RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 7, ES3001, doi:10.2205/2005ES000179, 2005
[77] Thermal convection in a viscous mantle is described by the distribution of the convective velocity vectors Vi(x, y, z), temperature T(x, y, z) and pressure p(x, y, z). These unknown functions are found by solving the system of momentum-, heat-, and mass-transfer equations
![]() | (1) |
![]() | (2) |
![]() | (3) |
![]() | (4) |
[78] Equation (1) means that the acceleration of a fluid element is proportional to the pressure gradient, the resultant of the viscous friction forces, and the gravity force. Equation (2) means that the variation in the temperature of a fluid element is controlled by conductive heat flux and heat generation by internal sources of this element. According to Equation (3), the density variation of the fluid in a given unit volume is controlled by the mass influx from the surrounding fluid.
[79] The inertial terms on the left-hand side of the momentum transfer Equation (1)
are on the order of
kr/h10-23 relative to the other terms of
the same equation and can therefore be neglected. Using the Boussinesq approximation,
we set
r = r0(1-aT) in the last, buoyancy-related term of Equation (1)
and
r = r0 in all remaining terms of Equations (1-3). The pressure will be
measured from its hydrostatic distribution
p(z) determined by the condition
p0 = -r0 g. We introduce dimensionless variables with the following
measurement units: the mantle thickness
D for length,
D/k for velocity,
D2/k for time,
T0 for temperature,
m0 for viscosity,
h0 k/D2 for pressure
and stresses, and
kT0/D2 for heat source density.
[80] The convection equations (1-3) in these variables take the form
![]() | (5) |
![]() | (6) |
![]() | (7) |
![]() | (8) |
Citation: 2005), Evolution of mantle plumes and uplift of continents during the Pangea breakup, Russ. J. Earth Sci., 7, ES3001, doi:10.2205/2005ES000179.
Copyright 2005 by the Russian Journal of Earth Sciences (Powered by TeXWeb (Win32, v.2.0).