A simple quasi-three dimensional model of longshore currents over arbitrary profile

Abstract

The long shore current maximum observed in the trough of a barred beach during the nearshore dynamics experiment DELILAH at Duck, North Carolina, is not predicted by present theory. The simplest longshore curren models balance cross-shore changes in the alongshore wave momentum (radiation stress) with the alongshore bottom shear stress. Waves break over the bar, reform in the trough and again break on the foreshore resulting in changes in the radiation stress, which predicts two jets, one over the bar and the other at the foreshore, which does not agree with the observed current maximum in the trough. The advection of the momentum of the longshore current by mean cross-shore currents as a source of momentum mixing is investigated. The longshore current is strongest toward the surface and decreasing to zero at the bottom. The cross-shore mean current has an onshore transport in the wave crest/trough region and an offshore transport beneath (undertow). The net interaction can induce significant lateral mixing of the alongshore momentum of the mean currents, which is shown using a simplified three- dimension model of nearshore currents to explain much of the differences with observations.