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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 687
Ship Wake Detectability in the Ocean Turbulent Environment
A.Benilov, G.Bang (Stevens Institute of Technology, USA)
A.Safray, I.Tkachenko (Institute of Oceanology, Russian Academy of Sciences, Russia)
ABSTRACT
The turbulent structure of ship wake and ocean upper layer is presented in this study. We discuss results of: 1) theory
on the turbulent ship-wake and the ocean upper layer turbulence under surface waves effects including wave breaking—
an analytical study; 2) based on k-ε turbulent closure a couple 3-D non-steady numerical model (wake+upper layer)
which includes the wave breaking; 3) experimental investigation (preliminary results) in the Davidson Laboratory towing
tank on ship-wake detection by measuring turbulence in-situ.
The theoretical analysis of the ship-wake turbulence uses the shear-free model, self-modeling and Kolmogorov's
hypothesis for the purpose of closure. The environmental turbulence in the ocean upper layer has been formulated by the
assumption of horizontally uniform hydrodynamic field and k-ε group model under the existence of surface waves and its
breaking. Based on k-ε turbulent closure a couple 3-D non-steady numerical model (wake+ upper layer) which includes
the wave breaking, has been used, in the shear-free approach, to carry out numerically the ship-wake detectability in the
ocean turbulent environment. Both of the analytical and numerical results show the 3-D structure of the ship wake for
different wind conditions and ship speeds, and the detection range on the ocean surface and the detectability in depth of
the ship wake in terms of ship parameters and the wind speed.
The experimental study is destined to verify the theoretical and numerical prediction on detectability of turbulent
ship wake under different experimental conditions. The wake turbulence significantly exceeds the natural level of
fluctuations in the tank and the vibration noise produced by the towing system. The wake turbulent spectrums have well
expressed Kolomogov's range. The ship-wake turbulence is well detectable and Kolmogorov's range can be identified
even for the most remote location of the probe (~10 Ls, Ls is the ship length) as well under the random surface wave
condition.
1. INTRODUCTION
1.1. Ship Wake. The physical mechanism of ship wake in the ocean is a result of the turbulence generated by
moving ship. The turbulent diffusion defines the region of the turbulent wake that is spreading in time. Naudascher (1965)
studied the wake of self-propelled bodies. He found that the wake width has a power law behavior. Field measurements
for ship wakes have been made by Milgram et al. (1993) and they found the wake width has a power law of x1/5 behavior
where x is a distance from the ship. Hoekstra & Ligtelijn (1991) measured the maximum value of turbulence intensity in
each cross-section of the wake of a 5m long ship model. The result shows that the turbulent kinetic energy has a x−4/5
asymptotic behavior. The result of measurements done by Milgram et al. (1993), Hoekstra & Ligtelijn (1991) agree with
the text books written by Birkhoff & Zarantonello (1957, chapter 14), and Tennekes & Lumley (1990, chapter 4).
Dommermuth et al (1996) performed numerical large-eddy simulations on turbulent free-surface flows. They obtained
probability distributions of velocity field in the wake and compared the results with experimental measurements.
Another aspect of ship wake detection is the surface nonuniformity of surfactants. The physical mechanism allowing
the detection of ship-wake on the ocean surface is a result of the diffusion of the surface-active substance in the turbulent
region of the wake (Peltzer et al. 1991, Benilov 1994, 1997, Zilman and Miloh 1996). The turbulent diffusion forms the
surface nonuniformities of this substance as well as the associated nonuniformities of the surface tension, which
effectively suppress the centimeter band of surface waves that is responsible for the radar
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 688
image of a wake (Poulter et al., 1994). The distribution features of the variance and mean gradient of the surface-active
substance are the cause of a specific image of the far wake that looks like a “railroad track” (Milgram et al., 1993).
When the sea surface is moderately wind roughened, typically by winds of 2.5 to 7.5 m/s (5 to 15 knots), synthetic
aperture radar (SAR) images of ship wakes, obtained from aircraft or spacecraft, often appear as a long, narrow, dark
streak against a brighter background. The dark streak images can have lengths of tens of kilometers at the lower end of
the wind range. The spacecraft image of the ocean surface with the ship wake image shows that the visible length of the
ship-wake image reaches about 100 km (Naval Air Warfare Center Aircraft Division, Waiminster, PA, 1992/ in Benilov
(1994, 1997a)).
1.2. The Upper Layer Turbulence. The turbulent upper layer of the ocean has a complex vertical structure defined
by influences of different physical mechanisms such as energy and momentum transfer, the presence of surface waves
and their breaking, the turbulent energy production by mean shear flow, the wave motions of the fluid, and the effect of
the Coriolis force.
