Articles | Volume 24, issue 2
Nonlin. Processes Geophys., 24, 237–253, 2017
Nonlin. Processes Geophys., 24, 237–253, 2017

Research article 06 Jun 2017

Research article | 06 Jun 2017

Ocean swell within the kinetic equation for water waves

Sergei I. Badulin1,2 and Vladimir E. Zakharov1,2,3,4,5 Sergei I. Badulin and Vladimir E. Zakharov
  • 1P. P. Shirshov Institute of Oceanology of the Russian Academy of Sciences, Moscow, Russia
  • 2Laboratory of Nonlinear Wave Processes, Novosibirsk State University, Novosibirsk, Russia
  • 3Department of Mathematics, University of Arizona, Tucson, USA
  • 4P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
  • 5Waves and Solitons LLC, Phoenix, Arizona, USA

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.

Short summary
In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.