clean free surface where only the viscosity of the fluid is
responsible for wave damping and a surface covered by an
infinitely stiff, incompressible film are also included. The
figure shows that the presence of a surfactant film greatly
increases the rate of decay of capillary-gravity waves less
than 20 cm in wavelength. Note also that a small change in
surface elasticity can result in a significant change in cap-
illary and small surface gravity wave damping for a given
wavelength.
We close this subsection by noting that in the pres-
ence of a turbulent free surface boundary layer, the actual
surfactant-induced wave damping could be different than
predicted by Dorrestein's laminar analysis. However, it
seems likely that the effect of turbulence would be small
here, on the basis of the vanishing vertical turbulence veloc-
ity at the free surface found by Brumley and Jirka (1987)
and the very small depth, O(IJ/~), of the wave-induced lam-
inar surface boundary layer.
x
J
X 09
-
o
tr: 0.8
as
0.7
1.0 1
;~
Clean Surface. Es = 0.0
-Elasticity, Es - 2 0
~~( ~ Elasticity, Es - 50
~= / f- o Elasticity, Es = 10.0
,/ -~ Elasticity, Es = 25.0
~ ~ Elasticity, Es=45.0
:~,~4 ~ Infinitely stin Surface
1 10
Wavelength, L (cm)
Figure 11. Wave energy decay in a surfactant film
100
4.2 Data and Conditions Used for the Model
Computations
(16b) Calculations were carried out using data that were ob
tained in the wake of a Navy ship at a speed of 12.9 m/s
(25 kt) on January 28th, 1989. The Navy ship reported a
wind speed of 5 knots whereas the R/V Sea Tech reported
wind speeds varying between 7 and 9 knots while in the
wake. These vessels reported disparate and varying wind
directions with angles between 30 and 90 degrees with re
spect to the cross-wake direction. We cannot fully resolve
the disagreement over the wind speed. However, the direc
tion of the short waves is clearly visible on a videotape made
from the R/V Garnet Banks during the surface tension mea
surements. This direction is about 50 degrees with respect
to the cross-wake direction.
The uncertainty of the actual wind speed is unfortu-
nate for the modelling of L-band Bragg scattering waves.
For these, the model growth rate terms from the wind and
nonlinear interactions have the same order of magnitude as
the dissipation terms from turbulence, viscosity and surfac-
tants. Thus the L-band waves can be modelled as growing or
decaying, depending on the chosen wind speed within the re-
ported range. The same difficulty applies to C- and X-band
waves in the first few ship lengths of the wake. However, it is
not severe in the far field at C- and X-band because there, for
all the reported wind speeds, these waves grow outside the
surfactant bands and decay in the strong surfactant bands.
We will use a wind speed of 7 knots at an angle of 50
degrees from the cross-wake direction in our model calcula-
tions here. However, we must point out that if 9 knots were
chosen very little wave attenuation would be predicted in
the wake for L-band waves, and if 5 knots were chosen the
waves would be predicted to decay, even outside the wake.
The SAR image with which model calculations will be
compared was made from an aircraft flying parallel to the
wake. Thus the predominant Bragg scattering waves to
which the SAR is most sensitive propagate directly across
the wake. For our estimated wind direction, the value of
to be used in Equation 5 is 50 degrees.
Surface tension measurements were obtained along
three wake crossings centered at 3735 m, 11978 m and 21316
meters aft of the ship. These surface tension distributions
are shown in Figure 8. Regions of decreased surface tension
544
OCR for page 545
- ~ ~
EN i* >.*s ~, sit ~ ~ ~ ~ ~
=,,~,~,~,,~,,,~.~s*i.:~.,,S,,.,,,..~,~:~^r~....5 ~ ~ ~--~
Figure 12. L-band SAR image of the Navy ship wake (courtesy of J. Lyden, ERIM)
relative to the ambient value are caused by increased film
pressure of a compacted surfactant in those regions. Each
of the three crossings has two edge bands of compacted film
as well as one or more additional bands between the edge
bands.
Figure 12 is an L-band SAR image of the Navy ship
wake obtained from an aircraft during the same time that
the surface tension measurements in the ship wake were be-
ing made by STEMS as it was towed across the wake by
the R/V Garnet Banks. C- and X-band data were also ob-
tained simultaneously by the multi-band aircraft SAR. We
will compare the multiband SAR backscatter intensity data
with model calculations using the surface tension data from
the 3735 m cut and film elasticity values calculated from
the pressure-area curve of the water sample obtained prior
to the 25 knot run as input to the model.