In contrast to atmospheric boundary layers over land, where mean velocity shear is the main source of turbulence
energy, the turbulence in the upper layer of the ocean is governed not only by mean velocity shear, but also by surface
waves. The transport of momentum, heat, moisture and salt occurs across the air-sea interface and is affected by the ocean
surface waves. Therefore surface waves play an important role in the air-sea interaction system.
The turbulent motion in the upper ocean is a highly specific example of turbulence in a liquid whose free surface is
subject to wind friction. The result of this action is the formation of waves, pure drift currents and turbulence, which lead
to strong vertical mixing of the surface layer. In contrast to boundary layers at a solid wall where mean velocity shear is
the main source of the turbulent energy, the turbulence in the upper ocean is governed in many respects by the nature of
waves. The total mean atmospheric stress not only induces ocean currents through the action of the shear stress alone but
also supplies momentum to growing surface waves. A part of the momentum and energy is transferred directly from the
wind to drift currents, while another part goes into surface waves. Wind waves contain a considerable amount of
momentum and energy and they redistribute the momentum and energy over great distances and supply energy to drift
currents and turbulence by their breaking. The wave breaking creates a highly turbulent environment within the top few
meters of the ocean, and the wave dissipation by the breaking intensifies turbulence in the ocean mixed layer (Drenann et
al., 1992). Wave breaking provides a mechanism for injection of both momentum and turbulent kinetic energy from the
surface winds to the water. Experimental results indicate that the relative energy that is lost from the wave motion due to
a single breaking lies between 10−2 and 10−1 (Melville and Rapp, 1985). The energy transferred per unit time from the
wind to the water surface is an order of pure drift currents (Kitaygorodskiy, Miropolskiy, 1968; Kitaygorodskiy, 1970).
Therefore, the turbulence of the upper ocean is nourished by the energy supplied from the waves. Consequently, the
turbulence characteristics should depend on the state of the ocean surface.
A moving ship leaves a long wake trail behind and makes it possible to monitor the traveling ships long range by
means of radar systems. Turbulent sensors are also able to detect “in situ” the wake turbulence in the case of complex
environment situation.
Since the properties of a ship wake are expected to depend on the speed and size of the ship, theoretical study should
be provided to analyze the wake properly. In the ocean, many natural atmospheric and oceanic features interact with the
wake. Therefore, the natural ocean turbulence should be studied to identify the ship wake from an oceanic environment.
2. THEORETICAL MODEL
2.1. Wake Turbulence. A ship traveling with a constant speed is considered as an active source of turbulence, and
the turbulence is developed within the boundary that is growing in time and characterizes the scale of the turbulence. To
describe the dynamic behavior of the turbulence in the ship wake, the following assumptions are made (Benilov, 1994,
1997a):
1. The wake turbulent kinetic energy significantly exceeds the upper layer turbulence that reduces the turbulent
wake problem to the turbulent region development in a non-turbulent liquid.
2. The main source of turbulence is a moving ship that means that all interactions between the wake turbulence
and environment do not
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 689
contribute in the wake dynamics and allows us to reduce the problem to the shear-free turbulent model.
3. The characteristic scales of change along moving direction L, kinetic energy kw, turbulent mixing length ℓ and
the speed of ship Us are such that
These assumptions reduce the wake problem to an axisymmetrical and non-stationary model of development of a
certain cylindrical turbulent region with the axis of symmetry located on the ocean surface at vertical coordinate z =0. The
axis of symmetry in the plane (z, y) has the coordinate (0, 0), where y is the horizontal transverse coordinate. For the wake
problem, the time t can be converted to the longitudinal coordinate x, the distance from the ship in the direction along the
wake, by transforming x=Ust.
The change of kinetic energy, kw, in time and space we may describe within the framework of the TKE equation in a
shear free approximation, where self-modeling and Kolmogorov's hypotheses are used for the purpose of closure. The
integration gives the solution in the following form
(1)
where a is the ship beam, the constant C is an invariant of the problem equaled
(2)
λ is the eigenvalue of the boundary value problem which is an algebraic function of closure parameters. This solution
gives the size of the turbulent wake in time, and TKE of the wake, kw, is in proportion with Because the closure
parameter of the turbulent scale is unknown, the eigenvalue of the boundary value problem, λ, can be obtained by
measurements. The measurement done by Milgram et al. (1993) gives λ=8. The parameter C depends on the ship
turbulence coefficient St that characterizes the efficiency of the ship propeller to generate the wake turbulence. The final
solution of the problem gives expressions for TKE and dissipation rate in the wake area, and the wake size (Benilov and
Bang, 1999).
