Parameterized Ekman Layers on the Tilted f-plane: Quasigeostrophic Convection

Rapidly rotating Rayleigh Benard convection is known to generate a narrow Ekman layer on a no-slip boundary. This Ekman layer may be parameterized by boundary conditions which extend the geostrophic interior all the way to the boundary, known as pumping conditions. Here, pumping conditions are derived through a decomposition into inner and outer asymptotic solutions for the tilted f-plane, for both no-slip and stress-free boundaries. Investigated are the linear stability as well as the fully nonlinear single-mode solutions for various colatitudes using the pumping boundary conditions. Critical Rayleigh and wavenumbers are shown to converge to their asymptotic quantities in the rapidly rotating (high Taylor number) limit, and the asymptotic composite solutions are in good agreement with the directly computed numerical solutions.