Monash Geodynamics Seminar Series

Fluid-Mechanical Problems in Very Viscous Convection
Professor John Lister
Department of Applied Mathematics and Theoretical Physics, University of Cambridge

1pm, Friday 4th April 2008
Lecture Theatre S12, Building 25
Monash University, Clayton Campus (map)

Abstract: The huge viscosity of the Earth's mantle, and the large viscosities involved in industrial processes such as glass manufacture, provide motivation to revisit some of the `classic' fluid-mechanical problems in convection in the regime of very viscous (Stokes) flow. In this regime, fluid inertia is negligible, but thermal inertia plays an important role through the balance between advection and diffusion in the heat equation. The `classic' problems are simple to pose, and a physical understanding of the solutions provides a backdrop that may assist with intepretation of large-scale, more realistic computations of mantle convection.

Three problems will be described -- plumes, thermals and horizontal convection. Viscosity variations with temperature are neglected. 1. An exact similarity solution is obtained for the rise of a thermal (fixed release of buoyancy) in which all lengths increase like t^(1/2). At large Rayleigh number this solution differs substantially in form from Griffiths' (1986) spherical blob model. 2. An asymptotic solution is obtained for steady rise of a plume from a heated circular disc. The flow in the slender plume is coupled to the flow in the boundary layer over the disc, which in turn determines the heat transport into the plume. 3. Convection in a box can be driven by a horizontal temperature gradient applied to the top boundary, all others being insulated. Numerical solutions up to Ra=10^10 reveal a complicated flow structure, the dominant features of which are a strong near-surface circulation and a stratified interior.

Visit: http://www.itg.cam.ac.uk/people/John/

-- MeganHough - 30 Mar 2008
to top