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The table shows the parameter values used in the numerical experiments.
In many studies of mantle convection,
the Prandtl number is assumed to be infinite
since the viscosity is much larger than the thermal diffusivity.
Accordingly, the kinematic viscosity of the upper mantle
is estimated to be
0.5 x 1018 m2 sec-1,
and that of the lower mantle to be
2 x 1018 m2 sec-1
(e.g. Honda 1997).
In this study, we fixed the Prandtl number to 10
in order to take into account the large kinematic viscosity of the mantle.
The Rayleigh numbers are varied from 104 to 106.
The appropriate value of the Rayleigh number is estimated to be
105-106 for upper mantle convection,
and 106-107 for whole-mantle convection
(Jarvis and Peltier, 1989, Honda 1997).
The horizontal size of the plate is varied from 4 to 6,
but the plate thickness is fixed to 0.1.
This corresponds to a plate of 290 km thickness
in the case of whole-mantle convection,
and of 67 km thickness for upper mantle convection.
The initial conditions are those of zero velocity
throughout the model domain motion
and a conductive thermal regime
corresponding to a localized warm disturbance.
We perform our calculations using a grid comprising 960 nodes
in the x(horizontal) direction
and 80 in the z(vertical) direction.
A 4th-order Runge-Kutta scheme is employed for the time integration.
We use the Arakawa Jacobian scheme for finite differentiation
of the nonlinear terms and the relaxation method is used
to compute the stream function from vorticity.
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| Parameter |
Value(s) used in numerical experiments |
| Prandtl number Pr |
10 |
| Rayleigh number Ra |
104, 105, 106 |
| Thickness of plate d |
0.1 |
| Horizontal sizes of plate L |
4, 5, 6 |
Table : Parameter values for numerical experiments.
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