2.2. Upper Layer Turbulence. The atmospheric action on the ocean surface results in the energy and momentum
fluxes. These fluxes generate the ocean mean flow, surface waves and small-scale turbulence, which play an important
roll in the upper ocean dynamics. Mean shear flow is the one of the main sources of the small scale turbulence, in this
respect, the turbulence of the ocean upper layer should be similar to the classical shear turbulence when the mean shear
energy production dominates. The effect of the surface wave on turbulence appears two ways. The first one is wave
breaking, which produces significant energy flux to the small-scale turbulence and the momentum flux to the mean flow
on the surface. The second one is the local vorticity production caused by the instability of the surface waves (Benilov et
al 1993). This effect should also be taken into account in the balance of momentum and turbulent kinetic energy of the
ocean upper layer. The turbulence itself affected by the mean shear flow, wave motion and wave breaking may reveal
contributions of these energy sources through the turbulent kinetic energy and dissipation rate (Melville 1985, 1994,
1996; Benilov 1997). It will create the sub-layer in the upper ocean where the energy balance takes different forms.
Thus the theoretical model of the dynamics of ocean upper layer has to include equations which describe the mean
flow, turbulent kinetic energy, interaction between turbulence and surface waves, wave breaking, and turbulent mixing
length. The boundary conditions have to describe the fluxes of momentum and energy produced by the wave breaking as
well as atmospheric action on the ocean surface.
To describe dynamic behavior of the turbulence in the upper layer, the random hydrodynamic field is assumed to be
uniform in horizontal planes, which means all statistical characteristics of the turbulence and surface waves are functions
of vertical coordinate and time. The momentum flux from the atmospheric boundary layer to the ocean, τa, has two
components which are the direct momentum flux to the wind current, τc, and the momentum flux to the surface
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 690
waves, τw. The momentum flux τw can be expressed as a combination of τww, the momentum flux for the wave growth,
and τwb, the momentum flux produced by wave breaking. Since τwb finally goes to the wind current, the total momentum
flux to the wind current in the upper ocean, τc, is τc=τcd+τwb.
In general, they satisfy the inequality
(3)
The energy flux to the mean flow can be expressed as
(4)
where is the surface drift velocity. This energy flux also appears to be a result of both the direct action of
the wind on the ocean surface and the wave breaking.
The presence of the free surface under powerful component of water motion, surface waves and wave breaking,
makes a distinction between upper layer turbulence and wall turbulence in the constant friction sub-layer. This means that
the result of wall turbulence cannot be applied to the ocean upper layer.
The mean momentum per unit area of the surface wave and the energy density of the wave motion can be obtained as
(5)
(6)
where C0=g/ω0 (t) the phase velocity of the surface wave at the spectral peak frequency ω0(t), β is the Phillips'
constant. A simple physical situation is to be found when the wind blows steadily over a large area for a long enough
period. Under this condition, the wind stress has magnitude and it is transmitted to the underlying water in a
statistically homogeneous wave field. Following Longuet-Higgins (1969) we estimate momentum and energy fluxes τwb
and qwb produced by the wave breaking as some fraction of the total momentum Mw and Ew. To find out these fluxes, let
τwb and qwb be proportional to the wave momentum and energy decay per characteristic wave frequency ω0 as following
(7)
where γ1 and γ2 are numerical constants representing the proportionality of the wave momentum and energy spent in
the wave breaking, and
(8)
and the customary values β≈0.01 and (ρa/ρw)
Using the estimate for fully developed waves
≈10−3, the numerical value of γ1 can be obtained;
(9)
This is the highest value that γ1 can have because the momentum flux from air to wave, τw, has been taken as the
total flux from air to water, Therefore, numerical estimates of γ1 and γ2 can be written as
(10)
The numerical values found here are in good agreement with the Longuet-Higgins' averaged estimate (1969). They
calculated the relative energy lost from the wave motion due to the breaking as 10−4. The experimental estimate of the
single breaking event (Melville and Rapp, 1985) shows this quantity as 10−1~10−2. This discrepancy may be explained by
the intermittence of the wave breaking. As a measure of the wave breaking intermittence, the relative area occupied by the
wave breaking events may be accepted. Then, the estimate of Melville and Rapp multiplied by the intermittence value 10
−3~10−2 will take same order of magnitude with the Longuet-Higgins' estimate and the estimate in (4.44). The fluxes
induced by wave breaking can also be written in the inequality forms as
(11)
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 691
(12)
Typical ocean condition can be applied to find an example of numerical values τwb and qwb. Taking a phase velocity
of the wave as C0≈10m/s which corresponds to the moderate wind condition,
(13)
This estimate shows the momentum flux induced by wave breaking in a fully developed situation can be compatible
with the total value of the momentum flux from the atmosphere, which is
(14)
where Cu≈10−3 is the drag coefficient of the ocean surface. The highest estimate of the energy flux due to the wave
