Controlling Thermal Chaos in the Mantle by Feedback due to Radiative Thermal Conductivity
Wednesday, October 10, 2001 - 11:00am - 12:00pm
The role of nonlinear aspects of thermal conductivity has been neglected in studies of mantle convection, even though it is well known from solid-state physics, that it is temperature- and pressure-dependent. The temperature equation acquires a distinct nonlinear character by virtue of the nonlinear term involving the square of the temperature gradient. We have employed the recently developed thermal conductivity model by Hofmeister (Hofmeister, Science, 1999) in both 2-D and 3-D mantle convection studies. The thermal conductivity of mantle materials has two components, the lattice component klat from phonons and the radiative component krad due to photons. The temperature (T) derivatives of these mechanisms have different signs, with d klat /d T negative and d krad /d T positive. This attribute of a positive temperature derivative on the part of k-rad offers the possibilities for the actual temperature at the core-mantle boundary (CMB) to be a stabilizing factor on boundary layer instabilities at the core-mantle boundary. We have parameterized the weight factor between krad and klat with a dimensionless number f , where f =1 corresponds to the reference conductivity model given by Hofmeister (1999). For this thermal conductivity model (f = 1 ) we have found that by increasing the temperature at the CMB, Tcmb , from 3000 to 4200 K, the boundary layer instabilities are quenched more and become more stabilized. For purely basal heating situations the time-dependent chaotic flows at Tcmb = 3000K become stabilized for values of f between 1.5 and 2. As we increase the Tcmb to 4000 K the critical value of f, fc, needed for flow stabilization is correspondingly reduced .These results argue for the possible constraints on Tcmb from the presence of radiative thermal conductivity in the deep mantle and the development of secondary instabilities on the CMB. Too high a Tcmb would quench the instabilities. This work is the first to address the important role played by variable thermal conductivity in controlling chaotic flows in mantle convection, the number of hotspots and the attendant mixing of geochemical anomalies.