Nonlinear gravity-capillary waves generated by the passage of a pressure distribution over a sheared channel with constant vorticity are investigated. The problem is modeled using the full Euler equations. The harmonic part of the velocity field is formulated in a canonical domain through the use of the conformal mapping, which flattens the fluid domain onto a strip. The Froude number is considered to be nearly-critical and the Bond number critical. The shear effect changes drastically the pattern of the generated waves for large times. Moreover, depending on the intensity of the vorticity, the wave solutions can become smoother with small amplitudes.

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.

Particle paths beneath small amplitude periodic forced waves in a shallow water channel are investigated. The problem is formulated in the forced Korteweg-de Vries equation framework which allows to approximate the velocity field in the bulk fluid. We show that the flow can have zero, one or three stagnation points. Besides, differently from the unforced problem, stagnation points can arise for small values of the vorticity as long as the moving disturbance travels sufficiently fast.