The Fast Discrete Interaction Approximation Concept

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.

The Fast Discrete Interaction Approximation Concept

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 nearly two-times enhancing 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 the FDIA in modern versions of world-wide used wind-wave models.

Role of Nonlinear Four-Wave Interactions Source Term on the Spectral Shape

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements of ocean waves over the past decades and found that the measured power spectrum has (a) a very high central peak (characterized by the parameter γ, developed in the 1970s in the JONSWAP program) and (b) enhanced high-frequency channels which lead to the phenomenon of “bimodality”, also a well-known phenomenon. We discuss how a numerical hindcast of the Draupner storm (1995) with the standard code WAVEWATCH-III with full Boltzmann interactions also reflects these previously experimentally determined spectral shapes. Our results suggest that the use of the full Boltzmann interactions (as opposed to the discrete interaction approximation often employed for forecasting/hindcasting) is important for obtaining this characteristic physical spectral shape of the power spectrum.

Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

The canonical interaction between a two-dimensional weak Gaussian disturbance (entropy spot, density spot, weak vortex) with an exothermic/endothermic planar shock wave is studied via the linear interaction approximation. To this end, a unified framework based on an extended Kovásznay decomposition that simultaneously accounts for non-acoustic density disturbances along with a poloidal–toroidal splitting of the vorticity mode and for heat release is proposed. An extended version of Chu’s definition for the energy of disturbances in compressible flows encompassing multi-component mixtures of gases is also proposed. This new definition precludes spurious non-normal phenomena when computing the total energy of extended Kovásznay modes. Detailed results are provided for three cases, along with fully general expressions for mixed solutions that combine incoming vortical, entropy and density disturbances.

SELF-SIMILAR AND LASER-LIKE REGIMES IN NUMERICAL MODELING OF HASSELMANN KINETIC EQUATION FOR OCEAN WAVES

The absence of mathematically justified criteria in the models of prediction of wind waves of the ocean, used by the world’s largest centers NOAA (USA) and ECMWF (UK), based on numerical modeling of the Hasselmann kinetic equation, led to erroneous hierarchy and erroneous nonlinear interaction approximation, wind forcing and waves dissipation terms due to wave-breaking. Existing models of wind waves operate in the paradigm of the adjustable «black box», each time requiring reconfiguration. On the basis of numerical simulation, we were able to construct a model, taking into account the wind forcing of the power type in combination with the «implicit» dissipation.