A numerical study of axisymmetric flow regimes in a rotating annulus with local convective forcing

A numerical study of axisymmetric flow regimes in a rotating annulus with local convective forcing Susan Wright, Sylvie Su, H´el`ene Scolan, Roland Young and Peter Read Atmospheric, Oceanic & Planetary Physics, University of Oxford peter.read@physics.ox. ac.uk Abstract We present a numerical study of 2D axisymmetric flows in a rotating annulus convectively forced by local thermal forcing via a heated annular ring at the bottom near the external wall and a cooled circular disk near the centre at the top surface of the annulus. Two vertically and horizontally displaced heat sources/sinks are arranged so thatstatically unstable Rayleigh-B´enard convection would be induced above the source and beneath the sink, emulating local vigorous convection in the tropics and polar regions in the Earth’s atmosphere or oceans with a stably-stratified baroclinically unstable zone in mid-channel. Several distinct flow regimes are identified and characterized with reference to variations in the (squared) ratio P of Ekman layer thickness to the thermal boundary layer thickness (proportional to rotation rate Ω). Corresponding scalings for quantities such as azimuthal velocity and Nusselt number with P are consistent with convective transfer ∼ Ra 0.329±0.018 and control of meridional transport by Ekman layers in rotating flow. Introduction Complex interactions between turbulent convection and stably-stratified flows in the pres- ence of background rotation play major roles in a wide range of problems in atmospheric and oceanic science, astrophysics and industrial flows. If a heat source is located at a lower geopotential than the sink, Sandstr¨om’s theorem (Coman et al., 2006) would lead one to expect a strong, thermally-direct circulation to result. In the atmosphere of the rotating Earth, however, a situation prevails where heat sources and sinks are displaced horizontally as well as vertically, in which heating is located equatorwards and near the surface, due to the absorption of sunlight near the ground in the tropics and subsequent emission and re-absorption by the atmosphere of upwardly re-radiated thermal emission, and cooling from above by net thermal emission, predominantly at high altitude in mid- high latitudes [e.g. see Chan and Nigam (2009) and references therein]. The resulting circulation spontaneously partitions itself into a convectively unstable/neutral region in the tropics that interacts with a baroclinic region at mid-latitudes that, despite being cooled from above, is statically stable. The mechanisms behind the formation of this statically stable region in mid-latitudes are only partially understood quantitatively, despite the apparent ability of numerical climate models to reproduce it in simulations. This lack of detailed understanding is due in part to the inability of such models to represent small-scale convection explicitly, requiring the use of parameterization methods that are empirically calibrated or ‘tuned to reproduce the observed structures. But in particular, there is no well established, objective theory to account for the magnitude of the vertical thermal gradient in the mid-latitude atmosphere, although there is an ongoing debate among climate scientists as to the possible role of fully developed, baroclinic instabilities in acting to stabilise their own thermal environment [e.g. see Schneider (2006); Zurita-Gotor and Lindzen (2007)]. VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016