Surface waves from bottom vibrations in uniform open-channel flow

The linearized problem of water waves radiated out from a two-dimensional oscillatory bottom source is studied analytically. The fluid depth is constant, and there is a uniform basic flow. There are two, three or four wave components radiated from a singular bottom source. The far-field expressions for the different wave components are determined, with the application of radiation conditions. The wave amplitudes with associated energy fluxes are calculated and compared with the hydrostatic shallow-water approximation. Trapped modes are identified for supercritical flow.