LXXXII. The effect of eddy viscosity on ocean waves

Abstract

The effect of turbulence on ocean waves appears to call for an eddy viscosity which, while being large compared with the molecular viscosity, is small compared with the eddy viscosity found to apply to currents. A recent suggestion that the eddy viscosity should be taken as proportional to λ ^4/3 whereλ is the wavelength, seems to the author to be unsatisfactory. It is proposed, instead, that the coefficient of eddy viscosity N, applicable to waves, should be of the form N=Kca, where c is the speed of propagation, a is the amplitude and K is a constant. This form is indicated on dimensional grounds and is shown to be in conformity with v. Karman's similarity hypothesis for shearing flow. With K of the order of 5 × 10^-5, the eddy viscosity would be large enough to account entirely for the observed rate of decay of ocean swell, while its effect on the attenuation of waves with depth would still be negligible. In the initial formation of waves, only the molecular viscosity need be considered. A possible effect of eddy viscosity on waves in the generating area would be to limit the steepness of the longer waves to a value less than the breaking steepness, even when the duration and fetch were unlimited.