The film pressure - area curve for the surfactant mate-
rial is needed to relate the film elasticity Es to the measured
surface tension. A subsurface water example was collected
prior to the 25 knot run for later film pressure versus area
measurements in the Chemistry Division at NRL. The re-
sults of these measurements, plotted as the natural loga-
rithm of the film pressure (in mN/m) versus the natural
logarithm of the surface area (in cm2), are shown in Fig-
ure 13. These data have been fitted with three straight line
segments so that for each portion of the fitted curve we have
II = CAn, (17)
where n is the slope of the portion and C is a characteristic
constant of that portion of the curve. Then, from equation
(2), we find that
Es =-nII (18)
or, specifically from the three segment fit in Figure 13,
~ 0.0 II < 0.20,
E _ J 5.21II 0.20 ~ II < 4.42, (19)
s - ~ 2.90II 4.42 < II < 8.58,
~ 1.27H ~ ~ 8.58.
As was noted in section 3.2, we make the assumption
that the surfactant material adsorbing at the water surface
in the laboratory sample has the same physical properties as
that which had adsorbed on the sea surface during the test.
It is quite possible that the film elasticity determined from
545
the subsurface water sample is not exactly representative of
the film elasticity of the material in the surfactant bands.
Nevertheless, the value of the film pressure at each location
across the wake used in equation (19) to determine the cross-
wake elasticity distribution used in the energy calculations
is that measured by STEMS.
_ ~
E ~ = -~.27
g
X
E
h
J
~58 mN/m
- 6~ n = -2.90
- ~4.42 mN/m
Awn = -5.21
. . . . . . , . , . ~ , . ~
4.2 4.4 4.6 4.e 5.0 s.2 5.4 5.6
Ln Fllm Area, (cm.~2)
Figure 13. Measured surfactant film pressure-area curve
It is very difficult to nearly impossible to determine
the exact composition of the material in the surfactant
film bands measured during the January Field Experiment.
There are literally hundreds of different materials present
in these film bands. Surface chemists (Frew et al., 1990,
Barger and Means, 1985) agree that the major constituents
of these film bands are relatively soluble, highly oxygenated
and condensed, but poorly defined polymeric materials of
high molecular weight. However, it is not the composi-
tion of the material in the bands that is important, but
rather the effects of physical properties of the material on
the ambient wave field. A small change in surface elastic-
ity will lead to significant changes in capillary and small
surface gravity wave damping. Given the relative similarity
in the pressure-area curves of the water samples obtained
during the Field Experiment with hundreds of samples ob-
tained from varied locations throughout the major oceans
(Frew, 1990, Barger and Means, 1985; Barger et al., 1988)
we feel confident that the physical properties of the films
present during the Field Experiment are representative of
many films throughout the major oceans. To properly char
OCR for page 546
acterize and measure the physical properties of surfactants
that are important for wave damping studies, controlled nat-
ural surfactant materials must be developed by extracting
the material from natural seawater samples. Comparing the
physical properties of these extracted films, which we now
know the concentration of, with untreated seawater samples
will provide some insight into the concentration of the ma-
terials in the untreated samples.
Surface tensions throughout the wake, for use in the
model computations, are found by interpolating between
measurements on the wake cuts. This requires an estimated
surface distribution on a wake cut at the ship stern. For
this, we have hypothesized two eight meter wide edge bands
whose centers are spaced two ship beams apart. The surface
tension used in the bands is 12 mN/m which is the lowest
value we measured in the actual cuts.
When integrating the energy balance equation, the re-
sults at each time step must be restrained to prescribed up-
per and lower limits. The upper limit is the ambient energy
level outside the wake. For the lower limit we have used 20
percent of the ambient inasmuch as this is the typical re-
duction in wave energy level we measured directly in wakes
during the experiments.
-
m
-
~ 30
c
-
, 25
.=
a:
-
m 2
-
~O
-
~ -2
Q
-4
.=
-6
-1 85
The initial condition we used for the model computa-
tions has the energy reduced to 20 percent of the ambient
level at the ship stern over a distance of one ship beam. The
initial energy is taken as linearly rising from this depressed
level back to the ambient level on each side of the ship over
a distance of one-half a ship beam, thus making the entire
depressed zone two ship beams wide.