breaking can be compared with equation (4) that shows the energy flux goes to the mean flow. The highest estimate of qc
has the common form
(15)
where kd is the coefficient of the wind surface drift and its customary estimate is kd~1/30. In the fully developed
situation, the ratio between qc and qwb can be found
(16)
This estimate shows that the energy flux produced by the wave breaking significantly exceeds the energy flux to the
mean flow. In quasi-steady approach of the upper ocean turbulence, the energy flux qc represents the energy influx from
the surface waves to the turbulence. Therefore, the estimate (16) shows that the wave breaking plays an important role in
the forming the upper layer turbulence regime. It is assumed that the surface waves are fully or almost developed, and the
wind condition changes slow enough to adapt the steady approach. This assumption reduces the number of unknown
surface fluxes since τww=qww=0. It gives τw=τwb and qw=qwb. In the case of developed waves, the momentum flux
produced by wave breaking may have same order of magnitude with the momentum flux from the atmosphere. Therefore,
the simplest hypothesis can be made as Then, the momentum flux to the wind current τc becomes
(17)
The turbulent kinetic energy, k, in the ocean upper layer may have discrepancies with regular turbulent models
because the potential motion due to the surface waves has very strong impact on dynamic behavior. Various attempts to
derive the equation of turbulent kinetic energy with presence of the potential wave component in the random velocity
field of the upper ocean have been undertaken by Benilov (1973, 1997b), Benilov and Lozovtski (1976) and
Kitaigorodski and Lumley (1983). In the sub-layer of constant friction, the turbulent kinetic energy budget with the
presence of surface wave is
(18)
where kv is the wave kinetic energy, σ is the ratio of the turbulent Prandtl numbers, σ=Prk/Prkv. The transport
equation for the dissipation can be taken in the form of k-ε turbulence theory with additional term Πv that represents the
wave source of dissipation increase:
(19)
where Prε is the turbulent Prandtl number, C1 and C2 are constants. Their typical values are Prε=1.3, C1=1.44 and
C2=1.92 (Hoffmann, 1989). Since the wave motion becomes smaller in depth, Πv→0 at the location far enough from the
ocean surface. From these results the turbulent diffusion of the turbulent kinetic energy and the wave kinetic energy is
dominant in the range of depth where the wave motion is vigorous, or 0≤x3≤Lw−v where Lw−v is the thickness of the wave-
turbulent sub-layer. In this layer, energy produced by the mean shear flow
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 692
may be neglected since turbulent energy produced by the wave breaking exceeds the mean shear effect significantly in the
vicinity of the ocean surface. And the σ can be obtained as an eigenvalue of the problem,
(20)
Then ε(0) can be found as
(21)
Below the wave-turbulent sub-layer there is a transitional diffusive sub-layer in the range Lw−v≤x3≤Lw where Lw is
the lower boundary of the transitional diffusive sub-layer. In this region, the turbulent diffusion still exceeds the mean
shear contribution in the turbulent kinetic energy budget but the effect of wave motion becomes insignificant. The
diffusive turbulent sub-layer is a transition zone between the wave-turbulent surface layer and the layer where mean shear
flow controls turbulent regime. By changing the variable from x3 to z=x3−Lw−v, where z=x3−Lw−v we have the expressions
for the TKE and the dissipation rate as
(22)
(23)
where
(24)
(25)
Qw−v is the energy flux at z=0, and R, v1, v2 are algebraic functions of the closure constants. The solutions show that
the turbulent diffusion mechanism gives the power laws for k and ε. And the turbulent mixing length becomes a linear
function of the vertical coordinate. The exponents v1, v2 can be found as v1=8.462, v2=4.974 from the standard values of
the closure constants.
Following after the transitional diffusive sub-layer, there is an another sub-layer located in the range Lw≤x3≤L where
the mean shear production of turbulent energy is dominant. In terms of classical steady turbulent boundary layer problem,
this sub-layer corresponds to the logarithmic turbulent sub-layer (Monin and Yaglom, 1987).
Figure 1. Ship Wake Detection Range under the Various Conditions
2.3. Ship Wake Identification. The combination of the ship-wake and the upper layer turbulence gives the detection
range on the ocean surface and the detectability in depth of the ship wake in terms of ship parameters and the wind speed.
2.3a. Surface Detection Range. The detection range xd can be obtained from the turbulent kinetic energy of the ship
wake along the x axis and the surface turbulent kinetic energy of the ocean upper layer. Introducing the notation that kw is
the kinetic energy of the ship wake along the x axis, which gives the maximum value in the cross-section of the wake, and
ke is the surface kinetic energy of the environmental turbulence, the detection range is a solution of the equation
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(26)
Cv=0.09, β=10−2 and C0=Ua, the detection range xd can be found
After substituting ST=14.25, λ=8,
from the expression
(27)

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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 693
This is the detection range based on fully developed waves. It is shown in Figure 1 with the case of no wave
breaking. Since the turbulent kinetic energy of the natural ocean surface ke (0) has been formulated from the hypothesis
that all the energy transferred from atmosphere transports to the wave breaking, ke (0) can be expected to be the highest
value that the ocean can have.
