This paper discusses the effect of rotation on the boundary layer in high Reynolds number flow over a ridge using a numerical method based on stabilised finite elements that captures steady solutions up to 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, 2018). In all cases considered the boundary layer remains attached, even at large Reynolds numbers, provided the Rossby number of the flow is sufficiently small. At any fixed Rossby number 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.

翻译：本文基于稳定有限元数值方法，研究了旋转效应对高雷诺数（高达$10^6$量级）山脊流动中边界层的影响。该方法能够捕捉稳态解。结果与浅水流动的边界层计算以及Machicoane等人（Phys. Rev. Fluids, 2018）报告的深水流动实验观察进行了验证。在所有考虑的案例中，只要流动的罗斯比数足够小，即使在大雷诺数下，边界层也保持附着。在任何固定罗斯比数下，当雷诺数足够高时，流动发生分离，在山脊背风侧形成一个稳定的回流区。当雷诺数更高时，未发现稳态流动。这种稳态解的消失与实验中观察到的非定常性转变高度吻合。