4.3 Computations and Comparisons With
Measurements
Results of calculations for the spectral energy ratio
(E/Ea) along the SAR look direction at a center distance of
3735 m aft of the Navy ship are shown in Figures 14, 15 and
16. This is the distance of our closest wake crossing mea-
surements for which the surface tension distribution is also
shown in the figures. The results are expressed in dB down
from the ambient, [lOlog~O(E/Ea)~. For these calculations
we have used 60.0 mN/m for the value of surface tension in
the regions where oil 21 did not spread and we do not know
the lower surface tension limit (see Section 3.3.2~. The re-
sults are shown for three wavelengths: 15.9 cm, 3.6 cm and
2.0 cm which correspond to the L-, C- and X-band wave
78
E 73
c
o
~ 68
i
a) Cross-wake Surtace Tension 3735 m aft, Wake Width, 117 m (6.93B)
Wake Width ~
I !r. . - ' , Id, lo,.,
Inner
Bande
/N
~Edge Band
b) lUeasured Relative Intensity, (L-band SAR)
~4
k Wake Width >I
Libel , W1
20 - ~ . . . . ~ . . . . .
c) Calculated Spectral Energy Ratio of L-Band (15.9 cm) Waves
`, 1'- Wake Width ~
-
it,
-135 -85 -35 1 5 65 1 1 5 165
Cross-Wake Distance, (m)
Figure 14. Calculated spectral energy ratio of L-band waves together with the measured cross-wake surface
tension and SAR intensity distributions 3735 m aft of the ship
546
OCR for page 547
78
-
£
a
73
o
,_
£
68
63
:'
6
a) Cross-wake Surface Tension, 3735 m aft; Wake Width, 117 m (6.93B)
| ~Wake Width:
Edoe Band ~
Inner |
Bande 1
~1
~Edge Band
11 -
-
m
-
._
us
-
fir:
m 4]
-
A~
b) Measured Relative Intensity (C-band SAR)
|< Wake Width:
-
c) Calculated Spectral Energy Ratio of C-band (3.6 cm) Waves
~2
C O
Al
-2
Q -4
i.=
-8
-195 -145 -95 -45
|< Wake Width:-
Edge Band ~,
It_
I Inner
Bande
,/~1
~Edge Band
5 55 105 155
Cross-Wake Distance, (m)
Figure 15. Calculated spectral energy ratio of C-band waves together with the measured cross-wake surface
tension and SAR intensity distributions 3735 m aft of the ship
lengths at the incidence angle of 52 degrees used for SAR
images of this experimental run. The measured SAR cross-
sections at 3735 m aft are also shown in the figures. The
SAR intensity data shown are averaged longitudinally over
a length of 100 meters. The X-band signal to noise ratio was
near unity for this run, so that any direct comparison with
the data may be subject to some error.
The mathematical model predicts L-band waves have
not recovered to ambient levels and are attenuated across
the entire wake. Conversely, the C- and X-band waves are
predicted to have recovered to ambient levels except in and
immediately downwind of zones of compressed surface films.
These findings are consistent with the SAR measurements
at the same location shown in the figures. The L-band SAR
data shows the full width attenuation and several of its vari-
ations in intensity across the wake can be visually "matched
up" with spectral energy variations in the mathematical pre-
dictions. Correlations between the regions of the largest
backscatter intensity reduction in the SAR data and the re-
gions of lowest surface tension are evident in the C- and
X-band data as well. The reductions in image intensity in
these regions are about 6 dB at L-band and 5 dB at C-band.
Corresponding attenuations predicted by the mathematical
model are about 5 dB at L-band and 7 dB at C- and X-band.
The latter value is set by the arbitrary minimum energy level
of 20 percent of the ambient level used for the computations.
As is predicted by the mathematical model, the C- and
X-band SAR data show backscatter intensity in the wake
to be nearly at ambient levels except in isolated regions
whose locations are in reasonable correspondence with zones
of measured surfactant concentration.
