| Abstract | Previous analyses of waves on shear currents impose the stream profile a priori as a function of depth. In the present formulation, a stream function (x,y,t) is assumed to exist and unknown a priori, for a stable, two dimensional combined fluid flow of a stream of finite depth with a free surface wave disturbance of finite wave length, periodic and of permanent form. We show that the retained expression of the stream function is a quadratic in y, the vertical coordinate. The so-called current profile is not, at the outset, imposed on the solution. First and second order wave undulations can be developed for this case. |
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