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OCR for page 174
The Thermal Conditions of Venus
VLADIMIR N. ZHARKOV AND V.S. SOLOMATOV
Schmidt Institute of the Physics of the Earth
ABSTRACT
This paper examines models of Venus' thermal evolution. The models
include the core which is capable of solidifying when the core's temperature
drops below the liquidus curve, the mantle which is proposed as divided into
two, independent of the convecting layers (upper and lower mantle), and the
cold crust which maintains a temperature on the surface of the convective
mantle close to 1200°C. The models are based on the approximation of
parametrized convection, modified here to account for new investigations
of convection in a medium with complex rheology.
Venus' thermal evolution, examined from the point when gravitational
differentiation of the planet was completed (4.6 billion years ago), is divided
into three periods: (1) adaptation of the upper mantle to the thermal
regime of the lower mantle: approximately 0.5 billion years; (2) entry of
the entire mantle into the asymptotic regime approximately three to four
billion years; (3) asymptotic regime. The parameters of a convective planet
in an asymptotic regime are not dependent on the initial conditions (the
planet "forgets" its initial state) and are found analytically. The thermal
flux in the current epoch is ~50 ergs cm2s-~. We consider the connection
between the thermal regime of Venus' core and its lack of magnetic field.
After comparing the current thermal state of thermal models of Venus and
Earth, together with the latest research on melting of the Fe-FeS system
and the phase diagram of iron, we propose that Venus' lack of its own
magnetic field is related to the fact that Venus' core does not solidify in the
contemporary epoch. The particular situation of the iron triple point (y -
- melt) strengthens this conclusion. We discuss the thermal regime of the
174
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AMERICAN AND SOVIET RESEARCH
175
Venusian crust. We demonstrate that convection in the lower portion of
the crust plays a minor role in regions with a particular crust composition,
but that effusive or intrusive heat transport by melt, formed from melting
of the crust's lower horizons, is the dominant mechanism for heat transport
to the surface.
MODIFIED APPROXIMATION OF PARAMETRIZED CONVECTION
Models of Venus' thermal evolution, calculated in approximation of
parameterized convection (APC), were examined in the works of Schubert
(l979~; lbrcotte et al. (~1~79~; Stevenson et al. (1983~; Solomatov et al.
(1986~; and Solomatov et al. (1987~. In parameterizing, dependencies were
used that were obtained from studying convection in a liquid with constant
viscosity. They were inferred to be true in cases of more complex rheol-
ogy. New numerical investigations of convection in media with rheology
that is more appropriate for the mantle (Christensen 1984a, b, 1985a, by
and theoretical research (Solomatov and Zharkov 1989) necessitated the
construction of a modified APC (MAPC).
Let the law of viscosity be expressed as (Zharkov 1983~:
~ = b/Tm-i exp [Ao/T (`p/po`) ]
(1)
where T denotes the second invariant of the tensor of tangential stresses,
p is density; b and L are considered here to be the constants within the
upper and lower mantles; m ~ 3; Ao denotes the enthalpy of activation for
self diffusion (in K); and where p = pO is the reference value of density
selected at the surface of each layer.
1b describe convection in such a medium, following Christensen (1985
a), we will use two Raleigh figures:
R ttgp^Td3 (2)
R c~gp/\Td3 `3'
XrlT
where ~ denotes the thermal expansion coefficient; g is the acceleration of
gravity; AT is the mean superadiabatic temperature difference in the layer;
d denotes layer thickness, X is the coefficient of thermal diflusivi~; and ale
and AT are defined by the formulae:
b Ao
To = _~ exp T ; To = 0° d2
~ Ao ~~ p )L
x
.
(4)
(5)
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176
PLANETARY SCIENCES
The dependence of the Nusselt number (determined in terms of the
thickness of the thermal boundary layer b) on RaO and RaT, where m = 3,
is parameterized by the formula
Nu = 2f' = a]?~a§°Ra§T.
In the case of free boundaries (lower mantle):
a = 0.29 ,BO = 0.37, AT = 0.16.
In the case of fixed boundaries (upper mantle):
a = 0.13, ,l]O = 0.35, AT = 0.15.