4.4 Influence of Variations in Model Input
Parameters
Because of uncertainties about the accuracy of some
of the formulations used for the source terms in the energy
balance equation, a study of the influence of variations in the
source terms should be done. Although a complete study of
this type cannot be included in this paper, we will show the
influences of a few variations. The effects of source term
variations on the wake 3735 meters and further aft will be
s47
OCR for page 548
78
E 73
o
._
c
68
63
a) Cross-wake Surface Tension 3735 m aft; Wake Width, 117 m (6.93B)
~ Wake Width ~
^- ~ ~- ~_-we_
--lo ~1
Edge Band ~ j
Inner till 1 l
Bands | ~
~ 1~'
*- Edge Band
25 ~
m
,~ 20
-
~ 15
.~
to
to
-
m 4.
As
2
o
-2
Q
on
-4
.~; -6
a.
-1 95
b) Measured Relative Intensity, (X-band SAR)
|< Wake Width ~
c) Calculated Spectral Energy Ratio of X-band (2.0 cm) Waves
|~----- Wake Width:
| Inner |
I Bands l I
~ ~Edge Band
-145 -95 -45
Cross-Wake Distance, (m)
5 55 105 155
Figure 16. Calculated spectral energy ratio of X-band waves together with the measured cross-wake surface
tension and SAR intensity distributions 3735 m aft of the ship
most pronounced for L-band waves since the others have
regrown to the ambient level except in the surfactant bands.
We will compare results with source term variations with
the base case L-band results shown in Figure 14.
Figure 17 shows the predicted L-band energy distribu-
tion 3735 meters aft when the wave energy decay rate due to
turbulence in the ambient sea is reduced to seventy-five per-
cent of the value used to produce Figure 14. This changes
the decay rate in the wake because the ship-induced turbu-
lent decay is taken as diminishing with distance aft (equa-
tions 10 and 14) until it becomes equal to the ambient level.
The effect of the modest reduction in decay from turbulence
is strong with significant wave attenuation remaining only in
the regions of strong surfactant concentration on the down-
wind side of the wake instead of all across the wake as in the
base case.
Figure 18 shows the effect of raising the energy input
due to nonlinear interactions by fifty percent. Compari-
son with Figure 14 shows the significant change that can
be caused by such an increase in the energy transfer from
nonlinear interactions.
As was discussed in Section 3.3.2, we were not able to
determine the maximum value of the surface tension de-
crease in the regions where oil 21 did not spread. For the
original model calculations shown in Figure 14, we used 60.0
mN/m as the surface tension in these regions. It is entirely
possible that that surface tension value could have been as
low as 42.0 mN/m. Figure 19 shows the effect of decreas-
ing the surface tension value in these regions to 42.0 mN/m.
42.0 mN/m is the lower limit on the surface tension value
that can be associated with the compacted surfactant mate-
rial at the surface during the Field Experiment. Decreasing
the surface tension increases the surfactant damping in these
regions. Comparing the two figures shows that the possible
variation in surfactant damping is shown to have a marked
effect on the L-band wave energy levels.
Figure 20 shows the results of eliminating the effect of
the reduction in wind growth rate due to surface smoothness.
For this computation, The wind energy input rate was set
to:
Sw = 0.05a~u*/c)2Ecos8. (20)
548
OCR for page 549
m 1
Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves
1 _ 1
=2~-, ~ .
0 -3
Cal -185 -135 -85 -35 1 5 65 115 165
Cross-Wake Distances, (m)
Figure 17. Calculated spectral energy ratio of L-band waves when the ambient turbulence level is reduced
by seventy-five percent
m 1
-
~ O
c
-
-1
0
Q
.2
a,
-
Calculated Spectral Energy Ratio of L-Band (15.9 cm) Waves
-3 ......
-1 85
1~ Wake Width .1
~ ,rv: ~
,,,,,,,,,,V .
-1 35 85 -35 15 65
Cross-Wake Distance, (m)
115 165
Figure 18. Calculated spectral energy ratio of L-band waves when the energy input due to nonlinear
interactions is increased by fifty percent
m 2
0
~-2
Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves
O~
L Wake Width lo|
L= :4L 74~1 ~
0 -8
-1 85 -1 35 -85 -35 1 5 65 1 1 5 1 65
Cross-Wake Distance, (m)
Figure 19. Calculated spectral energy ratio of L-band waves when the surfactant damping is increased
549
OCR for page 550
al 1
-
-
c
us -1
o
-
, -2 ~
Q
V}
~3
.p
_ .
