### WATER WAVES ON A BILINEAR SHEAR CURRENT

#### Abstract

A water wave theory is presented to describe waves propagating on a bilinear shear current flowing in the direction of the waves. The theory is derived assuming an ideal fluid in which a current exists, having a vertical velocity profile which varies linearly from a mean water level velocity of Ug, an interfacial velocity Uj at depth, d, and a bottom velocity Uj$. The theory is developed first for small amplitude waves and then extended to any arbitrary order by a numerical perturbation technique for symmetric waves. For measured waves, an irregular form of the theory is presented to provide a representation of these waves for analysis.

#### Keywords

current; bilinear shear current; shear current

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