### Abstract

The purpose of this article is numerical verification of the thory of weak turbulence . We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence . Comparison of the results demonstrates pretty good applicability of the weak turbulent approach. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading as well as formation of Zakharov-Filonenko spectrum I_{ω} ∼ ω^{-4}. To achieve quantitative coincidence of the results obtained by different methods one has to accomplish the Hasselmann kinetic equation by an empirical dissipation term S _{diss} modeling the coherent effects of white-capping. Adding of the standard dissipation terms used in the industrial wave predicting model (WAM) leads to significant improvement but not resolve the discrepancy completely, leaving the question about optimal choice of S_{diss} open. Numerical modeling of swell evolution in the framework of the dynamical equations is affected by the side effect of resonances sparsity taking place due to finite size of the modeling domain. We mostly overcame this effect using fine integration grid of 512 × 4096 modes. The initial spectrum peak was located at the wave number k = 300. Similar conditions can be hardly realized in the laboratory wave tanks. One of the results of our article consists in the fact that physical processes in finite size laboratory wave tanks and in the ocean are quite different, and the results of such laboratory experiments can be applied to modeling of the ocean phenomena with extra care. We also present the estimate on the minimum size of the laboratory installation, allowing to model open ocean surface wave dynamics.

Original language | English (US) |
---|---|

Title of host publication | Tsunami and Nonlinear Waves |

Publisher | springer berlin |

Pages | 135-172 |

Number of pages | 38 |

State | Published - 2007 |

Event | 2006 International Meeting on Tsunami and Nonlinear Waves - Calcutta, India Duration: Mar 6 2006 → Mar 10 2006 |

### Other

Other | 2006 International Meeting on Tsunami and Nonlinear Waves |
---|---|

Country | India |

City | Calcutta |

Period | 3/6/06 → 3/10/06 |

### Fingerprint

### ASJC Scopus subject areas

- Global and Planetary Change
- Environmental Science(all)
- Earth and Planetary Sciences(all)

### Cite this

*Tsunami and Nonlinear Waves*(pp. 135-172). springer berlin.

**Numerical verification of the Hasselmann equation.** / Korotkevich, Alexander O.; Pushkarev, Andrei N.; Resio, Don; Zakharov, Vladimir E.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Tsunami and Nonlinear Waves.*springer berlin, pp. 135-172, 2006 International Meeting on Tsunami and Nonlinear Waves, Calcutta, India, 3/6/06.

}

TY - GEN

T1 - Numerical verification of the Hasselmann equation

AU - Korotkevich, Alexander O.

AU - Pushkarev, Andrei N.

AU - Resio, Don

AU - Zakharov, Vladimir E

PY - 2007

Y1 - 2007

N2 - The purpose of this article is numerical verification of the thory of weak turbulence . We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence . Comparison of the results demonstrates pretty good applicability of the weak turbulent approach. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading as well as formation of Zakharov-Filonenko spectrum Iω ∼ ω-4. To achieve quantitative coincidence of the results obtained by different methods one has to accomplish the Hasselmann kinetic equation by an empirical dissipation term S diss modeling the coherent effects of white-capping. Adding of the standard dissipation terms used in the industrial wave predicting model (WAM) leads to significant improvement but not resolve the discrepancy completely, leaving the question about optimal choice of Sdiss open. Numerical modeling of swell evolution in the framework of the dynamical equations is affected by the side effect of resonances sparsity taking place due to finite size of the modeling domain. We mostly overcame this effect using fine integration grid of 512 × 4096 modes. The initial spectrum peak was located at the wave number k = 300. Similar conditions can be hardly realized in the laboratory wave tanks. One of the results of our article consists in the fact that physical processes in finite size laboratory wave tanks and in the ocean are quite different, and the results of such laboratory experiments can be applied to modeling of the ocean phenomena with extra care. We also present the estimate on the minimum size of the laboratory installation, allowing to model open ocean surface wave dynamics.

AB - The purpose of this article is numerical verification of the thory of weak turbulence . We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence . Comparison of the results demonstrates pretty good applicability of the weak turbulent approach. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading as well as formation of Zakharov-Filonenko spectrum Iω ∼ ω-4. To achieve quantitative coincidence of the results obtained by different methods one has to accomplish the Hasselmann kinetic equation by an empirical dissipation term S diss modeling the coherent effects of white-capping. Adding of the standard dissipation terms used in the industrial wave predicting model (WAM) leads to significant improvement but not resolve the discrepancy completely, leaving the question about optimal choice of Sdiss open. Numerical modeling of swell evolution in the framework of the dynamical equations is affected by the side effect of resonances sparsity taking place due to finite size of the modeling domain. We mostly overcame this effect using fine integration grid of 512 × 4096 modes. The initial spectrum peak was located at the wave number k = 300. Similar conditions can be hardly realized in the laboratory wave tanks. One of the results of our article consists in the fact that physical processes in finite size laboratory wave tanks and in the ocean are quite different, and the results of such laboratory experiments can be applied to modeling of the ocean phenomena with extra care. We also present the estimate on the minimum size of the laboratory installation, allowing to model open ocean surface wave dynamics.

UR - http://www.scopus.com/inward/record.url?scp=84892275510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892275510&partnerID=8YFLogxK

M3 - Conference contribution

SP - 135

EP - 172

BT - Tsunami and Nonlinear Waves

PB - springer berlin

ER -