Effects of Topography and Current on Horizontal Irrotational Waves in Shallow Water

Based on the Boussinesq assumption,derived are couple equations of free surface elevationand horizontal velocities for horizontal irrotational flow,and analytical expressions of the correspondingpressure and vertical velocity.After the free surface elevation and horizontal velocity at a certain depth areobtained by numerical method,the pressure and vertical velocity distributions can be obtained by simplecalculation.The dispersion at different depths is the same at the O(ε)approximation.The waveamplitude will decrease with increasing time due to viscosity,but it will increase due to the matching ofviscosity and the bed slope.thus,flow is unstable.Numerical or analytical results show that the waveamplitude.velocity and length will increase as the current increases along the wave direction.but theamplitude will increase.and the wave velocity and length will decrease as the water depth decreases.

Effects of Topography and Current on Horizontal Irrotational Waves in Shallow Water

Based on the Boussinesq assumption, derived are couple equations of free surface elevation and horizontal velocities for horizontal irrotational flow, and analytical expressions of the corresponding pressure and vertical velocity. 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 different depths is the same at the O (ε) approximation. The wave amplitude will decrease with increasing time due to viscosity, but it will increase due to the matching of viscosity and the bed slope, thus. flow is unstable. 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 decrease as the water depth decreases.