# The Dynamical Consequences in Mantle Convection from a Nonlinear Constitutive Relation in the Temperature Equation due to variable Thermal Conductivity

Monday, March 18, 2002 - 2:30pm - 3:30pm

Keller 3-180

David Yuen (University of Minnesota, Twin Cities)

In mantle convection one normally attributes all of the nonlinearities in the physical properties, such as the rheology, to the momentum equation. But in mantle convection the momentum equation is elliptic. In contrast , for an infinite Prandtl number fluid, which aptly describes the mantle convection, the governing master equation in time is the temperature equation. With constant thermal conductivity, this equation is a parabolic equation with the nonlinear coupling coming from the advection term involving the velocity and the gradient of the temperature. But the presence of variable thermal conductivity , which depends on both temperature and pressure, will introduce three nonlinear terms in the temperature equation from the divergence of the heat-flux vector, which is K (T,P)grad T where K is the thermal conductivity and T and P are the temperature and hydrostatic pressure. Mantle thermal conductivity has two components with vstly different behavior in their temperature-dependence. They are respectively the phonon-assisted and photon-promoted thermal conducitivities. As a consequence of variable thermal conductivity, the nonlinear terms in the energy equation impart a different character to both the convective pattern and the charcteristic timescales of convection.Some outstanding features , which are different from mantle convection with constant conductivity, are (1.) larger plumes are developed in the lower mantle from the radiative component of the conductivity and a high temperature at the core-mantle boundary( CMB). (2.) plumes and convective patterns can be stabilized by a high temperature at the CMB. (3) the timescale for thermal cooling of the mantle is longer with variable thermal conductivity. These results would argue for the important role played by variable thermal conductivity in the thermal coupling between the core and mantle, since the temperature at the CMB would vary with time.