Wave-wave interactions in finite depth water

In this study we present a new formulation for the nonlinear wave-wave inte raction source function in finite water depth. The formulation, denoted the reduced integration approximation (RIA), is shown to compare well with pub lished formulations, both for shallow water wave-wave interactions [Herteri ch and Hasselmann, 1980; Polnikov, 1997; Hashimoto et al., 1998; A. Masuda and K. Komatsu, manuscript in preparation, 1998] and also for the asymptoti c deep water limit: (1) the Hamiltonian formulation proposed by Lin and Per ie [1997], by (2) Hasselmann and Hasselmann [1981], and (3) the line integr al transformation of Web [1978] and Resio and Perrie [1991]. Of these deep water formulations, that of Lin-Perrie generalizing the Hamiltonian represe ntation of Zakharov [1968] to finite depth water, is notable for its simpli city, efficiency and its ability to apply to very shallow water (kh approxi mate to 0.3), and highly nonlinear (epsilon less than or equal to 0.3) inte ractions. RIA is based on an analysis of the main resonance domain, which r educes the six-dimensional integration to a quasi-line integral to minimize computational time. In terms of computational time, RIA is a thousand time s faster than the EXACT-NL version formulated by Hasselmann and Hasselmann [1981], with similar accuracy. Thus RIA can be considered a candidate for o perational forecasting in finite depth water, in the sense that the discret e interaction approximation was presented as a candidate for operational de ep water wave forecasting by Hasselmann et al. [1988].