Modelling Spectral Dissipation in the Evolution of Wind Waves


Principal Investigator

Michael Banner

School of Mathematics

University of New South Wales


Jose Alves

School of Mathematics

University of New South Wales


h01 - VPP

The ability to predict the evolution of the energy
spectrum of wind waves is of central importance
in upper ocean dynamics. Major applications involve sea state forecasting and correcting satellite remote sensing data of the oceans for the effect of waves. Recent investigations have shown that present state-of-the-art wind wave models predict spectra that show significant differences when compared to observations. The limitations of present models seem to be related to shortcomings in the formulation of the dissipation source function that accounts for energy losses due to wave breaking. This project aims to investigate modified forms of the dissipation function that incorporate recent advances on the knowledge of wave breaking derived from observations and exact computations of non-linear wave evolution. The objectives are (1) to improve the skill of state-of-the-art wind wave models for predicting integral properties of the wave field, such as total energy and peak frequency and (2) to reconcile details of the computed and observed directional wave spectra.




What are the results to date and the future of the work?

The evolution of wind wave spectra under fetch-limited conditions has been the central focus of the project so far. The sea state is said to be fetch-limited when the wave field no longer varies in time for a given distance from a shoreline perpendicular to the wind direction. This simple one-dimensional case allows the use of a numerical model (Exact-NL) that calculates explicitly the non-linear wave-wave interaction source term. This allows a detailed account of the impacts of the other source terms (wind input and dissipation) on the spectral evolution. New formulations of the dissipation source term can, in this way, be optimally evaluated. Future work will address more complicated two-dimensional wave generation scenarios, which will require the use of operational wind-wave forecast models. This will allow an assessment of the new dissipation function under more realistic situations.

Considerable progress was obtained in the formulation of our new dissipation function since the beginning of the project in March 1998. The new formulation is a spectral adaptation of results recently reported for breaking onset obtained through numerical modelling of non-linear wave evolution and from observations of wave breaking in the field. The modified form

Appendix B -



of the dissipation term has a strongly nonlinear dependence on the local steepness properties of the spectrum. Comparisons of computations and observations of fetch limited growth have shown that the new dissipation function provides a better description of the integral properties of the wave field during active growth compared with previous formulations,. Details of the full two-dimensional spectrum are also better described by our modified dissipation function.

Improvements remain to be achieved, particularly close to the point of evolution where the spectrum is fully developed. At this stage the spectrum stops growing because the dominant waves at the spectral peak propagate faster than the wind speed and a balance between input and dissipation should occur within higher frequency spectral components. Presently, the dissipation is not strong enough at full development. Solutions to this problem are presently being tested, including a revision of the available formulations of the wind forcing source term. The expected outcome is the development and choice of forcing functions that provide optimal numerical results and describe more accurately the physics of wind wave generation, not only for the idealized fetch limited case, but also in operational forecasting of two-dimensional wave fields.

What computational techniques are used?

The fetch-limited evolution experiments employ a numerical model that solves the energy balance equation and computes explicitly the full non-linear wave-wave interaction integral. Parametric functions of the wave spectrum are employed to calculate wind forcing and dissipation through breaking (white-capping). The model computes the evolution of the wind-wave spectrum along a one-dimensional grid with dynamically-adjusted spatial increments. A first order upwind finite difference scheme is used. The directional wave number spectrum is defined on a polar grid with grid points spaced according to a geometrical progression.

The implementation of the wind wave model WAM in the VPP is due to occur as soon as a final stable form of the dissipation function is obtained from the fetch limited experiments. WAM is an operational model presently used by research institutes and forecast centres worldwide, including the Australian Bureau of Meteorology. The main characteristic of WAM is the use of a parametric representation of the non-linear interaction source function, which allows its application on larger scale problems. Dissipation and wind forcing are prescribed as in Exact-NL. The operational model WAM will be used to assess if the improvements obtained with our new dissipation function in idealized cases can be extended to real case scenarios, where a two-dimensional wave field forced by transient atmospheric systems evolves in space and time. These cases cannot be simulated by the Exact-NL model due to prohibitive demands of CPU time required by the exact solution of the non-linear interaction integral.

- Appendix B