A conservative nonlinear filter for the high-frequency range of wind wave spectra

Filtering of the high-frequency part of a wind wave spectrum may be useful in a numerical wind wave model for various reasons. First, it can be used to augment (or be part of) a parameterization of the resonant nonlinear interactions, that are essential to third-generation wind wave models. Second, when combined with a dynamic time stepping scheme for source term integration, it may result in smoother (and hence faster) wave model integration. In this study, such a filter is proposed, based on the traditional Discrete Interaction Approximation (DIA) for the resonant four-wave nonlinear interactions. This filter retains all conservative properties of the interactions. For small time steps and/or smooth spectra, it is formulated as a traditional source term. For larger time steps and/or non-smooth spectra it is formulated as a filter. This formulation guarantees stability of the filter itself and will enhance overall computational stability in a full wave model. The stability properties of this filter are illustrated using traditional wave growth computations. Examples are given where the filter improves model economy, and where it is shown to remove spurious high-frequency noise from a wave model.