Generation of waves by a moving plate in stratified shallow water

The generation of waves inside an ideal two-layer stratified shallow water by the uniform motion of a vertical plate partially immersed in the fluid mass is studied in two dimensions. The fluid is assumed to occupy an infinite channel of constant depth. Two distinctive cases are studied according to whether the submerged part of the moving plate is smaller or greater than the upper layerʹs depth. In the first case, the lower fluid layer is not influenced by the motion of the plate up to the second order of approximation and local perturbations, only, are created in the upper layer. For the second case, progressive waves of the first order are shown in both layers besides local perturbations of the second order in the lower layer only. Passing to the limit of homogeneous fluids, local perturbations only remain. This passage to the limit shows that the stratification of the fluid mass is significant for the generation progressive waves. The systems of stream lines are drawn for stratified and homogeneous fluids.