In the case of weak wind, we may apply the condition of momentum flux continuity on the air-water interface to find
the environmental turbulence. It can be seen that, for the weak wind, the two upper sub-layers can be neglected because
there is no wave breaking. Therefore, the wall turbulence is developed practically from the surface in the case of weak
wind with no wave breaking. The friction velocity u*w in the water is
(28)
According to the theory of wall turbulence, the turbulent kinetic energy does not depend on the depth and is
proportional to As an estimate for our application, the kinetic energy can be assumed to have the same order of
magnitude of It gives the detection range of the ship wake in the case of weak wind with no breaking as
(29)
According to Beaufort wind scale and specifications, (29) corresponds to light breeze wind with speed of 2.4~4.4m/s
(4~6knots). Under this situation, small wavelets are generated and there is no wave breaking. Whereas (27) corresponds
to a strong wind with speed of 11.4~13.8m/s (22~27knots). This condition generates large waves and white foam crests.
The ship wake detection range for those two conditions are shown in Figure 1.
2.3b. Ship Wake Identification in Depth. The ship wake identification below the ocean surface can be made by
comparing the turbulent kinetic energy of the wake and environmental ocean turbulence. If we let
Figure 2. Detectability of Ship Wake by Kinetic Energy in Depth (with Wave Breaking)
(30)
where kD is the detectable kinetic energy. Then, if kD is positive, the wake can be detected. The detectable kinetic
energy profile at the specific distance along the wake axis can be obtained as
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(31)
Equation (31) shows the detectable kinetic energy distribution everywhere inside the wake. This is valid only for
fully developed waves, which corresponds to a strong breeze wind. A simple estimate can be made by assuming the ship
speed Us=10m/s, the ship beam a=10m, ship length Ls=100m and wind

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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 694
velocity Ua=10m/s. The results are shown in Figure 2. It shows the detectable kinetic energy distribution at various
distances from the ship. For the case of weak wind with no wave breaking, kD can be written as
Figure 3. Detectability of Ship Wake by Kinetic Energy in Depth (without Breaking)
(5.12)
The turbulent kinetic energy of environmental turbulence for the weak wind case is constant through the depth of a
statistically steady layer where the Coriolis force is not effective, which is called the constant friction layer. The results
are shown in the Figure 3. The ship parameters are the same as fully developed case, but a wind speed of 4m/s is applied.
3. NUMERICAL MODEL
Based on k-ε turbulent closure (Mohammadi and Pironneau, 1994) a couple 3-D non-steady numerical model (wake
+upper layer) which includes the wave breaking, has been used to carry out numerically the ship wake detectability in the
ocean turbulent environment. The previous theoretical analysis shows that the shear-free turbulence can be applied to the
couple model. Using this result as an assumption, we significantly simplify the governing equations of the model.
Galerkin's finite elements method was applied to solution of the turbulence transport equations. We present results of
numerical experiments, which have been carried out using the software created for above discussed the numerical k-ε—
turbulent model of the ship wake in the turbulent ocean environment. Table 1 presents the conditions of the experiments:
the ship speed Us and the wind speed Ua. The results show the 3-D structure of the ship wake for different wind
conditions and ship speeds (Figures 4, 5). Figure 4 shows the body of the wake for calm situation (a—theoretical result)
and within environmental turbulence (b—numerical experiment). Here, R0 is the wake radius; Ls is the ship length; a is
the ship beam. At the left of Figure 5, different colors show the surface manifestation of the wake for different winds, the
condition that the wake TKE meets the surface environmental TKE associated with the wind speed defines the wake
boundary. The side view at the right of Figure 5 shows the wake cross-section along the wake axis by the equi-kinetic
energy isolines. In the ranges of the wind speed Ua=3−10m/s and ship speed Us=3−10m/s the wake has the surface range
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of detectability up to 4 km in x-direction (Ls=100 m, a=10 m), and the submerged range also up to over 4 km. The surface
range decreases with the growth of wind speed. The maximum length of the submerged range is 3–4 km and descends
deeper with the growth of wind speed reaching about one ship beam of depth below the free surface for Us=Ua=10 m/s.
The maximum of the wake width is about 70 m. The depth of wake penetration in the ocean exceeds 30 m for the
condition of the numerical model. Thus, the total scales of the detectable body of the wake may reach 3–4 km length, 70
m width, and 30 m depth. The turbulent kinetic energy k(x, 0, 0) in

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Us,
Ua,
m/s
m/s
Side View.
