Modeling Mantle Convection: A Significant Challenge in Geophysical Fluid Dynamics David A. Yuen, S. Balachandar and U. Hansen

Here for convenience it is assumed that the Lewis number, Le = KIV, is a constant, where V is the concentration diffusivity and note that there is no source term for C in eqn (13.7).

(J"ij ( 1) (E* +PV*) TJ = eij = Asn-l exp RT . (13.13)

Mantle viscosity is thus dependent on stress, temperature and pressure. Viscosity in terms of the second invariant of the strain-rate tensor, e, is obtained by replacing sn-l in the above equation and solving for TJ. Viscosity then takes the form

Thermal-chemical convection studies have been carried out to hopefully explain many

Balachandar, S., Yuen, D.A. and D.M. Reuteler, Time-dependent three-dimensional compressible convection with depth-dependent properties, Geophys. Res. Lett., 19, 22472250, 1992.