Wave-current interactions over bottom with appreciable variations in both space and time

Abstract

In shallow water conditions, current and wave propagation cannot be simulated separately and then superposed linearly. In these conditions, in fact, the fluid dynamics of the wave and current motions and, as a consequence, the responses of the movable bed are significantly different from those expected for a linear superposition of a current with a sinusoidal wave. Thus, wave nonlinearity and the wave-current interaction effects become important factors that need to be considered. A model should be also able to reproduce the fluid dynamics under shallow water conditions over significant slopes and time-bed-level changes. This paper presents a 1DH mathematical formulation of a hydrodynamic model and its numerical solution. The model is able to reproduce all characteristic shallow water phenomena, including: (i) wave-wave and wave-current interaction effects; (ii) important ratios between the current and wave velocities; (iii) significant bed slopes and sudden time-bed-level changes, and (iv) friction stresses at the bottom and at the free surface. Different orders of mathematical approximations and appropriate application examples are also presented