Laura K. Currie

The bulk properties of convection in stellar and giant planet interiors are often assumed to be independent of the molecular diffusivities, which are very small. By contrast, simulations of this process in rotating spherical shells, which are typically driven by conductive boundary heat fluxes, generally yield results that depend on the diffusivity. This makes it challenging to extrapolate these simulation results to real objects. However, laboratory models and Cartesian-box simulations suggest that diffusion-free dynamics are more readily obtained if convection is driven using prescribed internal heating and cooling instead of boundary fluxes. Here, we apply this methodology to simulations of Boussinesq, hydrodynamic rotating spherical shell convection. We find that this setup unambiguously yields diffusion-free behavior for some bulk properties of the convection, such as the radial temperature contrast and the convective heat transport. Moreover, the transition from prograde to retrograde equatorial zonal flow is diffusion free and only depends on the convective Rossby number. The diffusivity dependence of other bulk properties is regime dependent. In simulations that are rotationally constrained, the convective velocities and the strength and structure of the zonal flow are diffusion dependent, although the zonal flow appears to approach a diffusion-free state for sufficiently high supercriticality. In simulations that are either uninfluenced by rotation or influenced by rotation only at large scales, diffusion-free convective velocities and zonal flows are obtained. The result that many aspects of our idealized simulations are diffusion free has promising implications for the development of realistic stellar and giant planet convection models that can access diffusion-free regimes.

A mechanism by which the surface zonal flows of giant planets can be gradually attenuated with depth is explored. The zonal flow is driven by an imposed forcing in a thin layer near the surface. A meridional circulation is set up, analogous to the Ferrel-like cells observed in Jupiter's atmosphere. Acting on a stably stratified thin surface layer, the meridional flow induces a horizontal temperature anomaly which leads to a gradual reduction of the zonal winds with depth, governed by the thermal wind equation. Our model is a Boussinesq plane layer, with gravity acting parallel to the rotation axis. A suite of fully three-dimensional time-dependent numerical simulations has been performed to investigate the model behavior. Below the forced stable layer, convection is occurring, typically in the form of tall thin cells. The fluctuating components of the three-dimensional flow can be driven by either the convection or the Reynolds stresses associated with the jet shear flow. When fluctuations are mainly driven by convection in the form of tall thin columns and the forcing is relatively weak, the horizontal temperature anomaly persists much deeper into the interior than when it is driven by shear flow. The zonal jets can therefore extend deep into the interior, consistent with the Juno gravity data.

Models of astrophysical convection, such as mixing length theory, typically assume that the heat transport is independent of microphysical diffusivities. Such ‘diffusion-free’ behaviour is, however, not observed in numerical simulations employing standard fixed-flux or fixed-temperature boundary conditions, except possibly in extreme parameter regimes that are computationally expensive to achieve. Recent numerical and experimental work has suggested that internally heated and cooled convection can exhibit diffusion-free scalings in more numerically accessible regimes. Here, we present direct numerical simulations of 2.5D Cartesian rotating thermal convection driven by an internal heating and cooling function. The use of distributed heating and cooling functions alleviates sharp thermal boundary layers that would otherwise be present, allowing the flows to be simulated with modest computational resources. We show that for high Rossby numbers this set-up recovers mixing length theory scalings for the heat transport. The velocity amplitudes, in contrast, are observed to display diffusion-limited scalings. By comparing against boundary-driven rotating convection, we show that internally heated cases have a larger fraction of their thermal dissipation occurring in the bulk of the fluid. We suggest this is connected to the increased convective efficiency observed in these cases. Our results indicate that 2.5D internally heated convection can be used as a computationally inexpensive test-bed to investigate some aspects of diffusion-free heat transport.

Convection in stars and planets must be maintained against viscous and Ohmic dissipation. Here, we present the first systematic investigation of viscous dissipation in simulations of rotating, density-stratified plane layers of convection. Our simulations consider an anelastic ideal gas, and employ the open-source code Dedalus. We demonstrate that when the convection is sufficiently vigorous, the integrated dissipative heating tends towards a value that is independent of viscosity or thermal diffusivity, but depends on the imposed luminosity and the stratification. We show that knowledge of the dissipation provides a bound on the magnitude of the kinetic energy flux in the convection zone. In our non-rotating cases with simple flow fields, much of the dissipation occurs near the highest possible temperatures, and the kinetic energy flux approaches this bound. In the rotating cases, although the total integrated dissipation is similar, it is much more uniformly distributed (and locally balanced by work against the stratification), with a consequently smaller kinetic energy flux. The heat transport in our rotating simulations is in good agreement with results previously obtained for 3D Boussinesq convection, and approaches the predictions of diffusion-free theory.

We consider the effect of stratification on systematic large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focusing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.

We consider the effect of stratification on systematic, large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focussing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.

Convection in astrophysical systems must be maintained against dissipation. Although the effects of dissipation are often assumed to be negligible, theory suggests that in strongly stratified convecting fluids, the dissipative heating rate can exceed the luminosity carried by convection. Here, we explore this possibility using a series of numerical simulations. We consider two-dimensional numerical models of hydrodynamic convection in a Cartesian layer under the anelastic approximation and demonstrate that the dissipative heating rate can indeed exceed the imposed luminosity. We establish a theoretical expression for the ratio of the dissipative heating rate to the luminosity emerging at the upper boundary, in terms only of the depth of the layer and the thermal scale height. In particular, we show that this ratio is independent of the diffusivities and confirm this with a series of numerical simulations. Our results suggest that dissipative heating may significantly alter the internal dynamics of stars and planets.