Stability and waves on a two-dimensional inviscid shear flow (Q1905629)

The stability of an inviscid parallel flow with a free surface is considered. The numerical solution technique is a spectral method. The eigenvalues are found by converting the resulting quadratic eigenvalue problem into a linear eigenvalue problem, using the QR method. The bottom of the liquid layer is treated as either a rigid boundary or in contact with an infinite layer of initially still liquid. A linear and an exponential velocity profile is examined.