An empirical investigation of source term balance of capillary-gravity waves
Résumé
Phillips (1984) describes an approach to establish the dissipation function, D, in the equilibrium region of gravity waves from the functional dependence of the saturation spectrum, B, on the ratio of wind friction velocity and wave phase speed, r. In particular, if B can be expressed as a power-law function of r, and D can be expressed as a power-law function of B, then the coefficient and exponent of D(B) can be obtained from the coefficient and exponent of B(r), assuming local balance between the wind input and dissipation functions in the equilibrium region, and employing an empirically established wind input function. For shorter waves that are influenced by both gravity and surface tension, the balance of source/sink terms is much more complicated. For example, other generation and dissipation mechanisms, such as three-wave interaction, parasitic capillary wave generation, capillary wave reflection by orbital currents, micro scale breaking and viscous dissipation, may all be of the same order of importance in the energy and momentum balance. Phillips' approach, however, can still be applied to the analysis of the dynamic balance between the wind input and the D function, which is now treated as the sum of the remaining source/sink functions. We examine the dependence of B on r in the capillary to short gravity wave region in laboratory experiments. Indeed, the results appear to fit the power-law function nicely. A set of parametric equations is proposed for the derivation of the D function.