Attached and separated rotating flow over a finite height ridge

Abstract

This article discusses the effect of rotation on the boundary layer in high Reynolds number flow over a ridge using a numerical method based on stabilized finite elements that captures steady solutions up to a Reynolds number of order ${10}^6$. The results are validated against boundary layer computations in shallow flows and for deep flows against experimental observations reported in Machicoane et al. [Phys. Rev. Fluids 3, 034801 (2018)]. In all cases considered the boundary layer remains attached, even at arbitrarily large Reynolds numbers, provided the Rossby number of the flow is less than some critical Rossby number of order unity. At any fixed Rossby number larger than this critical value, the flow detaches at sufficiently high Reynolds number to form a steady recirculating region in the lee of the ridge. At even higher Reynolds numbers no steady flow is found. This disappearance of steady solutions closely reproduces the transition to unsteadiness seen in the laboratory.