3
3, 5,
7, 10
Table 1. Conditions of the numerical experiments
Figure 4. The Body of the Wake within Environmental
Turbulence (Ua=5m/s). Equi-Kinetic Energy Isolines. 3D
7
3, 5,
7, 10
SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT
Top View, b—Side View)
10
3, 5,
7, 10
normalized form conforms the theoretical and Milgrem's power law that well approximates experimental data.
Figure 5. Ship-Wake Equi-Kinetic Energy Isolines (a—
695

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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 696
4. EXPERIMENTAL STUDY
The experimental study is destined to verify the theory of turbulent ship-wake parameters in different kind of
experimental conditions. The diagram (Figure 6) shows experimental setup. The ship-model and the hot film anemometer
(HFA) probe are mounted on the carriage at the fixed distance L between them. The carriage moves with steady speed U
(towing speed). The model with propeller generates a turbulent ship-wake. The hot film probe moving with the same
speed measures the turbulence in ship-wake cross-section at the distance L from the ship-model. This distance varies from
test to test. There are three basic measurement systems: Propeller Rotation Controller (PRC), HF Anemometer (A), and
Data Acquisition System (DAS). The PRC manages the propeller rotation to produce a given value of the driving force, F,
during the test. The Anemometer measures turbulent velocity fluctuations. The DAS collects data from the Anemometer
and PRS. The model scales are 30 cm x 160 cm. The signal produced by the driving force, F, controls the motor
(propeller rotation) keeping the driving force, F, to be equal zero during the test. The towing speed has a constant value
during the test. The probe support construction gives opportunity to put the HF sensor at an arbitrary location in the wake
area and turbulent upper layer. The ship-wake detection by this experimental setup can be done for different wave
conditions including wave breaking (Figures 7–13). The signal of the wake is detected at the distances of the ship up to
approximately L~10 Ls (Ls is the ship length) with correspondences to the actual ship speed up to 20 knots. Figure 7
presents an example of the ship wake turbulence in this experiment in terms of u′-spectrums, Su′u′, versus frequency, f, for
two the ship speeds Us=0.63 m/s (the actual ship speed 10 knots) and Us=1.26 m/s (the actual ship speed 20 knots) at the
distance from the ship—model 1.63 m that corresponds one ship length L. The wake turbulence significantly exceeds the
natural level of fluctuations in the tank and the vibration noise produced by the towing system. The turbulent spectrums
have well expressed Kolomogov's range that allows estimating the dissipation rate. Figure 3c is an example of the wake
turbulent spectrums at different distances x from the ship model (x from 1 ship length L to 10 L). One can see that even
for the most remote location of the probe (~10 L) the ship-wake turbulence is well detectable and Kolmogorov's range can
be identified. Figure 13 shows the spectrum of wake turbulence at the distance 5.4 L from the ship model and the
spectrum environmental turbulence in the case of running spectral waves. The model speed corresponds to the actual ship
speed 20 knots, and the surface waves correspond to the actual developed wind waves for the wind speed about 12 m/s. It
can be seen that the wake turbulence for that location still significantly exceed the level of the environmental noise and
has the well identified Kolmogorov's range. Thus the turbulent sensors can also detect the wake turbulence in the case of
complex environment situation.
Figure 6. Experimental setup.
Figure 7. Examples of ship-wake turbulence for two values of actual ship speed.
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cm/s.
SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT
Figure 8. Turbulent spectrums along the wake axis at different distances from the ship model.
Figure 9. Turbulent spectrums in the wake cross section at the distance L=4.2 m from the model, model speed U s=68
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cm/s.
cm/s.
SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT
Figure 11. Turbulent spectrums in the wake cross section at the distance L=13 m from the model, model speed Us=202
Figure 10. Turbulent spectrums in the wake cross section at the distance L=8 m from the model, model speed Us=202
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cm/s.
s, wave elevation variance 2.54 cm, spectral peak frequency 1 Hz.
SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT
Figure 13. Wake turbulence under spectral waves conditions at distance L=13 m from the model, model speed 126 cm/
Figure 12. Turbulent spectrums in the wake cross section at the distance L=13 m from the model, model speed Us=68
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 700
5. CONCLUSION
Theoretical base, numerical modeling and experimental study on ship wake detection in the ocean turbulent
environment has been developed.
All these studies demonstrate that the ship-wake turbulence is well detectable and Kolmogorov's range can be
identified.
The turbulent sensors can detect the wake turbulence in the case of complex environment situations and at significant
distances from a ship.
In case of strong wind conditions there is significant submerged wake body that can be detected by the turbulent
sensors.
We express our deep gratitude to the ADD of Republic of Korea for support of this work.
REFERENCES
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(Translated in English).
