Second Approximation to Gravity Wave Attenuation

A second approximation is developed for the viscous damping of cnoidal waves propagating over a smooth horizontal bed. Experimental data are needed to examine the ranges of validity of the theory, although it may possibly apply at greater depths than does the first approximation and over a wider range of heights than does the theory of sinusoidal wave damping. Calculated attenuation coefficients vary markedly with wave height itself and for shallow water they are considerably larger than those predicted by sinusoidal wave theory, whereas for intermediate depths they are slightly smaller. The variation of wave number with distance, not predicted by the first approximation, is also determined. The damping of second order Stokes waves is shown to be given by the sinusoidal wave approximation.