Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing

Abstract

Abstract:We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS) code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system's behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.

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

“…2a and as shown in numerical simulations of axisymmetric flow 2D regimes of the same system (see Fig. 5 and Wright et al 2017), the formation of a statically stable though baroclinically unstable zone in the central area is expected at equilibrium, sandwiched between convectively unstable regions over/underlying the heated or cooled boundaries. Shraiman and Siggia (1990) and review by Chillà and Schumacher (2012)].…”

“…By unwrapping the spherical domain, this leads to the usual atmosphere-like cylindrical configuration, but where local differential heating at the horizontal boundaries is used to emulate the radiative heat sink in the upper atmosphere in the polar regions and the heat source near the ground in tropical regions. This allows the possibility of the formation of a statically stable (though baroclinically unstable) zone, sandwiched between convectively unstable regions over/underlying the heated or cooled boundaries (Wright et al 2017) and permits a possible feedback of the resulting baroclinic instability onto the background stratification. Figure 2 illustrates the experimental configuration, with the fluid contained within an annular channel between two upright, rigid, coaxial, thermally insulating cylinders and a flat (or conical), horizontal base, within which the outermost δ hot = 10 cm in radius is maintained with a constant heat flux and equilibrates at a corresponding temperature T b , while for r < b − 10 cm, the lower boundary is thermally insulating (perspex material).…”

“…Errors bars shown are illustrating standard deviation on the averaging period at a given rotating rate When background rotation is significant, two regimes were identified as a function of the rotation rate and classified as a function of P, the ratio of (non-rotating) thermal boundary layer to Ekman boundary layer thicknesses (Read 1986;Read et al 2014;Wright et al 2017). An (r, z) cross section of the temperature field from axisymmetric numerical simulations by Wright et al (2017) of the similar configuration as the current experiment is illustrated in Fig. 5 for the range P [0.1-1].…”

“…5 for the range P [0.1-1]. A secondary density current that flows beneath the heat sink, down the side of the inner cylinder and along the base towards the heat source, was found under very weak rotation conditions (Wright et al 2017). For weak rotation (defined as 0.05 P 0.2), this is replaced by a more uniform thermal gradient, with almost vertical isotherms close to the inner and outer cylinders, confined to Stewartson layers on the vertical boundaries, in association with a developing vertical shear in the azimuthal velocity (see Fig.…”

“…For weak rotation (defined as 0.05 P 0.2), this is replaced by a more uniform thermal gradient, with almost vertical isotherms close to the inner and outer cylinders, confined to Stewartson layers on the vertical boundaries, in association with a developing vertical shear in the azimuthal velocity (see Fig. 5 and Wright et al 2017).…”