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The Sea Hydrophysical Institute ed. AN USSR, Sevastopol, pp. 102–112.
Benilov, A.Y., and Lozovatsky, I.D., 1977. Semi empirical Methods of the Turbulence Description in the Ocean, In Monograph: The Turbulence and
Diffusion of the Ingredients in the Sea, The Co-Ordination Center of the COMECON (SEV), Information Bulletin, Vol. 5, Moscow, pp. 89–97.
Benilov, A.Yu., T.G.McKee and A.S.Safray, 1993, “On the Vortex Instability of Linear Surface Wave”, In: Numerical Methods in Laminar & Turbulent
Flow, Vol. VIII, part 2, Pineridge Press, U.K., pp. 1323–1334.
Benilov, A.Y., 1994, A Discussion of the Turbulent Nature and Possible Causes of the Ship Wake Radar Image. TR-SIT-DL-9409–20704,. Stevens
Institute of Technology, Hoboken, NJ, 49 pp.
Benilov, A.Y., 1997(a), Ship—Wake Turbulence, In: NUMERICAL METHODS in LAMINAR & TURBULENT FLOW, vol. 10, Edited by: C.Taylor,
University of Swansea, U.K., Pineridge Press.
Benilov, A.Y., 1997(b), The Ocean Upper Layer With the Presence of the Surface Waves and Their Breaking, TR-SIT-DL-9707, Stevens Institute of
Technology, Hoboken, NJ, 54 pp.
Benilov, A.Y. and G.C.Bang, 1999, Ship Wake Detection in the Ocean Upper Layer, TR-SIT-DL-9904, Stevens Institute of Technology, Hoboken, NJ,
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Birkhoff G. and E.H.Zarantonello, 1957, “Jets, Wakes and Cavities”, Academic, San Diego, Calif.
Drenann, W.M., K.K.Kahma, E.A.Terray, M.A. Donelan, and S.A.Kitaygorodskiy, 1992, “Observations of the enhancement of kinetic energy
dissipation beneath breaking wind waves”, Edited by M.L.Banner and R.H.Grimshow, Springer—Verlag, New York, pp. 95–101.
Hoekstra M., J. Th. Ligtelijn, 1991, “Macro wake features of range of ships”, Technical Report 410461–1-PV, Maritime research Institute Netherlands,
Wageningen, The Netherlands.
Hoffman Klaus A., 1989, “Computational Fluid Dynamics For Engineers”, A Publication of Engineering Education System, Austin, Texas.
Kitaygorodskiy, S.A. and Yu. Z.Miropolskiy, 1968, “Dissipation of Turbulent Energy in the Surface Layer of the Ocean”, Izv. Acad. Sci. USSR,
Atmospheric and Oceanic Physics, Vol. 4, No. 6, (Translated in English).
Kitaygorodskiy, S.A., J.A.Lumley, 1983, “Wave-Turbulence Interactions in the Upper Ocean Part I: The Energy Balance of the Interacting Fields of
Surface Wind Waves and Wind Induced Three Dimensional Turbulence”, J. of Physical Oceanography, Vol. 13, No. 11, pp. 1977–1987.
Longuet-Higgins, M.S., 1969, “On the Wave Breaking and the Equilibrium Spectrum of wind-Generated Waves”, Proc. Roy. Soc., London, Vol. A310,
No. 1501, pp. 151–159.
Melville, W.K., and R.J.Rapp, 1985, Momentum flux in breaking waves, Nature, 317, 514–516, 1985.
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 701
Melville, W.K., 1994, “Energy dissipation by breaking waves”, J. Phys. Oceanogr., 24, 2041–2049.
Melville, W.K., 1996, “The role of surface-wave breaking in air—sea interaction”, Annual Review of Fluid Mechanics, Vol. 28, 279–321
Milgram J.H., R.D.Peltzer, and O.M.Griffin, 1993, “Suppression of Short Sea Waves in Ship Wakes: Measurements and Observations”, J. Geophysics
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Monin A.S., A.M.Yaglom, 1965, “Statistical Hydromechanics: Turbulence Mechanics Part 1”, (1967, Part 2) Moscow, Fizmatgiz, pp. 639. (Fifth
printing, 1987, Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1–2. The MIT Press)
Naudascher, E., 1965, “Flow in the Wake of Self-Propelled Bodies and Related Sources of Turbulence”, J. Fluid Mech., V. 22, No. 1, pp. 625–656.
Phillips O.M., 1966, “The Dynamics of the Upper Ocean”, Cambridge University Press.
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Tennekes, H. and J.L.Lumley, 1990, “A First Course in Turbulence”, 13th Printing, MIT Press, Cambridge, MA.
