Some effects of boundary conditions and fluid properties on vacillation in thermally driven rotating flow in an annulus

Abstract

A series of laboratory experiments have been carried out which demonstrate the conditions favourable for vacillation in baroclinic thermally driven flows in a rotating annular convection chamber. As earlier studies have indicated amplitude vacillation occurs close to the transitions between dominant wave numbers in the regime under which regular waves are observed. Amplitude vacillation is shown to be less common when the depth of the system is decreased; it is not greatly affected by the use of a free or rigid upper boundary condition. It is however much more frequent when the Prandtl number of the convecting fluid is increased from 11 to 74 although in these experiments other parameters of the system, eg the isotherm slopes, were necessarily changed. Shape vacillation is only significant in the experiments when the upper surface is free; it is not influenced by the nature of the fluid.

An heuristic argument is advanced to account for the observations of amplitude vacillation. This is shown to be dependent on the extent to which changes in the zonally averaged structure of the flow which result when the wave amplitude is perturbed, are balanced by the transports of heat into the flow.