Sloping convection in a rotating fluid

TLDR

Theoretical studies of sloping convection stem from ideas about large‑scale mid‑latitude atmospheric circulation, and the phenomenon is expected to occur widely in natural systems such as oceans, geophysics, planetary science, and astronomy. The waves are driven by the interaction of slight vertical motions with the potential energy field from differential heating, and dissipated by friction mainly in boundary layers on the apparatus walls. When the rotation rate exceeds a critical value, Coriolis forces suppress overturning and generate non‑axisymmetric baroclinic waves confined to jet streams; these waves are regular between two critical rates, with decreasing azimuthal wavelength that triggers barotropic instability and transfers kinetic energy to multiple scales.

Abstract

Abstract Laboratory experiments on thermal convection in a fluid which rotates about a vertical axis and is subject to a horizontal temperature gradient show that when the rotation rate Ω exceeds a certain critical value ΩR (which depends on the acceleration of gravity, the shape and dimensions of the apparatus, the physical properties of the fluid and the distribution and intensity of the applied differential heating) Coriolis forces inhibit overturning motion in meridian planes and promote a completely different type of flow which has been termed 'sloping convection' or 'baroclinic waves'. The motion is then non-axisymmetric and largely confined to meandering 'jet streams', with trajectories of individual fluid elements inclined at only very small (though essentially non-zero) angles to the horizontal. The kinetic energy of the waves derives from the interaction of slight vertical motions with the potential energy field maintained by differential heating, and it is dissipated by friction arising largely in boundary layers on the walls of the apparatus. Provided that Ω, though greater than ΩR, does not exceed a second critical value ΩI, the waves are characterized by great regularity; they are either steady or undergo periodic 'vacillation' in their amplitude, shape and other properties. The azimuthal wavelength decreases with increasing Ω until at Ω=ΩI it reaches a sufficiently low value, ∼1.5 times the radial dimension of the wave, for nonlinear processes to overcome various constraints associated with the anisotropy of the flow, thereby rendering the main baroclinic wave barotropically unstable by transferring kinetic energy to larger as well as smaller scales of motions. Theoretical investigations of sloping convection have their origin in ideas concerning the large-scale mid-latitude circulation of the Earth's atmosphere, modern work on which includes important studies based on numerical models. Conditions favouring sloping convection should be fairly common in natural systems and the process is expected to underlie various phenomena of interest to oceanographers, geophysicists, planetary scientists and astronomers.