Inertial scaling of dissipation in unsteady breaking waves

Abstract

Wave dissipation by breaking, or the energy transfer from the surface wave field to currents and turbulence, is one of the least understood components of air–sea interaction. It is important for a better understanding of the coupling between the surface wave field and the upper layers of the ocean and for improved surface-wave prediction schemes. Simple scaling arguments show that the wave dissipation per unit length of breaking crest, ϵl, should be proportional to ρwgc5, where ρw is the density of water, g is the acceleration due to gravity and c is the phase speed of the breaking wave. The proportionality factor, or ‘breaking parameter’ b, has been poorly constrained by experiments and field measurements, although our earlier work has suggested that it should be dependent on measures of the wave slope and spectral bandwidth. In this paper we describe inertial scaling arguments for the energy lost by plunging breakers which predict that the breaking parameter b = β(hk)5/2, where hk is a local breaking slope parameter, and β is a parameter of O(1). This prediction is tested with laboratory measurements of breaking due to dispersive focusing of wave packets in a wave channel. Good agreement is found within the scatter of the data. We also find that if an integral linear measure of the maximum slope of the wave packet, S, is used instead of hk, then b ∝ S2.77 gives better agreement with the data. During the final preparation of this paper we became aware of similar experiments by Banner & Peirson (2007) concentrating on the threshold for breaking at lower wave slopes, using a measure of the rate of focusing of wave energy to correlate measurements of b. We discuss the significance of these results in the context of recent measurements and modelling of surface wave processes.