Linear Analysis of Longshore Currents Instability over Mild Slopes

Longshore current instability is important to nearshore hydrodynamic and sediment transport. This paper investigates the longshore current instability growth model based experimental data with different velocity profiles of slopes 1:100 and 1:40 by adopting a linear shear instability model with the bottom friction effects. The results show that: (1) Only backshear mode exists in the instability of longshore current for slope 1:40 and frontshear and backshear modes may exist slope 1:100. (2) The peaks of linear instability growth mode for slope 1:100 correspond to three cases: the dominant peak is formed by the joint action of both frontshear and backshear, or by backshear alone without the existence of the smaller peak or formed by either the frontshear or backshear. (3) Bottom friction can decrease the corresponding unstable growth rate but it cannot change the unstable fluctuation period. The results of fluctuation period, wavelength and spatial variation obtained by the analysis of linear shear instability are in good agreement with experimental results.