Rectified flow along a vertical coastline

Abstract

Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by y H ⪢ O (1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by y H ⪅O (1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δ y , of the rectified current is shown to scale as δ y H ∼ RoRo t −1 E 1 2 , where Ro is the Rossby number Ro t is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling.