Linear stability of a layered fluid with mobile surface plates
Abstract
We develop a general method of calculating the linear stability of a fluid with homogeneous layers that is heated from below. The method employs a propagator technique to obtain expressions for the fluid velocity, stress, and temperature. The principal advantage of the method is the ease with which solutions are adapted to a wide variety of boundary conditions and fluid properties. We demonstrate the utility of the method using three examples which quantify the effects of (1) Theological layering, (2) mobile plates at the surface, and (3) multiple phase transitions. Each example is presented in the context of Earth's mantle. In the first example, we predict that convection becomes confined to the upper mantle once the viscosity increase between the upper and lower mantle exceeds a factor of 2000, consistent with the nonlinear calculations of Davies (1977). In the second example we find that the heat flux variations in a convecting fluid with variably sized, surface plates (Gable et al., 1991) can be attributed, in part, to changes in the critical Rayleigh number. The linear stability of a fluid with multiple phase transitions is significantly affected by the locations of the transitions. We find that phase transitions have their largest effect when they are located at the center of the fluid layer and become much less important when they are located near the exterior boundaries.
 Publication:

Journal of Geophysical Research
 Pub Date:
 October 1994
 DOI:
 10.1029/94JB01556
 Bibcode:
 1994JGR....9919885B
 Keywords:

 Convection;
 Earth Mantle;
 Fluid Flow;
 Phase Transformations;
 Rheology;
 Stability;
 Boundary Layer Flow;
 Heat Flux;
 Mobility;
 Pressure;
 Rayleigh Number;
 Stress Analysis;
 Geophysics;
 Tectonophysics: Dynamics of the lithosphere and mantle;
 Tectonophysics: Heat generation and transport (except hydrothermal);
 Tectonophysics: Rheology of the lithosphere and mantle