Numerical modeling of the constant flux spectra for surface gravity waves in a case of angular anisotropy

The process of constant flux spectra formation is studied numerically, for the case of angular anisotropy. The method of investigation is based on a n umerical solution of the nonlinear four-wave kinetic equation for gravity w aves, added with the terms of a source and a sink for wave energy. Stationa ry solutions of such an equation are just the constant flux spectra under i nvestigation. Two principally different situations were considered: the case of a constan t energy flux to the high frequencies (the case of "flux up") and the case of a constant wave action flux to the low frequencies (the case of "flux do wn"). It was found that, for the case of flux down, the stationary two-dime nsional spectra are angularly isotropic, independently of the initial aniso tropy of the system. But for the case of flux up, the stationary spectra ha ve specific angular anisotropy. For both cases, corresponding one-dimension al spectra have shapes close to ones analytically derived in [Dokl. Akad. N auk SSSR, 170(1996) 1292-1295 (in Russian); Izv. Akad. S. USSR, Atmos. Ocea n Phys. 18 (1982) 970-979], for the case of angular isotropy. Numerous feat ures of the process considered are specified, and the mentioned peculiariti es of the results are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.