The role of dissipation in the evolution of ocean swell

Dissipation of ocean swell, inferred from published oceanographic data, is investigated to determine if laboratory results on the dissipative stabilization of narrow-banded wave trains are applicable to ocean swell. Three issues are addressed. (i) Dimensional decay rates of ocean swell are about a million times smaller than typical decay rates of laboratory waves. Nevertheless, when decay rates are nondimensionalized using scales of dispersive and nonlinear effects, the dimensionless decay rates of ocean swell are comparable to those of laboratory waves, indicating that dissipation and nonlinear effects can influence ocean swell on the same time scale. (ii) The stability of ocean swell to small perturbations is examined within the theoretical framework of nonlinear Schrödinger-type models that either do or do not include dissipation. As in laboratory experiments, for swell with small enough nonlinearity, dissipation can inhibit and eventually stop the growth of small perturbations before nonlinearity becomes important. And as in laboratory experiments, we document herein an example of ocean swell with stronger nonlinearity that exhibits frequency downshifting, which is not predicted by any nonlinear Schrödinger-type model, including higher-order models, with or without dissipation. (iii) Given that dissipation can influence the evolution of ocean swell, we compare the predicted decay rates of four (published) dissipative models with observed decay rates, both in the ocean and in a laboratory wave tank. The model that presupposes an inextensible film on the free surface agrees best with measured rates of dissipation of ocean swell.