Finite-amplitude interfacial waves in the presence of a current

Abstract

Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simplc analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of sclccted cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existencc of steady solutions are examined.