A study of baroclinic instability in a cylindrical annulus with the temperature gradient imposed on the lower surface

Abstract

Laboratory experiments and numerical modelling studies have been performed for a rotating, thermally driven fluid system in a cylindrical annulus with a vertical rotation vector and axis of symmetry. The thermal forcing was through the imposition of an axisymmetric temperature gradient on a thermally conducting lower boundary, with additional heating through the outer sidewall. The upper and inner walls were nominally insulating. Flow patterns were observed in the experiments through the use of small, reflective flakes (Kalliroscope) in the working fluid, which was water. The rotation rate and temperature difference were varied to construct a regime diagram in thermal Rossby number–-Taylor number space. The curve separating axisymmetric flow from wave flow is ‘knee-shaped’, similar to the side-heated and -cooled baroclinic annulus which has been extensively investigated previously. Very near the transition curve, the initial wavenumber persists indefinitely, but well into the wave regime the initial wavenumber is higher than the equilibrated value. Far enough into the wave regime, the initial waves have wavenumbers several times that of the equilibrated value, and the initial disturbances form near the outer wall very early in the experiment. Numerical studies indicate that these waves are effective in distributing heat and that they occur in a region of positive static stability. These waves rapidly grow inward to fill the annulus and reduce in number as weaker waves are absorbed by the stronger ones. The period of transition between these waves and the equilibrated long-wave pattern is characterized by irregular flow. Closer to the transition curve, the temporal transition to longer waves as the flow equilibrates is simpler, with initial waves filling the annulus. In that case, the transition is characterized by a slow process of individual waves weakening and merging with adjacent waves.