Régimes of sloping thermal convection in a rotating liquid “annulus”

Abstract

Listen

Translate article

Wide-ranging laboratory investigations of thermally-driven flows in a baroclinic liquid of low viscosity and thermal conductivity in apparatus bounded by concentric cylindrical side-walls have (a) identified the dynamically-significant dimensionless parameters in terms of which the impressed conditions can be expressed, (b) stimulated advances in theoretical research on nonlinear dynamical systems, (c) established that under most (mechanical and thermal) boundary conditions, the action of gyroscopic (Coriolis) forces ensures that the dominant mode of heat transfer is “sloping thermal convection” (STC), and (d) provided insights into flows occurring in natural rotating fluid systems on length-scales up to thousands of kilometres. STC is characterised by relative flow that is nearly horizontal nearly everywhere, in wide-ranging patterns of waves and eddies which exhibit jet streams and fronts and which in some cases are spatially and temporally highly regular and in others are highly irregular (“chaotic”). Some of these manifold laboratory flows have their counterparts in the gaseous atmospheres of the Earth, Jupiter, Saturn and other spinning planets. When Coriolis forces are not quite strong enough to promote baroclinic instability leading to STC, heat transfer and associated generation of kinetic energy by buoyancy forces is effected by axisymmetric meridional overturning involving inter alia radial flow in end-wall Ekman boundary layers and vertical flow in side-wall boundary layers. Otherwise Coriolis forces promote quasi-geostrophic non-axisymmetric STC in the main body of the fluid. “Barotropic stability” due to enstrophy constraints renders this STC regular (i.e. spatially and temporally periodic) when the azimuthal scale of the flow exceeds a critical value found to satisfy a remarkably simple criterion. At shorter scales, enstrophy constraints weaken and no longer suffice to prevent inter-mode kinetic energy exchanges characteristic of “geostrophic turbulence”. The present article on rôle of boundary layers and on other aspects of annulus flows is largely intended to guide future investigations of crucial details of the dynamical processes that underlie fully-developed STC, some made possible by the ever-improving techniques of computational fluid dynamics.