Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid

Abstract

In this paper we report a laboratory investigation of the motion within a rotating cylinder of fluid subject to internal heating and to cooling at the outer cylindrical sidewall. The internal heating is supplied by ohmic dissipation as an electric current passes between the outer sidewall and an axial wire. The experiments focus on the formation of eddy features and the associated zonal jets. To identify how the flow regimes generated in this continuously forced system are modified by the presence of a radial depth gradient, experiments have been performed with both horizontal (f-plane) and oppositely sloping boundaries. Endwall configurations which 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 and even planetary interiors. Stable, coherent, regular eddy features are observed over a wide range of rotation rates (Ω) in both horizontal and oppositely sloping endwall experiments. In the f-plane experiments regular modes with azimuthal wavenumbers m=1 and m=2 are observed. The regular wave regime of the ∂D/∂r>0 endwall experiments consists of modes with azimuthal wavenumbers m=1 to 5. Only the mode m=1 is seen in the regular wave regime of the ∂D/∂r<0 endwall experiments. The regular eddy structures produced in the ∂D/∂r>0 (∂D/∂r<0) endwall experiments are seen to be “vertically trapped” close to the bottom (top) boundary, whilst the amplitude of the f-plane modes is found not to vary substantially with depth. Further effects of the radial depth gradient are the observed reduction in the lateral scale of the eddy features in the ∂D/∂r>0 endwall experiments, which leads to the formation of between two and three independent trains of eddies within the lateral domain at sufficiently high values of Ω. Within the non-axisymmetric flow regimes of all three endwall configurations the number of zonal jets observed in the lateral domain of the experiment is larger than expected from the form of the background thermal forcing. The radial scale of the multiple zonal jets seen in the oppositely sloping boundary experiments is, however, much larger than a barotropic Rhines scale Lβ, suggesting that Lβ cannot be used to predict the radial wavenumber of the zonal mean flow in this continuously forced system.

Turbulence, waves, and jets in a differentially heated rotating annulus experiment

“…We used an apparatus with a relatively large gap width ͑b − a͒, which at high rotation rates allowed us to reach Taylor numbers an order of magnitude greater than had previously been used in experimental studies with sloping boundaries. 17 As mentioned in Sec. I, the top and bottom boundaries of the annulus can be either flat or sloping.…”

“…16 One past investigation involving internally heated fluids in a slightly different setup began to show evidence of zonal jet formation at high rotation rates. 17 However, it was not possible in that study to investigate the behavior of the jets in detail.…”

“…For a barotropic fluid ͑no variation in velocity with depth͒, the effects of sloping topography are the same as those of the planetary ␤-effect. A "topographic beta parameter" 17 can be defined…”

Saturn Atmospheric Structure and Dynamics

“…However, other cloud-level sources of turbulence, such as thunderstorms, might be capable of generating the observed fluxes. Indeed laboratory studies of geostrophic turbulence on a -plane, dominated either by baroclinic instabilities (Bastin and Read 1998;Wordsworth et al 2008) or unstablystratified convection (Condie and Rhines 1994;Read et al 2004Read et al , 2007, show a strong tendency to develop eddy-driven barotropic jets, so the question as to which process dominates on the gas giant planets must remain open until further evidence on the respective characteristics of baroclinic instability and deep convection becomes available.…”

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

“…Thus, this setup has proven to be a simple enough system to capture the fundamental physics and with enough complexity to represent nonlinear features and transition sequences to chaos similar to those of atmospheric dynamics (Hignett et al 1985;Früh and Read 1997;Bastin and Read 1998;Read 2003;Von Larcher and Egbers 2005;Wordsworth et al 2008;Vincze et al 2014). It has also proved valuable as a tractable 'test bed' within which to test numerical codes and methods (Harlander et al 2011;Vincze et al 2015) as well as to benchmark statistical-dynamical analysis methods in widespread use in meteorology, such as data assimilation (Young and Read 2013).…”