A laboratory study of baroclinic waves and turbulence in an internally heated rotating fluid annulus with sloping endwalls

Abstract

New laboratory experiments have been performed in a rotating fluid annulus, subject to internal heating and sidewall cooling, in which a radial depth gradient has been created by the inclusion of oppositely sloping boundaries. Endwall configurations that cause the fluid depth ( D ) to increase with radius (∂ D /∂ r >0) and to decrease with radius (∂ D /∂ r <0) have been studied, as the former is applicable to the terrestrial atmosphere and oceans, while the latter may be relevant to deep atmospheres such as those of the giant planets. Even with the steepest boundary slopes, isolated or periodic chains of stable coherent eddies are observed with both endwall configurations, and these regular eddy modes are seen to drift relative to the walls of the convection chamber concordant with simple Rossby wave ideas. When the boundary slope (δ) is small, no difference is observed in the range of azimuthal wavenumbers seen in the regular wave regimes of the two endwall configurations. At larger values of δ, however, this symmetry is lost, since regular modes m =2 to 8 are observed with ∂ D /∂ r >0 endwalls, while only a large vertically trapped anticyclonic gyre is seen with ∂ D /∂ r <0 endwalls. The other effects of the radial depth gradient are the observed reduction in both the lateral and vertical scale of the eddy features, and the formation of two independent trains of eddies within the gap width at sufficiently high rotation rates in the ∂ D /∂ r >0 endwall experiments. The zonal mean flow is also found to develop a significant barotropic component, superimposed on the vertically and horizontally sheared zonal jets generated by the non-monotonic thermal gradient of the experiment. This barotropic component is predominantly prograde (retrograde) in the ∂ D /∂ r >0 (∂ D /∂ r <0) endwall experiments, and confined close to the outer (inner) wall where the fluid depth is greatest. There is evidence of the formation of increased numbers of zonal jets in the ∂ D /∂ r >0 endwall experiments above that expected from the form of the thermal forcing. These multiple zonal jets are highly localized in the vertical, and are trapped close to the top boundary. Their radial scale is, nevertheless, close to that given by the Rhines argument. No comparable increase in the radial wavenumber of the mean flow is observed in the ∂ D /∂ r <0 endwall experiments in the present system.