TY - JOUR
T1 - Ocean swell within the kinetic equation for water waves
AU - Badulin, Sergei I.
AU - Zakharov, Vladimir E.
N1 - Funding Information:
The authors are thankful for the support of Russian Science Foundation grant no. 14-22-00174. The authors are indebted to Victor Shrira and Vladimir Geogjaev for discussions and valuable comments. The authors are also grateful to Andrei Pushkarev for his assistance in simulations. The authors appreciate critical consideration of the paper by reviewers Gerbrant van Vledder and Sergei Annenkov. Their constructive feedback led to substantial revision of Sects. 3 and 4.
Publisher Copyright:
© 2017 Author(s).
PY - 2017/6/6
Y1 - 2017/6/6
N2 - 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.
AB - 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.
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U2 - 10.5194/npg-24-237-2017
DO - 10.5194/npg-24-237-2017
M3 - Article
AN - SCOPUS:85020299366
SN - 1023-5809
VL - 24
SP - 237
EP - 253
JO - Nonlinear Processes in Geophysics
JF - Nonlinear Processes in Geophysics
IS - 2
ER -