Abstract
Abstract. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2 × 106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height) due to wave–wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell). At longer times, wave–wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar) data. At the same time, the relatively fast weakening of wave–wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.
Highlights
Ocean swell is an important constituent of the field of surface gravity waves in the sea and, more generally, of the sea environment as a whole
Nonlinear wave–wave interactions have been sketched by Snodgrass et al (1966) as a novelty introduced by the milestone papers by Phillips (1960) and Hasselmann (1962)
In this paper we present results of extensive simulations of ocean swell within the Hasselmann equation for deep water waves
Summary
We reproduce previously reported theoretical results on the evolution of swell as a random field of weakly interacting wave harmonics. Simpler and more physically transparent approaches were presented (Zakharov and Pushkarev, 1999; Balk, 2000; Pushkarev et al, 2003, 2004; Badulin et al, 2005a; Zakharov, 2010) These more general approaches allow us to find higher-order terms of the anisotropic Kolmogorov–Zakharov solutions (Eq 6). The principal terms of the general Kolmogorov–Zakharov solutions (Eqs. 4–6) have the clear physical meanings of total fluxes of wave action, Eq (5), energy, Eq (4), and momentum, Eq (6), and do not refer to specific initial conditions. This is not the case for the higherorder terms. The link between these additional terms with inherent properties of the collision integral Snl and/or with specific initial conditions is a subject of further studies
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