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Pis'ma v Zh. Èksper. Teoret. Fiz., 2019, Volume 109, Issue 5, Pages 312–319 (Mi jetpl5839)  

PLASMA, HYDRO- AND GAS DYNAMICS

On the dissipation rate of ocean waves due to white capping

A. O. Korotkevichab, A. O. Prokofievb, V. E. Zakharovbc

a Department of Mathematics and Statistics, MSC01 1115, 1 University of New Mexico, Albuquerque, USA
b Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia
c Department of Mathematics, The University of Arizona, Tucson, USA

Abstract: We calculate the rate of ocean wave energy dissipation due to white capping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve the 3D Hamiltonian equation that includes three- and four-wave interactions. This model is valid only for moderate values of the surface steepness, $\mu < 0.09$. Then we solve the exact Euler equation for non-stationary potential flow of an ideal fluid with a free surface in 2D geometry. We use the conformal mapping of domain filled with fluid onto the lower half-plane. This model is applicable for arbitrary high levels of the steepness. The results of both experiments are close. The white capping is the threshold process that takes place if the average steepness $\mu > \mu_{\mathrm{cr}}\simeq 0.055$. The rate of energy dissipation grows dramatically with increasing steepness. Comparison of our results with dissipation functions used in the operational models of wave forecasting shows that these models overestimate the rate of wave dissipation by order of magnitude for typical values of the steepness.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0033-2018-0014
National Science Foundation OCE 1131791
Ministry of Education and Science of the Russian Federation -9697.2016.2


DOI: https://doi.org/10.1134/S0370274X19050060

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English version:
Journal of Experimental and Theoretical Physics Letters, 2019, 109:5, 309–315

Received: 13.12.2018
Revised: 13.12.2018
Accepted:27.12.2018

Citation: A. O. Korotkevich, A. O. Prokofiev, V. E. Zakharov, “On the dissipation rate of ocean waves due to white capping”, Pis'ma v Zh. Èksper. Teoret. Fiz., 109:5 (2019), 312–319; JETP Letters, 109:5 (2019), 309–315

Citation in format AMSBIB
\Bibitem{KorProZak19}
\by A.~O.~Korotkevich, A.~O.~Prokofiev, V.~E.~Zakharov
\paper On the dissipation rate of ocean waves due to white capping
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2019
\vol 109
\issue 5
\pages 312--319
\mathnet{http://mi.mathnet.ru/jetpl5839}
\crossref{https://doi.org/10.1134/S0370274X19050060}
\elib{http://elibrary.ru/item.asp?id=37090926}
\transl
\jour JETP Letters
\yr 2019
\vol 109
\issue 5
\pages 309--315
\crossref{https://doi.org/10.1134/S0021364019050035}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062638479}


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