Three dimensional linear and nonlinear surface wave patterns

We are interested in a mathematical and computational study of steady surface gravity waves in three dimensions. The most obvious example is the V-shaped wave pattern that forms at the stern of a steadily moving ship through an otherwise still body of water. As a prototype problem, we suppose there is pressure distribution applied to the surface of the water, characterised by some pressure scale P0 and horizontal length scale L , moving with constant speed U . In this simplified system, the pressure plays the role of the ship by causing a disturbance to the flow. The advantage of this set-up is that, unlike a real ship, the pressure does not pierce the surface of the water, which would complicate the system from a mathematical perspective