Effects of finite depth and current velocity on large amplitude Kelvin-Helmholtz waves

Over the past decades a large amount of work has been done on inviscid, steady progressive, gravity waves on a free surface. However, waves which occur in nature are never, in fact, free-surface waves, since they are always beneath a fluid of finite density, if only air. In spite of this, very little work has been done on finite-amplitude interfacial waves. Tsuji & Nagata (1973) carried out a perturbation expansion in wave amplitude to fifth order, for interfacial waves between two stationary fluids. Holyer (1979) extended the calculation using the computer and resorted to Pade approximants to sum the resulting series. Meiron & Saffman (1983) investigated numerically the limiting highest wave and demonstrated the existence of over-hanging gravity waves of permanent form.