Thermal Boundary Layer Structure and Flow Transitions - Convection with and without rotation

Abstract:

The magnetic fields of terrestrial planets result from turbulent rotating convection occurring in their liquid metal cores. Current modelling efforts are unable to access the extreme parameters relevant to planetary cores owing to the range of spatial and temporal scales needing to be resolved. The interaction of rotation and convection in the context of core dynamics is often studied using the analogue system of Rayleigh-Benard convection (RBC) rotated about the vertical axis. The convective heat transport is typically used to characterise convection and studies of rotating RBC find that the heat transport can exist in one of two regimes; one dominated by rotation and one resembling non-rotating convection. The transition between these regimes is thought to be controlled by thermal boundary layer (TBL) dynamics (King et al. Nature 2009, Julien et al. PRL 2012). To elucidate the physics of flow transitions in thermal convection it is crucial to have a robust definition of the thermal boundary layer that can be broadly applied to different configurations.

We consider the two most widely used methods of defining the TBL; `the local maxima' method which relies on the root-mean-square temperature fluctuation, $\sigma$, and the `linear intersection' method which uses the time averaged temperature profile, $\vartheta$. We test both methods using 2D simulations of RBC and 3D simulations of rotating RBC (having Ekman number, $E=10^{-7}$). The local maxima method is well suited for fixed temperature boundaries but cannot be applied to fixed-flux convection as the maxima in $\sigma$ are not pronounced. The linear intersection method defines the TBL by the intersection of linear fits to $\vartheta$ at mid-depth and close to the boundary; rotating RBC can maintain interior temperature gradients which can compromise the linear intersection method. The TBL prediction of each method is compared with theoretical predictions from the governing equations.

We propose an alternative method of defining the TBL by finding the location at which the advective and conductive contributions to the heat flux cross. We show that this method can be successfully applied to convection with or without rotation, driven by either fixed temperature or fixed heat-flux boundaries (with the latter being the relevant choice for terrestrial cores).