Effects of topography and current on horizontal irrotational waves in shallow water

Based on the Boussinesq assumption, derived are couple equations of free su rface elevation and horizontal velocities for horizontal irrotational flow, and analytical expressions of the corresponding pressure and vertical velo city. After the free surface elevation and horizontal velocity at a certain depth are obtained by numerical method, the pressure and vertical velocity distributions can be obtained by simple calculation. The dispersion at dif ferent depths is the same at the O (epsilon) approximation. The wave amplit ude will decrease with increasing time due to viscosity, but it will increa se due to the matching of viscosity and the bed slope, thus, flow is unstab le. Numerical or analytical results show that the wave amplitude, velocity and length will increase as the current increases along the wave direction. but the amplitude will increase, and the wave velocity and length will dec rease as the water depth decreases.