Verification of the shearstress boundary conditions in the undertow problem

Abstract

As part of a revision of the quasi-3D approach for coastal currents, the two-dimensional undertow problem is being restudied. Since the first proposal for approaches in the 1980's progress has been made by several researchers (e.g. Deigaard and Fredsoe, 1989) on the potential importance of contributions neglected initially, such as the time-mean correlation between horizontal and vertical wave-induced velocities. The effects of wave-decay, sloping bottom and oscillatory bottom boundary layer on this term, initially neglected, have now been derived formally and included in the undertow description. Before checking the effects in comparisons with measurements of undertow profiles, it is considered essential to first concentrate on an improved,or at least verified, formulation of the shearstress boundary condition at wave trough level. Since it is momentarily not feasible to make direct measurements of the shear stress condition at wave trough level, only indirect verification is possible e.g. by expressing the shearstress condition in terms of the set-up gradient. Existing small scale laboratory and recently acquired large scale laboratory results provide the set-up gradient data for this approach. The verification leads to theoretical improvements, and provides insight into possible differences between large and small scale situations.