Abstract
Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind–wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency–angular grid. This provides a nearly two-times enhancement of the speed of numerical calculation for the nonlinear evolution term in a wind–wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper, we demonstrate all details of the FDIA concept for several frequency–angular numerical grids of high-resolution with the aim of active implementation of the FDIA in modern versions of world-wide used wind–wave models.
Highlights
Where M21,2,3,4 ≡ M2 (k0, k1, k2, k3 ) is the second power of the matrix elements corresponding to the four-wave nonlinear interactions, δ1+2−3−4 ≡δ(σ1 + σ2 − σ3 − σ4 )δ(k1 + k2 − k3 − k4 ) is the Dirac delta-function responsible for the resonant feature of the four-wave interactions, and σi = σ(ki ) is the radian frequency of the wave component with wave vector ki
The results showed that in deep water, generalized multiple DIA (GMD) configurations can be found which remove most of the errors of the discrete interaction approximation (DIA)
Integration grid for kinetic integral will be considered in the polar co-ordinates where each of interacting wave vector ki is represented by the frequency–angular point
Summary
Nonlinear interactions between waves play a very important role in description of wind–wave evolution governed by the equation [1]. TSA has recently been two high frequency the energy containingsaving ones This allows a reasonable presented as a new method to estimate nonlinear transfer rates in wind waves, and has been tested for value of the quadruplets from the NL-term calculations, saving accuracy. TSA from has been measurements, even for cases with directional energy shearing, compared to the implemented in the wind–wave model WAVEWATCH III and shown to perform well for wave. The results showed that in deep water, GMD configurations can be found which remove most of the errors of the DIA Most of these improvements were implemented in a new version (4.18) of the WAVEWATCH code. The shortages of the original DIA become clear if we consider details of the original DIA
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