Theoretical and Experimental Investigation on Laminar Boundary Layers Under Cnoidal Wave Motion

An analytical solution is derived for a laminar boundary layer under cnoidal waves. Since the solution is expressed in terms of Fourier series expansion instead of elliptic functions, computation of velocity and bottom friction in a boundary layer can be made very easily. According to the present theory, the characteristics of the bottom boundary layer, such as velocity, bottom shear stress, and boundary layer thickness, show considerable differences from those under sinusoidal wave boundary layers with the increase of the Ursell number. Among these, one of the most distinct differences from purely harmonic boundary layers can be found in the time-variation of the bottom shear stress. A direct measurement of the bottom shear stress is made by using a hot-film sensor to compare with the present theory.