Thermal boundary layer structure in convection with and without rotation

Convection occurs in many settings from metal production to planetary interiors and atmospheres. To understand the dynamics of these systems it is vital to be able to predict the heat transport which is controlled by the thermal boundary layers (TBL). An important issue in the study of convective fluid dynamics is then to determine the temperature distribution within these thin layers in the vicinity of the bounding walls. Deviations from the classical Rayleigh-Bénard convection paradigm such as the addition of rotation or fixed heat-flux (rather than fixed temperature) boundaries compromise the standard ways of defining the width of the TBL. We propose an alternative method for defining the TBL using the location at which the advective and conductive contributions to the heat transport become equal. We show that this method can be robustly applied to two-dimensional (2D) nonrotating convection between no-slip boundaries with fixed temperature or fixed heat-flux thermal boundary conditions and three-dimensional (3D) rotating convection simulations with free-slip boundaries.