| Résumé | Earlier analyses of waves on shear currents impose the stream profile as a function of depth a priori. Nonlinear velocity distributions assumed at the outset were considered by many authors. In the present work we assume the existence of a stream function (x,y,t) unknown a priori, for a stable, two-dimensional combined fluid flow of a stream with a free surface wave disturbance of finite wave length, periodic and of permanent type. The fundamental equations of motion and boundary conditions of the combined field are those appropriate to an inviscid, incompressible fluid flow of finite depth with a free surface. The so-called 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 surface disturbance is assumed periodic and of unchanged form, then the retained expression of the stream function is a quadratic in y, the vertical coordinate. First and second order wave undulations are developed for this case together with their corresponding dispersion relations and flow characteristics |
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