Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] its used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshe ar but also upon the backshear and the maximum and the width of the current . Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-sho re extension of the order of the width of the current; but the frontshear m odes are localized closer to the coast than are the backshear modes. Moreov er, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical ana lysis performed on realistic current profiles confirm the behavior anticipa ted by the analytical model. The theory has been applied to a current profi le fitted to data measured during the 1980 Nearshore Sediment Transport Stu dies experiment at Leadbetter Beach that has an extremum of background vort icity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory base d only on backshear instability failed to do so.