{~6)
(7)
(~8)
The theoretical expression has the following appearance (Solomatov
and Zharkov 1989~:
2`m+2'RaO RaT+2 =0.23Ra°4Ra02
(9)
It is obtained from the balance of the capacities of viscous dissipation and
buoyancy forces, and is in good agreement with (7) and (8~.
The heat flow at the upper or lower boundary of the layer is equal to
F. _ aeATi
~— ~ ,
(10)
where ATi denotes the temperature difference across the thermal boundary
layer. Velocities at the boundary (u), mean tangential stresses in the layer
(~) and mean viscosity (~) are estimated by the formulae (mum:
or ~d2
a= 4 6,
T = (7'7lbe~ A ~ p ~ )
71 =—r exp _° (I P ~
(11)
(~12)
t`13)
The mean temperature of the layer, T. and the temperature of the top of
the lower thermal boundary layer, To;, can be calculated from the adiabatic
relationship through the temperature in the base of the upper thermal
boundary layer, Tu:
T = nTu; To = natty'
where n and no are constants.
(~14)
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AMERICAN AND SOVIET RESEARCH
177
With large RaT/RaO, the very viscous upper thermal boundary layer
becomes reduced in mobility, taking an increasingly less effective part in
convection, and the previous formulae are not applicable. Solomatov and
Zharkov (1989) estimated that the transition to a new convective regime
occurs when
RaT > RaT'r ~ 2Ra2; m = 3.
DESCRIPTION OF THE MODEL
(15)
There is no unequivocal answer to the question of whether convec-
tion in the Earth's mantle (or Venus') is single layered or double-layered.
Previous works explored the single-layered models of convection. Possi-
ble differences in the single- and double-layered model of Venus' thermal
evolution were discussed by Solomatov et al. (19863 and Solomatov et al.
(1987~. We propose here that convection is double-layered, and the bound-
ary division coincides with the boundary of the second phase transition at
a depth of approximately 756 kilometers (Zharkov 1983~.
The thermal model of Venus (Figure la) contains a cold crust, whose
role is to maintain the temperature in its base at approximately 1200°C
(melting temperature of basalts), the convective upper mantle, the con-
vective lower mantle, and the core. An averaged, spherically symmetric
distribution, T (r,t) is completely determined by the temperatures indicated
in Figure lb.
The thermal balance equations for the upper mantle, the lower mantle,
and the core are written as:
31r(Rr—R32)piCpi~i =4~Ri2Fi2 - 4~R~F~, (16)
3,r(R32—R3)p2Cp24~2 = 3~(Ri2
~)P2Q2 - 4~R22F2l + 4~R2Fc' (17)
—3,,R3CpCpc4tc + QC 1t = 4~R2Fc.
(18)
Indices "1," "2," and "C" relate, respectively, to the upper mantle,
lower mantle and the core. T denotes the mean layer temperature, Fit is
the heat flow from the mantle under the lithosphere. The heat flow at the
surface of the planet is obtained by adding to Fit, thermal flow generated
by the radiogenic production of heat in the crust (~11 erg cm~2s~~. The
radius of the lithosphere boundary (R~) differs little from the radius of
the planet (Ro) so that RL ~ Ro. It is supposed that almost all of the
radioactive elements of the upper mantle migrated into the crust when the
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178
dL
~cr
RO ~~ ~ ;~ TB - 1200°C
R,2 ~ \
convective
lover
mantle
liquid
outer
core
_ / solid
Rj ~ ~ inner
\ ~ core
V (a)
PLANETARY SCIENCES
| T
| Tm (r' '\\
1 l\\
- 6CL \Tu2
1 1
(b)
LT.2
W62P:
1I L' l\TR= 1~0°C
~11
Hits = 460°C
' I I I I ~
O Rj RC R12 RL RO R
FIGURE 1 (a) Diagram of Venus's internal structure. Radii are indicated for: the
planet Ro; the base of the lithosphere- RL; the boundary between the upper and
lower mantles R12; the core Rc; and the solid internal core Ri. The dashed line
illustrates the boundary of the lithosphere, which is an isothermic surface of TB =
1200°C = eonst; dCr and dL denote the thickness of the crust and the lithosphere. (b)
Schematic, spherically symmetric temperature distribution in the cores of Venus. Reference
temperatures are indicated for: the surface Ts; lithosphere base TB; base of the upper
thermal boundary layer of the upper mantle Tut; peak of the lower boundary layer of
the upper mantle TL1; boundary between the upper and lower mantles T12; base of
the upper boundary layer of the lower mantle TU2; peak of the lower boundary layer
of the lower mantle TL2; and the boundary between the core and the mantle Tom.
