Open AccessWave‐wave interactions in finite depth water
Author(s) -
Lin Ray Q.,
Perrie Will
Publication year - 1999
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/1999jc900026
Subject(s) - hamiltonian (control theory) , deep water , waves and shallow water , nonlinear system , transformation (genetics) , mathematics , mathematical analysis , physics , geology , mathematical optimization , quantum mechanics , chemistry , thermodynamics , biochemistry , oceanography , gene
In this study we present a new formulation for the nonlinear wave‐wave interaction source function in finite water depth. The formulation, denoted the reduced integration approximation (RIA), is shown to compare well with published formulations, both for shallow water wave‐wave interactions [ Hertench and Hasselmann , 1980; Polnikov , 1997; Hashimoto et al. , 1998; A. Masuda and K. Komatsu, manuscript in preparation, 1998] and also for the asymptotic deep water limit: (1) the Hamiltonian formulation proposed by Lin and Perrie [1997], by (2) Hasselmann and Hasselmann [1981], and (3) the line integral transformation of Webb [1978] and Resio and Ferne [1991]. Of these deep water formulations, that of Lin‐Perrie generalizing the Hamiltonian representation of Zakharov [1968] to finite depth water, is notable for its simplicity, efficiency and its ability to apply to very shallow water ( kh ≈ 0.3), and highly nonlinear (ε≤0.3) interactions. RIA is based on an analysis of the main resonance domain, which reduces the six‐dimensional integration to a quasi‐line integral to minimize computational time. In terms of computational time, RIA is a thousand times faster than the EXACT‐NL version formulated by Hasselmann and Hasselmann [1981], with similar accuracy. Thus RIA can be considered a candidate for operational forecasting in finite depth water, in the sense that the discrete interaction approximation was presented as a candidate for operational deep water wave forecasting by Hasselmann et al. [1988].