Powerlike-cosine Additions to Zakharov–Filonenko Spectrum

Abstract

Self-similar spectra for deep water surface waves are an object of both theoretical interest and practical value. The well-known Zakharov–Filonenko spectrum adequately describes natural wave spectra but misses the anisotropy inherent to them. This was amended by the Kats–Kontorovich spectrum via a small cosine addition. We perform a general study of powerlike-cosine anisotropic additions to the Zakharov–Filonenko spectrum with different angular harmonics. We find some new anisotropic approximate solutions. We calculate numerically the Kolmogorov constant for the momentum transfer by Kats–Kontorovich spectrum.