Thicknesses of the thennal boundary layers are given: 51 for the boundaries of the upper
mantle; 52 and [c for the boundaries of the lower mantle. The dashed line indicates
the core melting curve, which intersects the adiabatic temperature curve at the boundary
between the outer, liquid and inner, solid core.
crust was melted. Fc denotes the heat how from the core. The heat flow
at the boundary between the upper and lower mantles with a radius of R12
is continuous: F:2 = F21.
Heat production in the lower mantle (Q2) is defined by the sum
4
Q2 = ~ QoiExp [Ai (to—t)]
i=1
(19)
where Qoi and Ai denote the current heat production of the radioactive
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AMERICAN AND SOVIET RESEARCH
179
isotopes K' U. and Th for one kilogram of undifferentiated silicate reservoir
of the mantle and their decay constants. The concentrations of K, U. and
Th are selected in accordance with O'Nions et al. (1979~: U = 20 mg/t,
K/[J = 104, Th/U = 4.
The term, Qc dm/dt, in (18) describes heat release occurring when
the core solidifies after the core adiabat drops below the core liquidus
curve. It is supposed that the core consists of the mixture, Fe-FeS, and
as solidification begins from the center of the planet, sulfur remains in
the liquid layer, reducing the solidification temperature. The value Qc is
composed of the heat of the phase transition and gravitational energy.
According to the estimates of Loper (1978~; Stevenson et al. (1983),
and Solomatov and Zharkov (1989), Qc = (1-2) 10~°erg go-.
Mean temperature of the adiabatic core:
TC ~ ncTcM
(20)
where nc ~ 1.2, the mean core density is p = 10.5 g cm~3, Cpc = 4.7106
erg g~ ~ K- ~ (Zharkov and ~ubitsyn 1980; Zharkov 1983~.
The formulae for the melting Tamp) and adiabatic Tamp) curves are
written as follows:
2.24
Tip) = To(1—OC x) (I
Tacl(p)=Tcm~—
P _ 1.224 - 0.009405R —0.1586 (R ) - 0.05672 (R )
(21)
(22)
(23)
Here To denotes the temperature at which pure iron melts at the boundary
core of the radius Rc, where p = PCM = 9.59 g cm~3; cat ~ 2; x is the mass
portion of sulfur in the liquid core, depending upon the radius of the solid
core Ri, and the overall amount of sulfur in the core, xO:
x(Ri) = R3 - R3
(24)
The intersection of (21) and (22) defines the radius of the solidified core
Ri (Figure lb).
Convection in the upper mantle is parameterized by the MAPC with
the parameters (7) (for fixed boundaries) in the lower mantle; and by the
same formulae with the parameters (8) (for free boundaries). However,
the difference between (7) and (8) is not very substantial. The parameters
for the upper mantle are: be = 4.3 · 10~5dyne3cm~6s, AL = 6.9 · 104 K,
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PLANETARY SCIENCES
on = 3 · 10-5K-i, pi = 3.7 g cm-3, X~ = 10-2cm~2s~i, ~~ = 4.5 · 105erg
cm~is. 107erg g
and for the lower mantle:
b2 = 1.1 10~7dyne3cm-6s, Ao2 = 1.3 105K, cx2 = 1.5 10-5K-i, P2
= 4.9 g cm~3, X2 = 3 · 10~2cm~2s~i, ae2 = 1.8 · 106erg cm~is~iK~i, g =
900cm s-2, Cp2 = 1.2 107erg g~i, n2 = 1.13, nr2 = 1.26.
