Friction Coefficient for a Wave-Current Coexistent System

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Abstract
A friction coefficient f cw is derived for a wave-current coexistent system, by assuming a time-invariant eddy viscosity. It is found that f cw is a function of four parameters, Zn/Z0, ūc/ûw, ϕ and ûw/σZ0 in the case of a rough bottom, or Zn/am, ū0/ûw ϕ and ûwam/v in the case of a smooth bottom. Exact solutions for f cw are given, solved numerically and expressed graphically. Equations which approximate f cw are also derived, by using an asymptotic expansion and an empirically-obtained expression. Several phenomena such as the bottom shear stress, the velocity profile, the condition of incipient movement of sand particles, the sediment transport rate and the size of ripples are expressed in terms of the friction coefficient.

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