THE ROTATIONAL FLOW OF FINITE-AMPLITUDE PERIODIC WATER-WAVES ON SHEARCURRENTS

Earlier analyses of waves on shear currents impose the stream profile as a function of depth a priori. Nonlinear velocity distributions assu med at the outset were considered by many authors. In the present work we assume the existence of a stream function psi(x,y,t) unknown a pri ori, for a stable, two-dimensional combined fluid how of a stream with a free surface wave disturbance of finite wave length, periodic and o f permanent type. The fundamental equations of motion and boundary con ditions of the combined field are those appropriate to an inviscid, in compressible fluid flow of finite depth with a free surface. The so-ca lled current profile, i.e. y dependence, is unknown a priori, and not imposed at the outset on the solution. We show that if the free surfac e disturbance is assumed periodic and of unchanged form, then the reta ined expression of the stream function is a quadratic in y, the vertic al coordinate. First and second order wave undulations are developed f or this case together with their corresponding dispersion relations an d flow characteristics. (C) 1998 Elsevier Science Ltd. All rights rese rved.