NUMERICAL RESULTS AND ASYMPOTOTIC SOLUTION OF THE
MAPC EQUATIONS
The evolution of the planet began approximately 4.6 billion years ago.
The initial state of the planet was a variable parameter. The initial value
of TU2 is the most significant, since Tut, due to the low thermal inertia
of the upper mantle, rapidly adapts to the thermal regime of the lower
mantle (t < 0.5 billion years). The core has little effect on the evolution of
the planet in general and the majority of models do not take into account
its influence. TU2 was selected as equal to 2500, 3000, 3500 K The upper
value is limited by the melting temperature of the mantle, since a melted
mantle is rapidly freed from excess heat.
The upper mantle adapts to the thermal regime of the lower mantle for
the first approximately 0.5 billion years (Figure 2a, b). Then, after approx-
imately three to four billion years the entire mantle enters an asymptotic
regime which is not dependent upon the initial conditions. The evolution
picture in general is similar to the one described by Solomatov et al. (~1986~;
and Solomatov et al. (1987~. The planet is close to an asymptotic state in
the present epoch. Contemporary parameters of the models are:
Tu, = (1700-1720) K,
TO = (2500-25303 K,
TU2 = (2840-2870) K,
FL. = (35-40)erg cm-2
Al = (28-30)km
a2 = (13~140)km,
s,
u1 = (2.1-2.4)cm yr~
u2 = (0.~1.0)cm yr~
At = (5-6) bars,
r2 = (110-120) bars,
hi = (1-2~102i poise,
02 = (3-10~1~2 poise.
According to the criterion (15) MAP C are applicable throughout the
entire evolution, just as with the quasistationary criterion (Solomatov et al.
1987~.
The asymptotic expression for F~ in the first approximation is formu-
lated as (Solomatov et al. 1987~:
FL, = FQ (~1 + ~ ),
(25)
where FQ denotes the thermal flow created by the radioactivity of the lower
mantle, and tr is the characteristic time of decay:
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AMERICAN AND SOVIET RESEARCH
3500
'at 2500
Lo
Q
LO
2000
1 500
~ 100
CD
G
ace
0~
11
50
I
I - TU2(0) = 2500K
2 - TU2(0) = 30OOK
3 - TU2(0) = 3500K
~ L 1 ,
0 1 2 3 4 4.6
AGE t, BILLION YEARS
\
0~
~ I - TU2(0) = 2500K
\ \ 2 - TU2(0) = 30OOK
\ \ 3 - TU2(0) = 3500K
0 1 2 3
FIGURE 2 (a) Evolution of the base temperatures, TUT, T12 and Tu2, with differing
initial conditions. The core is not taken into account and is considered to be Tom = TL2
(Figure 1~. (b) Evolution of the thermal flow under the lithosphere, FL, with differing
initial conditions. The thermal flow to the surface is obtained lair adding ~ 11 erg cm~ls~1
to FL, generated by the radioactive elements of the crust. The dashed line indicates the
thermal flow generated bar radioactive elements of the lower mantle.
181
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182
dlnQ2 ~
~ dt )
equal ~5.67 · 109 years at the current time.
The time scale of thermal inertia of the mantle is equal to
tin = tint + tin2( 1 + t) ~
PLANETARY SCIENCES
(26)
(27)
where toll and 4n2 are the time scales for the inertia of each of the layers
individually:
s
_ MlnlCpl~Tl (1 + At + ~lAl(TUi—TB))
d2A2(Tu2Ui Tl2)~-
tint M2Q2
tins = 2 Q2 2 (~1~2 + - - T2 ~~ )
(28)
(29)
1 + nLls 1 + in + p2 - 1/3(~So—2~B2)Ao2(Tu2—Tl2)Tu22
an
1 + Al + >1A1(Tul—TB)TUI2 ' ~~
M1 and M2 denote the layer masses, s = R122 / Rr2. The values of (27)
through (30) are calculated in a zero approximation: Fl = FQ, and A =
Awn (p/pO)~.
