Baroclinic waves in a container with sloping end walls

Abstract

The effects of sloping upper and lower boundaries on baroclinic waves in a differentially heated rotating fluid annulus have been studied experimentally. Measurements have been made of the internal temperature structure, the transition from axisymmetric to non-axisymmetric flow, the wave numbers and flow types, the drift rates and the heat transfer. The sloping boundaries influence the baroclinic waves in two distinct ways: if they are parallel the energy releasing mechanism is directly affected, while if they are not parallel effects similar to the latitudinal variation of coriolis parameter in a planetary atmosphere (the (3-effect) are introduced. In order to identify essentially non-linear effects the results on the transition from axisymmetric to non-axisymmetric flow, the wave numbers and the drift rates have been compared with an appropriately extended version (by Hide) of Eady’s linear perturbation theory of baroclinic instability. In the case of the transition from axisymmetric to non-axisymmetric flow, when account was taken of concomitant changes in the internal temperature structure, surprisingly good agreement with linear theory was obtained. Within the regular wave regime, the azimuthal wave numbers agreed quite well when the theoretically predicted value was 1, 2 or 3 but for higher predicted wave numbers the observed wave numbers were smaller. In the case of oppositely sloping boundaries the observed drift rates relative to the mean flow were generally 30 % less than that of the unstable waves of the linear theory. Another departure from the linear theory also occurred when the boundaries sloped in opposite senses, namely the occurrence at sufficiently rapid rotation rates of two separate wave trains of limited radial extent and differing wave numbers and drift speeds; one dominated the flow near the inner cylinder and the other dominated the flow near the outer cylinder. This result suggests that the variation of coriolis parameter with latitude can determine the radial extent of the baroclinic waves. Apart from its intrinsic interest as a fluid-mechanical study this work bears on the role played by the (3-effect and large-scale topography in natural systems such as the atmosphere and oceans. It also shows that at the higher rotation rates used the sloping eeopotentials inevitably present in previous laboratory experiments on baroclinic waves have important effects, and in particular explains the failure of previous theories to account for the position of part of the transition from axisymmetric to non-axisymmetric flow.