Thermal winds forced by inhomogeneous boundary conditions in rotating, stratified, hydromagnetic fluid

Abstract

Lateral variations in the thermal boundary conditions at the horizontal boundary of an otherwise stably stratified fluid layer drive circulatory motion. For a rapidly rotating electrically conducting fluid, the introduction of a background vertical magnetic field reduces the dimensionless strength of the thermal wind from $O(1)$ to $O(E^{1/4})$ for prescribed temperature variation or to $O(E^{1/2})$ for prescribed heat-flux variation, where $E$ is the Ekman number. This is a significant effect when considering the spatially variable cooling of the Earth's core by the mantle. A general discussion of linear hydromagnetic flows identifies a large number of lengthscales inherent in the differential system as functions of the Ekman, Elsasser and stratification numbers, and shows that other scalings arise from the boundary conditions.