### A CLOSED-FORM SOLUTION FOR TURBULENT WAVE BOUNDARY LAYERS

#### Abstract

A general, closed-form solution is presented to the linearized equation describing the velocity in a turbulent boundary layer. The solution is valid for any type of time-varying free-stream velocity, although the focus of the paper is on oscillatory flows generated by surface waves propagating over the sea bottom. A primary objective is to employ the solution for waves with an asymmetric velocity field, where nonlinear effects are small enough to be neglected in the linearized turbulent boundary layer equation. The general solution is developed to more convenient forms for a few special cases, including a sinusoidally varying free-stream velocity and a velocity given by stream function theory. The solution is tested against two different data sets from oscillatory tunnels; one set involves a sinusoidal and the other set a cnoidal free-stream velocity.

#### Keywords

turbulent boundary layer; wave boundary layer; closed form solution

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