The time scale for thermal inertia, as compared with models based on
the conventional APC (Solomatov et al. 1986, 1987), has increased from
~ 2.5 · 109 years to ~3.5 · 109 years. The mantle and core temperatures
obtained are somewhat lower (by 300 K near the core). In the models with
the core, Tom ~ 3720K and Fc ~ 15 erg cm-2s-t in the contemporary
epoch. Since the adiabatic value is FC ~ 30 erg cm-2s-i, there is no con-
vection if solidification is absent, and a magnetic field cannot be generated
(Stevenson e! al. 1983~.
MAGNETISM AND THE THERMAL REGIME OF
THE CORES OF EARTH AND VENUS
We will estimate the temperatures in the Earth using the MAP C.
MAPC is not applicable to the Earth's upper mantle, since convection in
the Earth involves the surface layer, and rheology is, in general, more
complex. However, MAPC is applicable to the Earth's lower mantle. Let
us assume a value for the temperature at the boundary between Earth's
upper and lower mantles of
T12 = (2300 - 2500)I(,
(Zharkov 1983), and the thermal flow at this boundary is
(31)
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AMERICAN AND SOVIET RESEARCH
F2l=R2° (F—Fcr+CpM1 dtl)~80erycm~2s~l,
183
where F—FCr ~ 70 erg cm~2s~1 is the medium thermal flow from the
Earth, after deducting heat release in the crust (according to the estimates
of Sclater et al. 1980), dT~/dt ~ -100KJbillion years. (Basaltic Volcanism
Study Project 1981~.
We will assume the following values for the rheologic parameters:
b = 6.6 · 10~6dyne3cm~6s, A = 1.5 · 1051(, andAO = 1.3 · 105K.
The remaining parameters are listed in Zharkov (1983~.
As a result, we have:
TU2 = (2800-2900) K,
T';2 = (3600-3800) K,
TCm = (3800-40()()) K'
[2 = 1~.
The value of TCm - TL 2 depends upon Fc, which we will assume to be equal
to the adiabatic value of Fall ~ 30 erg cm~2s~~.
Therefore, the temperature at the boundary of the Earth's core, TCME
is greater than for Venus (TCMV) by a value of
TCME—TOM v = ( 100—300) If.
(33)
In order for Venus' core not to solidify, it is necessary that the adiabat of
the Venusian core not drop below the solidification curve during cooling.
Otherwise, solidification of the core will cause the core to mix by chemical
or thermal convection, and it will trigger the generation of a magnetic field
(Stevenson et al. 1983~. We will estimate the difference between TCME and
the temperature, TCrv (which is critical for the beginning of solidification),
at the boundary of Venus' core, with a single pure iron melting curve, Tm
(P) and a single equation of the state for iron p(P).
TCME is found from the intersection of the adiabat of the Earth's
core (22) and the liquidus curve (23), with a sulfur content in the core
of XE at the boundary of the Earth's inner core. Tcrv is obtained from
the intersection of the adiabat of Venus' core (22) and the liquidus curve
(23) with a sulfur content of xv. We then obtain (Solomatov and Zharkov
1989~:
TCME—Tcrv = (+300) . ( - 300),K, (34)
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PLANETARY SCIENCES
where XE—XV = 0 . o.m. Therefore, if xv ~ XE—(0 . 0.02) = 0.07
. 0.12; (with XE = 0.09 . 0.12; Aherns 1979), the core of Venus is not
solidifying at the present time, and a magnetic field is not being generated.
Complete solidification of the core would have led to the absence
of a liquid layer in the core and would have made it impossible for the
magnetic field to be generated. However, for this, the temperature near
the boundary of Venus' core should have dropped below the eutectic value,
which, according to the estimates of Anderson et al. (1987) is ~ 3000
K and according to Usselman's estimate (1975) is ~ 2000 K Such low
temperatures of the core seem to be of little probability.