~-.
a -185 -135
Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves
k Wake Width >I
I/ {N
- 8 5 - 3 5 1 5
Cross-Wake Distance, (m)
65 115 165
Figure 20. Calculated spectral energy ratio of L-band waves when the reduction in wind growth rate due
to surface smoothness is removed
Comparing Figure 20 with Figure 14 shows that, at least at
the 3735 meter location, the effect of this variation in wind
energy input is clearly observable.
Although a much more complete sensitivity study
should be done in the future, the above examples clearly
show that distributions of short waves in wakes are sensitive
to all of the terms in the energy balance equation. However,
it is because of the surfactant effects alone that attenuation
can persist into the very far wake. The other attenuating
effects and the energy input erects, at least to the extent
that we presently understand them, would lead to wave re-
growth to ambient levels in the very far wake if surface film
concentration did not persist into Ellis region. This is prob-
ably why SAR centerline images do not persist into the very
far wake when the sea is rough. The mixing associated with
wave breaking eliminates the bands of ship-induced surfac-
tant concentration in that situation.
5.0 SUMMARY AND CONCLUSIONS
Previous to this experiment in situ surface tension data
have never been measured to the resolution in surface ten-
sion obtained or with such a fine spatial resolution. Coupling
these measurements to the determination of the pressure-
area curves has for the first time allowed us to infer film
elasticity distributions for ocean water and to realistically
calculate the changes in wave amplitude due to the presence
of these surfactants.
The major process by which surfactants affect synthetic
aperture radar (SAR) or other radar images of the ocean
surface is through wave damping, and two important vari-
ables in this process are the Bragg scattering wave number
(if the incidence angle is not too large or small) and the sur-
face film elasticity as determined above. It is apparent from
our measurements, calculations, and comparisons with ob-
servations that surfactant films play an important role in the
formation and persistence of the centerline wake region. The
role is probably dominant in the far wake. In the near and
intermediate wake regions other influences on wave energy
cannot be neglected.
All of the ship wakes we have analyzed from the Field
Experiment have exhibited a banded structure for many
kilometers downstream. Even in one run in which the wind
speed was 9 Parsec the bands were measured at distances
nearly 20 km behind the target vessel. In lighter wind cases
bands were easily detected more than one hour late (equiv-
alent to 35 to 40 km behind the target). The width of the
wake slowly grew in time as indicated in Figures ~ and 10.
From our limited data analysis so far, we cannot reach any
conclusions about the dependence of these ship-generated
surfactant film bands on environmental parameters (wind
speed and direction, ambient surfactant concentration) and
ship operating characteristics (hull form, speed, number of
propellers). However, we conclude that continued analysis
of the remaining data will allow us to determine the effects
of both environmental and ship operating parameters on the
origin and downstream persistence of these ship wake sur-
factant bands.
As our sensitivity studies have shown, variations in each
of the source terms in the model (within our present knowl-
edge of what we can reasonably expect their variations to
be) have a strong effect on the L-band calculations. This
points out the need to learn more about these source terms.
Within the present model, the approximations for wind
wave regeneration and nonlinear energy transfer are both
subject to limited data on which to base the approximations.
Here again, both a careful analysis of available information
and additional laboratory experiments are indicated in or-
der to resolve the uncertainties which still remain after this
"first look" analysis. In particular, existing theories and ex-
periments apply to wave frequencies up to twice that of the
spectral peak. On the other hand, radar scattering waves
have frequencies about ten times that of the spectral peak.
That is why new experiments are needed.
Finally, wave damping by turbulence in ship wakes is
the least understood of all the source terms. Our knowl-
edge of wave damping by turbulence is very limited. Our
knowledge of the amount of turbulence that actually exists
in the wake more than a few ship lengths downstream is
non-existent. Like all the other uncertainties, this one can
only be fully resolved by careful experiments focused on the
hydrodynamics in question.
ACKNOWLEDGEMENT
This work was sponsored by the Ship Wake Consortium
and by the Surface Ship Wake Detection Program of the
Applied Research and Technology Directorate (Code 12) of
the Office of Naval Research.
550
- =~
OCR for page 551
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552
Representative terms from entire chapter:
wave energy
