Numerical Study on Frequency Downshift of Gravity Wave Spectra in Deep and Intermediate Water Depths Due to Nonlinear Energy Transfer

Abstract

Frequency downshift of gravity wave spectra in deep and finite water depths due to the nonlinear energy transfer are discussed. In deep water depths, numerical computationes of the nonlinera energy transfer are performed with DIA (Hasselmann et al., 1985), RIAM (Komatsu et al., 1993) and SRIAM (Komatsu et al., 1996). Then, differences in temporal changes of directional spectra computed with a modified WAM implemented with RIAM and SRIAM are compared with those computed with the original WAM implemented with DIA. In finite water depth, numerical computations are performed with a modified WAM implemented with FD-RIAM (Hashimoto, et al., 2002), an exact method, which was upgraded from an earlier version (Hashimoto et al., 1998) based on Komatsu et al., (2001). Differeces in frequency downshift of gravity wave spectra in deep and finite water depths are discussed based on the numerial results for various directional spectra in various water depths.

The Propagation of the Waves in the CTO S.A. Towing Tank

“…Other works devoted to gravity waves, like [3] and further [4] and [5], describes and proves that in the wind waves there are nonlinear interactions that cause the nonlinear energy transfer. It occurs in this way that the energy stream Snl is transferred from higher frequency bands to lower frequency bands of the wind wave spectrum.…”

“…In 2014 group of people from Kyushu University (Japan), carried out simulations and study for the method mentioned and for a few others methods of wave model implementation [5].…”

“…These papers ( [3], [4], [5]) describe the physics of the phenomenon and the methods of calculation Snl for wind waves spectra.…”

“…The mathematical model of nonlinear energy transfer proposed in [3] is described by formula (5), where: δSnl relates to the frequency f, δSnl + relates to the frequency (6) and δSnlrelates to the frequency (7). Furthermore, C is the strength of the nonlinear interaction parameter [3] and λ is the Hasselmann's shape parameter [8].…”

Frequency Downshifting in Wave Spectra in Coastal Zone and Its Influence on Mudbank Formation

“…As shown by numerical and laboratory experiments, for steep waves, a cascade frequency downshift is possible, and that occurs at a spatial distance of less than 10 wavelengths. As a result of numerical modeling, it was noted that the downshifting process for waves at deep and intermediate water depths are different [9]. The frequency downshift in wave spectra of shallow water is not observed always and the detailed mechanism is still not known.…”