Pressure in the iron triple point, ~ - ~—1, (liquid) approaches the
pressure in the center of Venus. This is significant for interpretation the
absence of the planet's own magnetic field. According to the estimates
of Anderson (1986), Pip ~ 2.8 Mbar (Figure 3), but is also impossible
to rule out the larger values of Pip. In the center of Venus, PA ~ 2.9
Mbar; at the boundary of the solid inner Earth's core, PIE = 3.3.Mbar;
and in the Earth's center, POE = 3.6 Mbar (Zharkov 1983). If Pcv <
Pip, the conclusion that there is no solidification of Venus' core is further
supported, since, in this case, the core's adiabat (critical for the beginning
of solidification) drops several hundred degrees lower. This stems from the
fact that reduction in the temperature of solidification of the mixture, ~—
Fe—FeS is greater than for the mixture ~—Fe—FeS by AS~/AS~ times,
where AS`/AS, denotes the ratio of enthropy jumps (during melting) equal
to ~ 2, according to Anderson's estimates (1986).
The latest experimental data on the melting of iron allow us to estimate
the melting temperature in the cores of Earth and Venus. Figure 3 shows
melting curves obtained by various researchers, and the ~—~ boundary,
computed by Anderson (1986~. With x = 0.09-0.12 and c' = 1 - 2 (formula
21), the full spread of temperatures at the boundary of the Earth's core,
leading to the intersection of the liquidus and adiabat curves, is equal to
TCME = 3500 . 47001(,
- with data from Brown and McQueen (1986) and
TCME = 4300 . 5400K,
(35)
(36)
- with data from Williams et al. (1987~.
The effect of pressure on viscosity of the lower mantle reduces the
effective Nusselt number and increases the temperature Of TCME and
TCMV by ~ 300 K (Solomatov and Zharkov 1989~. We obtain the estimate
TCME = 3800 . 4300If,
which is the best fit with (35).
(37)
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AMERICAN AND SOVIET RESEARCH
8000
7000
6000
By
5000
LLJ
~ 4000
i:
LL
LL
3000
2000
1 000
:
~ 1 1
~ me/
~ /
of/
, ,11 ,
1
1
I- ~ LL LL
1o ~1
1 1
1 1
l
/ 1
l
1 1
1 1
1 1
- 1 1 1
1 1, 1 1
1
185
2
Pressure, Mbar
3
FIGURE 3 Pure iron melting curves according to venous data and the boundary of the
phase transition fly Fe ~ Fe. The figures indicate melting euchres: 1 is from the study
by Williams et al. (1987~; 2 is from the study by Anderson (1986) and experimental data
from Brown and MeQueen (1986~; and 3 is based on the Lindeman formula with the
Grunehaisen parameter of G = 1.45 = eonst, using experimental data from Brown and
MeQueen (1986~. The transition boundary, ~—c, was constructed in the study by Anderson
(1986) and together with the melting eume gives us the location of the triple point. The
vertical segments illustrate errors in determining temperature for curves 1 and 2. The
boundary labels are as follows: CM is the boundary between the core and the mantle; C
denotes the center of the planet; I is the boundary of the solid inner core; and the final
letter indicates Earth (E) or Venus (V). fly - ~ -1 denotes the location of the triple point.
THE THERMAL REGIME OF THE VENUSL\N CRUST
What are the mechanisms by which heat is removed from Venus's
interior to the surface? Global plate tectonics, like Earth's, are absent on
the planet (Zharkov 1983; Solomon and Head 1982), although in individual,
smaller regions, it is possible that there are features of plate tectonics (Head
and Crumpler 1987~. A certain portion of heat may be removed by the
mechanism of hot spots (Solomon and Head 1982; Morgan and Phillips
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PLANETARY SCIENCES
1983~. Conductive transport of heat through the crust clearly plays a large
role. However, with a large crust thickness ~ > 40 km), as indicated by
data from a number of works (Zharkov 1983; Anderson 1980; Solomatov et
al. 1987), the heat flow of F ~ (40-50) erg cm-2s~i triggers the melting of
the lower crust layers and removal of approximately one half of heat flow
by the melted matter. The latter flows to the surface as lava or congeals in
the crust as intrusions.
We shall discuss the possibility of solid-state convection in the crust as
an alternative mechanism of heat removal through the Venusian crust.
