Wave‐wave interactions in finite depth water

Abstract

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].