Comments on “A New Coastal Wave Model. Part V: Five-Wave Interactions”

Abstract

Recent calculations by Lin and Perrie (1997) on the surface wave spectral energy fluxes due to the wave nonlinearity in deep and shallow water appeared after previously published works by Krasitski (1993), Shrira et al. (1996), and Kalmykov (1993, 1995, 1997), while presenting results that are qualitatively different from those obtained previously. This comment is on these obvious differences and why it appears that the conclusions of Lin and Perrie cannot be justified. Surface waves in deep water as well as in shallow water are very well described by the four-wave kinetic equation as shown by Hasselmann and Hasselmann (1985) and Herterich and Hasselmann (1980). Analogous computation of the five-wave kinetic equation for deep and shallow water show that a five-wave contribution is very small: only 3%–5% of the fourwave one (Kalmykov 1998). Therefore we can conclude that the four-wave kinetic equation still remains dominant for the shallow and deep water wave modeling and that all this discussion is of only academical interest. During the past 15 years many studies have been made in this area, some of which are not cited by Lin and Perrie (1997), including Parts I and II of the series leading to the present article under discussion (Part III). They present results of their own calculations of the spectral transfer rates in a JONSWAP spectrum, which are qualitatively different from various previously published results, while offering no explanation for the differences found. The subject of five wave–wave interactions among surface gravity waves is not new. First discussions concerning the energy transfer by five-wave interactions in wave spectra took place at Zakharov’s seminar in 1993 in Moscow, where the present author made a report (Kalmykov 1993). In experiments, it was first