Modulated Shear Flow

An analytical model based on Bowen and Holman is used to investigate the existence of instabilities due to the presence of a second extremum of the background orticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear 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-shore extension of the order of the width of the current but the frontshear modes are localized closer to the coast than the backshear modes. Moreover, 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.