The crust is constituted of an upper, resilient layer with a thickness of
de and a viscous one with a thickness of do = dCr—de.
The crust thickness of dCr is constrained in our model by the phase
transition of gabbro-eclogite, since eclogite, with a density higher than
that of the underlying mantle, will sink into the mantle (Anderson 1980;
Sobolev and Babeiko 1988~. The depth of this boundary is dependent
upon the composition of basalts of Venus' crust. We assume that dCr =
70 km (Yoder 1976; Zharkov 1983; Sobolev and Babeiko 1988~. It is
considered that radioactive elements are concentrated in the upper portion
of the crust, and the primary heating occurs via the heat flow from the
mantle of For; ~ 40 erg cm-2s~~. The boundary (de) of the resilient crust
is defined as the surface of the division between the region effectively
participating in convection and the nonmobile upper layer. Crust rheology
is described by law (1) with the parameters from Kirby and Kronenberg
(1987~. Four modeled rocks are considered: quartz diorite, anorthosite,
diabase and albite. Parameter m in (1) is close to 3 for them, so that the
formulae MAP C with parameters (8) for fixed boundaries is fully suitable
for estimating. In addition, criterion (15) is used to define the boundary,
de. At this boundary, which is regarded as the upper boundary of the
convective portion of the crust, the temperature is equal to
To = 733 + 20de (km), K.
The following physical parameters are assumed (Zharkov et al. 19693:
p = 2.89 cm~3,or = 2 · 10-5I(-i, Be = 2 . 105erg cm~is~iI(~i
(38)
.
Computations have demonstrated that the thickness of the resilient
crust is 20-30 kilometers. The mean temperature of the convective layer
of the crust has been calculated at ~ 1600K, 1700K, l900K and 2000K,
respectively, for quartz diorite, anorthosite, diabase, and albite, and exceeds
the melting temperature for basalts by hundreds of degrees. This means
that convection does not protect the crust from melting, and heat is removed
by the melted matter.
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AMERICAN AND SOVIET RESEARCH
187
We can estimate that portion of the heat which is removed by con-
vection. For this, let us assume the temperature in the base of the crust
to be TB = 1500K (approximately the melting temperature). We obtain
the Nusselt number from the formulae of MAPC, and find that it is ~1.7;
1; 0.6; and 0.5, respectively, for quartz diorite, anorthosite, diabase, and
albite. For ~ = const, and for complex rheology, as in (1), (Christensen
1984a and 1985a), convection begins at Nu ~ 1.5-2, as calculated according
to the formulae of APC (MAPC). Thus, where dCr ~ 70km, perhaps only
quartz diorite is convective, removing 25-30 erg cm-2s-i, while 10-20 erg
cm-2s-i is removed by the melt. The rate of convective currents is three
to five millimeters per year. It can be demonstrated that
Nu ~(dCr—de)°9
(39)
With dCr ~ 120 fun, convection also begins in anorthosite, while in
quartz diorite it occurs virtually without melting.
These estimates show that convection in the crust may play some role
in individual regions, depending on the thickness and composition of the
crust. It is not excluded that in individual regions, convection in the crust
makes its way to the surface. The bulk of the heat is, apparently, removed
by melted matter. The rate of circulation of material from the crust is,
with this kind of volcanism, 50-100 km3yr~~. This is three to five times
greater than crust generation in the terrestrial spreading zones. Another
process by which basalt material circulates is where new portions of melted
basalt reach the crust from the upper mantle, and basalt returns back to the
mantle in the eclogite phase. This process may trigger the accumulation of
eclogite in the gravitationally stable region between the upper and lower
mantles. It may lead to the chemical differentiation of the mantle. This
process has been noted for the Earth by Ringwood and Irifune (1988~.
Figure 4 illustrates various processes involved in heat and mass trans-
port.
The geological structures observed on Venus may be related to these
processes. Flat regions may be tied to effusive, basalt volcanism. Linear
structures in the mountainous regions may be related to horizontal defor-
mations which are an appearance of convections in the crust or mantle.
Ring structures may stem from melted intrusion or hot plume lifted towards
the surface from the bottom of the upper mantle.