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 702
DISCUSSION
D.Savitsky
Davidson Laboratory
Stevens Institute of Technology, USA
The authors present an excellent overview of the turbulent properties of ship wakes; ocean upper layer turbulence;
and their interaction. Further, the results of their recent model tests of ship wake turbulence and wave turbulence
measured separately and in combination (ship model running in head seas) are also presented. These experimental results
(particularly the combination of ship wake and wave turbulence fields) appear to be unique and constitute a valuable
contribution to the literature.
I have two questions for the authors. Concerning the turbulent wake of the ship alone, it would be useful if the
authors would identify the relative contributions of ship hull form; propulsor; and ship generated waves (which may
break) to the total turbulent wake field. Visual examination of the surface wake aft of a ship gives the impression that the
propulsor wake may dominate so that the particulars of the ship geometry may only be important in defining the propulsor
thrust and the concentrated kinetic energy it imparts into a diameter of fluid which is substantially smaller than the beam
of the ship. In any event it would be useful to understand the make-up of the term kw in their Equation (26) and how it
relates to ship form, propeller performance (especially cavitation effects), breaking of ship generated waves, air
entrainment and speed. Also, since that equation implies that the turbulent fields due to ship wake and waves are
independent properties that are directly additive, does the model data indeed support this assumption?
The second question concerns the turbulent properties of waves used in the authors' model tests. These waves are
generated mechanically; have no atmospheric wind on their surface; are probably devoid of air entrainment, and likely are
not continuously breaking. What is the authors' opinion on the characteristics of model wave turbulence fields vs. those in
full-scale wind generated breaking waves?
AUTHOR'S REPLY
None received.
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SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 703
DISCUSSION
K.Voliak
Russian Academy of Sciences, Russia
The reviewed paper consists of three sections: analytical, numerical, and experimental, united by a common idea to
show the ship wake turbulence against a background turbulence of the upper ocean.
The theoretical section is based on the assumption that the shear-free axisymmetrical unsteady turbulent motion with
some scaling parameters spreads into a nonturbulent fluid. Then the Kolmogorov's self-similarity solutions are used to
describe the cylindrical turbulent wake controlled by the ship beam, turbulence coefficient, and velocity, as well as by an
experimentally determined eigenvalue of the corresponding boundary problem.
The model of turbulence in the upper ocean is chosen as a quasisteady horizontally uniform random hydrodynamic
field with account of surface waves (breaking, in general) and mean shear flow. The latter factors allow authors to
separate three turbulent layers in the ocean medium vertical profile: wave-perturbed subsurface region, transitional
diffusive interlayer, and underlying classical logarithmic mean-shear half-space. When using quite general estimates for
the uppermost layer, the above vertical structure is presented in an explicit form.
The result of performed analytical estimates, based on comparison of the wake and the medium turbulence, is
presented in the form of technical formulas and diagrams containing ship and environment characteristics.
Further in the section devoted to numerical simulation, the authors directly model the wake—upper ocean interaction
by turbulent transport equations and present graphically a 3D structure of the ship wake depending on important
controlling parameters of the source and environment.
The experimental study with a propelled ship model in the laboratory tank, closing the paper, should, on authors'
opinion, verify the developed theory and numerical calculations. In fact the wake turbulence spectra are rather thoroughly
measured by a hot film anemometer across and along the tank behind the model. The anemometer sensitivity turns out
sufficiently high to measure very weak turbulence signals, even against the background of specially generated surface
waves.
All the three approaches used by authors of the reviewed paper do not overlap some compact concept of the ship
turbulent wake in the real ocean environment to an equal extend but rather complement each other. For example, no
layered structure of turbulence, developed analytically, is shown evidently in numerical and laboratory experiments.
However, the method of presentation used in the paper has own advantages to make perhaps the pattern of studied
phenomenon more voluminous.
Some questions can also arise, when reading the article. First, it would be desirable to take the sea wave
directionality into account in the model of upper turbulence, in parallel to the wake axial scale, though this task is not too
simple. Also the technical formulas derived can be readily simplified, for example, by lowering the accuracy in numerical
factors and exponents, as well as by expanding or approximating some terms, etc.
Second, on my opinion, it is important to widen the description of numerical model and the presentation of
calculated data, in particular, to show both the simplifications based on the developed theory and a possible restructuring
of the wake as it penetrates through the wave-perturbed zone into deeper layers.
In the experimental section, it is not clear how were the surface waves excited in the tank, and in general the
extensive wave modeling would be of crucial importance in view of the main problem posed in the work. An explanation
of the experiment scaling seems also to be not superfluous. Besides, a general accent on numerics and experiments
(maybe in oral presentation) can redistribute the reviewed material more symmetrically.
As a whole, the discussed study is well-grounded and comprehensive, its results are reliable and interesting to
researchers, especially such as data on the numerically modeled deepened ship wake.
AUTHOR'S REPLY
None received.
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