STABILITY AND WAVES ON A 2-DIMENSIONAL INVISCID SHEAR-FLOW

The stability of an inviscid parallel how with a free surface is consi dered. The numerical solution technique is a spectral method. The eige nvalues are found by converting the resulting quadratic eigenvalue pro blem into a linear eigenvalue problem, using the QR method. The result s are compared to an iterative scheme, and have been found to match to the first five decimal places. The bottom of the liquid layer is trea ted 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. The case with the infinite layer of liquid below the shea r layer has been found to be less unstable than the case with a rigid bottom for very long waves, more unstable for an intermediate interval of wavenumber, and about the same for very short waves.