Convection both in the mantle and in the crust is, apparently, nonsta-
tionary (as on Earth). This nonstationary nature stems from instabilities
occurring in the convective system. The characteristic time scale for such
fluctuations is t ~ d/u, where d ~ 1()~-109 cm is the characteristic dimension,
and u ~ 1 cm per year is the characteristic velocity. Therefore, character-
istic "lifespans" for various occurrences of instability are t ~ 108-109 years.
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PLANETARY SCIENCES
(a) Conductive heat (b) Heat removal by melted matter (c) Convection in the crust
~ ~ ~
(d) Lift of the mantle plume (e) Mande convection reaches (f) Basalt exchange between the
_~
it, ~ ,,~4 ~ ' ~ -, 9-i-?-
FIGURE 4 Process of heat transport through the Venusian crust: (a) transfer of heat
camed from the mantle by the mechanism of conductive thermal oonducti~t~r, (b) heat
removal by the melted matter which is formed as the basalt crest melts. The melted matter
may flow to the surface or form intrusions; (c3 convection in the crust which does not
reach the surface or reaching the surface; (d) lifting of hot plume from the bottom of the
upper mantle to the crust of Venus, taggenng enhanced heat flow, a flow of crust matenal,
and the sinking of the crust; (e) involvement of the crust in mantle convection with the
formation of spreading zones; (f) basalt exchange between the crust and the mantle. Basalt
is formed when the upper mantle partially melts and is returned back as eclogite.
Regional features of tectonic structures, thermal flows, volcanic activity and
so on, can exist for this length of time.
CONCLUSION
1. Modification of the approximation of parameterized convection
for the case of nonNewtonian mantle rheology led to no marked increase
in the time scale of thermal inertia of the mantle from two to three or three
to four billion years in comparison with the usual parameterization. The
thermal flow at the surface of Venus of ~ 50 erg cm~2s~i, is the product
of radiogenic heat release from the mantle (50%), heat release in the
crust (20%), and cooling of the planet (30%~. These figures for Earth are
approximately 40, 20, and 40% for the double-layered convection models.
Temperatures in the upper portion of the mantle are approximately 1700 K,
which is 50-100 K greater than on Earth. Given the existing uncertainties
in the concerning parameters, Tom ~ 3700-4000 K at the core bc>;undary
and may, possibly, be greater. This temperature is 100 300 K less than for
the Earth.
2. The magnetic field on Venus is absent. This is most likely due to
the lack of core solidification and, respectively, the lack of energy needed
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AMERICAN AND SOVIET RESEARCH
189
to maintain convection in the liquid core. For this, it is enough for the
sulfur content in Venus' core to be even a little bit less than on the Earth
(but not more than 2~30% less). This conclusion is stronger if the triple
point in the phase diagram for iron, ~—~—1, lies at pressures that are
greater than in Venus' center, but approximately less than in Earth's center.
3. At the values obtained for heat flows from Venus' mantle, the crust
melts, and the melted matter ~ < 100 km3 per year) removes about one half
of the entire heat. The remainder is removed conductively. In individual
regions, depending on the crust thickness and composition, a portion of the
heat may be removed by convection, reducing crust temperature and the
portion of heat removed by the melted matter. Flow velocities comprise
several millimeters per year. Due to the insufficiently high temperature of
the surface, convection in the crust separates from the surface as a highly
viscous, nonmobile layer with a thickness of 2~30 kilometers. In individual
regions, crust convection may emerge to the surface. Basalt circulation also
occurs by another way: the basalt is melted out of the upper mantle and
returned back in the form of eclogite masses, which sink into the lighter
mantle rock. It Is possible that this process triggers the accumulation of
eclogite at the boundary between the upper and lower mantles, resulting
in the chemical separation of the mantle. These processes may explain the
formation of various geological structures on Venus.
4. The nonstationary nature of convection In Venus' mantle and crust
determine regional features of tectonic, thermal and volcanic appearances
on the surface of the planet which have a characteristic duration of ~
108-109 years.
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Representative terms from entire chapter:
lower mantle
