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Authors: Hendrik L Tolman MMAB
Title:Optimum Discrete Interaction Approximations for wind waves Part 3: Generalized multiple DIAs
Additional Bibliographic Information:
MMAB Contribution Number:269
Keywords:Wind waves, DIA
Abstract:The present report is the third in a series assessing the potential of the Discrete Interaction Approximation for representing nonlinear interactions in wind wave models. This study addresses generalization of the DIA with multiple representative quadruplets to arbitrary depth, and particularly focuses on scaling behavior of this DIA with respect to depth. Major findings are that (i) shallow water quadruplet layouts need to be considered explicitly to assure proper conservation characteristics of a DIA, (ii) full shallow water expressions are needed to retain realistic shallow water interaction shapes, (iii) separate scaling functions with appropriate shallow and deep asymptotic behavior are needed to obtain proper scaling behavior for arbitrary depth, (iv) the choice of the underlying definition of spectral space has a notable (numerical) impact on the resulting interactions. Experiments with numerical optimization show that (a) an optimized generalized DIA configured like the traditional DIA requires approximately twice the computing time of the latter, (b) generalizing the quadruplet layout increases the costs by an additional factor of just below two, and (c) that the costs of the optimized MDIA scales linearly with the number of representative quadruplet realizations. As a side note that the assessment of the generalized multiple DIA, diffusion approaches to nonlinear interactions are addressed. It is shown that the traditional DIA with a quadruplet layout that is not resolved by the discrete spectral grid reduces to a simple diffusion operator that satisfies all conservation properties of the nonlinear interactions. A high-frequency filter based on such an approach is designed and optimized to be used in conjunction with the generalized multiple DIA, or with Neural Network Interaction Approximations.

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