On the spectral dissipation of ocean waves due to white capping

Abstract

The effect of white capping on the spectral energy balance of surface waves is investigated by expressing the white-cap interactions in terms of an equivalent ensemble of random pressure pulses. It is shown first that the source function for any non-expansible interaction process which is weak-inthe-mean is quasi-linear. In the case of white capping, the damping coefficient is then shown to be proportional to the square of the frequency, provided the wave scales are large compared with the white-cap dimensions. The remaining free factor is determined indirectly from consideration of the spectral energy balance. The proposed white-capping dissipation function is consistent with the structure of theenergy balance derived from JONSWAP, and the existence of a o-5 spectrum governed by a non-local energy balance between the atmospheric input, the nonlinear energy transfer and dissipation. However, closure of the energy balance involves hypotheses regarding the structure of the atmospheric input function which need to be tested by further measurements. The proposed set of source functions may nevertheless be useful for numerical wave-prediction. According to the model, nearly all the momentum transferred across the air-sea interface enters the wave field. For fetchlimited and fully developed spectra in a stationary, uniform wind field, the drag coefficient remains approximately constant. However, for more general wind conditions, this will not be the case and the wave spectrum should be included in an accurate parameterisation of the air-sea momentum transfer. * Contribution from the Sonderforschungsbereich 'Meeresforschung Hamburg' of the Deutsche Forschungsgemeinschaft. Boundary-Layer Meteorology 6 (1974) 107-127. All Rights Reserved Copyright 0 1974 by D. Reidel Publishing Company, Dordrecht-Holland* Following the established custom, we refer here to the variance spectrum of the surface displacement as the 'energy' spectrum. To convert later to genuine energy and momentum transfer rates, a factor p,,,g has to be added.

Source term balance in a severe storm in the Southern North Sea

“…Therefore, the most important characteristics of these formulations are summarized below. The oldest spectral whitecapping formulation is based on the pulse model of Hasselmann (1974), as adapted by the WAMDI group (1988) and Janssen (1991):…”

Vortex generation by deep-water breaking waves

“…Restrepo et al (2011) used a qualitatively similar parametrization of the body force, as well as a scaling assumption that the velocity induced by the breaking is weak, to analytically solve for the behaviour of currents and waves in the presence of wave breaking. While the effects of breaking may be weak in the mean (Hasselmann 1974), the velocity due to breaking is O(c) over short time scales (Rapp & Melville 1990).…”

Wave modelling – The state of the art

“…As mentioned above, the groundwork was set by Komen et al (1984) who first demonstrated the possibility of obtaining and tuning a form of the spectral dissipation function by considering ds S the balance of all source terms in the radiative transfer equation. They based their choice of the function form on a rather free interpretation of the Hasselmann's (1974) analytical model for whitecap dissipation as random pressure pulses, and introduced a set of wave evolution tests to verify the dissipation function. Once the proposed dissipation function was implemented in the evolution runs, the model had to reproduce the experimentally wellknown evolution of wave integral properties -variance and peak frequency.…”

“…The most mathematically well-advanced and most frequently utilised dissipation model is that due to Hasselmann (1974). This is an after-breaking class model as it relies on the distribution of well-developed whitecaps situated on the forward faces of breaking waves.…”

“…This is an after-breaking class model as it relies on the distribution of well-developed whitecaps situated on the forward faces of breaking waves. According to Hasselmann (1974), once there is an established random distribution of the whitecaps, it does not matter what caused the waves to break: the whitecaps on the forward slopes exert downward pressure on upward moving water and therefore conduct negative work on the wave. This model produces a linear dissipation.…”