Rotational flows over obstacles in the forced Korteweg-de Vries framework - V. Flamarion, Marcelo (2021)
In this work we investigate rotational waves resonantly excited by a submerged obstacle in a sheared shallow water channel with constant vorticity. In the weakly nonlinear, weakly dispersive regime, the problem is formulated in the forced Korteweg-de Vries framework. We compute the solution of the initial value problem for this equation numerically using a Fourier pseudospectral method with integrating factor. The water surface is initially taken at rest, and once the current is turned on, waves are immediately generated in the free surface. We identify the main effects of sheared current in the generated waves such as rotational solitary waves propagating upstream and sharp crested waves being generated.