Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity

Abstract

Abstract. The thermal conductivity of mantle materials has two components, the lattice component k lat from phonons and the radiative component k rad due to photons. These two contributions of variable thermal conductivity have a nonlinear dependence in the temperature, thus endowing the temperature equation in mantle convection with a strongly nonlinear character. The temperature derivatives of these two mechanisms have different signs, with ∂k lat /∂T negative and dk rad /dT positive. This offers the possibility for the radiative conductivity to control the chaotic boundary layer instabilities developed in the deep mantle. We have parameterized the weight factor between k rad and k lat with a dimensionless parameter f , where f = 1 corresponds to the reference conductivity model. We have carried out two-dimensional, time-dependent calculations for variable thermal conductivity but constant viscosity in an aspect-ratio 6 box for surface Rayleigh numbers between 10 6 and 5 × 10 6 . The averaged Péclet P e numbers of these flows lie between 200 and 2000. Along the boundary in f separating the chaotic and steady-state solutions, the P e number decreases and the Nusselt number increases with internal heating, illustrating the feedback between internal heating and radiative thermal conductivity. For purely basal heating situation, the timedependent chaotic flows become stabilized for values of f of between 1.5 and 2. The bottom thermal boundary layer thickens and the surface heat flow increases with larger amounts of radiative conductivity. For magnitudes of internal heating characteristic of a chondritic mantle, much larger values of f , exceeding 10, are required to quench the bottom boundary layer instabilities. By isolating the individual conductive mechanisms, we have ascertained that the lattice conductivity is partly responsible for inducing boundary layer instabilities, while the radiative conductivity and purely depthdependent conductivity exert a stabilizing influence and help to control thermal chaos developed in the deep mantle. These results have been verified to exist also in three-dimensional geometry and would argue for the need to consider the poCorrespondence to: F. Dubuffet (fabien@msi.umn.edu) tentially important role played by radiative thermal conductivity in controlling chaotic flows in time-dependent mantle convection, the mantle heat transfer, the number of hotspots and the attendant mixing of geochemical anomalies.

Web-Based interrogation of large-scale geophysical data sets from handheld devices

“…In the case of the viscous heating ("visc_heat") (Dubuffet et al, 2002) one can zoom in and view the histogram showing the strongly localized nature of the heating.…”

“…The stream function ("streamout") (Dubuffet et al, 2002) associated with this flow shows multi-cellular behavior. The structure and statistics can be analyzed at the interface between two cells with opposite signs.…”

“…The first four datasets (A-D) refer to a particular run of 1,051,139 data points (2049x513) with Ra = 5x10 6 , variable and constant thermal conductivity, and extended Boussinesq approximation with adiabatic and viscous heating (Dubuffet et al, 2002).…”

“…The temperature dataset (listed as "temperature" in the program's dataset listing) (Dubuffet et al, 2002) illustrates the branching of the upwellings and downwellings. One can zoom into the branch point and focus on the cold or hot branches, using the histogram and statistics tools to find the relative magnitude of these branches.…”

“…The adiabatic heating ("adiab_heat") (Dubuffet et al, 2002) can be interrogated to assess the amount of heat produced in the plume. Contour plots of the adiabatic heating function trace out the plumes.…”