Wave-wave interactions in finite depth water

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 (e≤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].