Ekman Arrest in a Turbulent Bottom Boundary Layer

Steady, along-slope geostrophic currents over a sloping bathymetry generate cross-slope Ekman transport than can advect buoyancy surfaces in a bottom boundary layer (BBL). The resulting horizontal buoyancy anomalies balance vertically sheared geostrophic flows that bring the total flow to rest. This is the classic Ekman arrest process that leads to a negligible integrated cross-slope transport.

Previous studies that focus on the Ekman arrest problem either assume constant diffusivity and viscosity or use simple turbulence closure methods such as Mellor-Yamada. Here, using Large Eddy Simulation (LES) techniques, we show that in a turbulence resolving (centimeter scale) model, the statistically steady-state cross-slope flow remains ~50% of the peak value after the Ekman arrest timescale. The leading order balance in the cross-slope direction is between the buoyancy force and Coriolis force. We examine the interactions between frictional and buoyancy forcing in this multiple-timescale system. Momentum, potential vorticity budgets and simple scaling analysis are presented to explain the possible discrepancies between idealized Ekman arrest results and the LES study with more realistic set-ups. A revised estimate of cross-slope transport would impact the predictions of coastal upwelling as well as water mass modification in the BBL over sloping bathymetry.