VERTICAL STRUCTURE OF HORIZONTAL VELOCITY IN REGULAR SHOALING WAVES

We investigate the parameterization of the vertical structure of horiz ontal velocity in a family of weakly nonlinear, weakly dispersive (Bou ssinesq) models developed by Nwogu. That model contains a free paramet er that specifies the depth about which the assumed quadratic velocity profiles are expanded, with most standard formulations recovered by p articular choices of this free parameter. Nwogu chose to optimize this model by selecting the parameter to best fit the linear dispersion re lation. Here we test the model by applying it to the nonlinear case of shoaling of regular (cnoidal) waves. A new data set documenting the v ertical dependence of horizontal velocity is presented and is used to evaluate the range of values of the free parameter for which the model gives good results. We show that the Boussinesq model optimized for t he best linear dispersion relation also gives the best approximation t o the local vertical structure in this strongly nonlinear case.