Geophysical and Astrophysical Fluid Dynamics

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.

Abstract:

We present an experimental study of flows in a cylindrical rotating annulus convectively forced by local heating in an annular ring at the bottom near the external wall and via a cooled circular disk near the axis at the top surface of the annulus. This new configuration is distinct from the classical thermally-driven annulus analogue of the atmosphere circulation, in which thermal forcing is applied uniformly on the sidewalls, but with a similar aim to investigate the baroclinic instability of a rotating, stratified flow subject to zonally symmetric forcing. Two vertically and horizontally displaced heat sources/sinks are arranged so that, in the absence of background rotation, statically unstable Rayleigh-Bénard convection would be induced above the source and beneath the sink, thereby relaxing strong constraints placed on background temperature gradients in previous experimental configurations based on the conventional rotating annulus. This better emulates local vigorous convection in the tropics and polar regions of the atmosphere whilst also allowing stably-stratified baroclinic motion in the central zone of the annulus, as in midlatitude regions in the Earth’s atmosphere. Regimes of flow are identified, depending mainly upon control parameters that in turn depend on rotation rate and the strength of differential heating. Several regimes exhibit baroclinically unstable flows which are qualitatively similar to those previously observed in the classical thermally-driven annulus, However, in contrast to the classical configuration, they typically exhibit more spatiotemporal complexity. Thus, several regimes of flow demonstrate the equilibrated co-existence of, and interaction between, free convection and baroclinic wave modes. These new features were not previously observed in the classical annulus and validate the new setup as a tool for exploring fundamental atmosphere-like dynamics in a more realistic framework. Thermal structure in the fluid is investigated and found to be qualitatively consistent with previous numerical results, with nearly isothermal conditions respectively above and below the heat source and sink, and stably-stratified, sloping isotherms in the near-adiabatic interior.