Warren Lecture with Stefan Llewellyn Smith

"Convection beyond Rayleigh and Bénard"

Stefan G. Llewellyn Smith
Mechanical and Aerospace Engineering, University California San Diego

ABSTRACT: Rayleigh–Bénard convection is a canonical flow in fluid mechanics, with applications in industry, geophysics, astrophysics, and beyond. Investigations have examined linear and nonlinear stability as well as deriving analytical bounds on quantities of interest, while laboratory and numerical experiments have given insight into the behavior at large Rayleigh numbers. Generalizations such as the case of convection in porous media, as well as the effect of rotation and magnetic fields, can be found in textbooks. Smith discusses two less well-known cases. First, periodically-driven convection, in which the temperature along one boundary varies periodically in time. This case provides a model for heating of the waters of Lake Superior in Spring. Second, horizontal convection, in which the temperature (or buoyancy) varies along a horizontal boundary. This case offers a simplified model, for example, large-scale oceanic flows induced by horizontal buoyancy gradients. Smith reviews previous known results and presents more recent work on the stability and behavior of these flows.