Rectified flow of a rotating fluid along a vertical sidewall

The motion field resulting from an oscillatory, rotating flow parallel to a vertical wall and bounded from below by a horizontal plane along which there is no slip and from above by a horizontal frictionless lid is investigated numerically by using primitive equations. The model is barotropic and forced by oscillatory, spatially uniform, along‐wall, and lateral pressure gradients. The pertinent parameters are the Rossby, temporal Rossby, and Ekman numbers. By means of simulated particle tracking, including a statistical analysis, and a consideration of momentum balances, the physical mechanisms leading to flow rectification are identified; i.e., the exchange of along‐wall momentum of fluid parcels communicating between the bottom Ekman layer, the vertical shear layer, and the fluid interior. A rectified flow is generated along the wall for all subinertial, inertial, and superinertial oscillation frequencies investigated. The direction of the rectified current is such that the sidewall is on the right, facing downstream, for a vertically upward or Northern Hemisphere rotation. The mean transports and widths of the rectified currents are determined as functions of the appropriate system parameters. The current width is much larger than the classical E^1/4 Stewartson layer thickness. The numerical results are in good agreement with recent laboratory experiments.