Evolution of one-dimensional wind-driven sea spectra

Dyachenko, Alexander; Kachulin, Dmitry; Захаров, В. Е.

doi:10.1134/s0021364015200035

Cited by 9 publications

(8 citation statements)

References 14 publications

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“…Preliminary results of this paper were published in [10]. Recently another numerical experiment using significantly simplified version of dynamical equations was published in [11]. Its results although based on different model, completely confirmed the results of the present paper as well as our main conclusion: dissipation functions used in operational models overestimate contribution of white capping to waves energy absorption and must be reexamined.…”

Section: Introductionsupporting

confidence: 86%

“…Widely used wave forecasting models WAM3 and WAM4 utilize the following dissipation functions depend-ing on wave number k: (11) where k and ω are the wave number and frequency, tilde denotes mean value; C ds , δ and p are tunable coefficients; S = k p σ is the "oceanographic" steepness; S P M = (3.02 × 10 −3 ) 1/2 is the value ofS for the Pierson-Moscowitz spectrum. The values of the tunable coefficients for the WAM3 case are: C ds = 2.35 × 10 −5 , δ = 0, p = 4 (12) and for the WAM4 case are:…”

Section: Comparison With Wave Forecasting Modelsmentioning

confidence: 99%

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On the Dissipation Rate of Ocean Waves due to White Capping

2019

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We calculate the rate of ocean waves energy dissipation due to whitecapping 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 for moderate values of surface steepness only, µ < 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 steepness. The results of both experiments are close. The whitecapping is the threshold process that takes place if the average steepness µ > µcr ≃ 0.055. The rate of energy dissipation grows dramatically with increasing of 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 steepness.

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Section: Introductionsupporting

confidence: 86%

Section: Comparison With Wave Forecasting Modelsmentioning

confidence: 99%

On the Dissipation Rate of Ocean Waves due to White Capping

2019

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“…It is a purely artificial construction, based on strong belief that the evolution of any wind‐forced spectrum must end up by the formation of the “fully developed sea.” This concept looked obvious back in 1984 (Komen et al, ) and now, likely, requires substantial revision. Phase‐resolving numerical modeling of JONSWAP spectrum evolution (e.g., Dyachenko et al, ; Korotkevich et al, ) found that the term can overestimate the dissipation due to the wave breaking by the order of magnitude. Summarizing, we conclude that the instability, driven by the wind input, is arrested not by white capping but by the resonant nonlinear interactions.…”

Section: Numerical Simulation Of Wind‐driven Wavesmentioning

confidence: 99%

Weak‐Turbulent Theory of Wind‐Driven Sea

Захаров

Badulin

Geogjaev

et al. 2019

Earth and Space Science

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We present a self‐consistent analytic theory of the wind‐driven sea—the weak‐turbulent theory. The base statement of the theory is that the four‐wave resonant interactions play the leading role in the energy balance of the wind‐driven sea. We study the exact solution of the stationary wave kinetic equation and the self‐similar solutions of wave kinetic equation both in fetch‐ and duration‐limited cases. The theory makes possible to explain the nature of universal power‐like energy spectra as well as the power‐like dependence of the total wave energy and peak frequency from the fetch and the duration.

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“…It is important that direct numerical solutions of both exact [88] and approximate [89] primordial Euler equations show that dissipation of the rogue waves does not make any significant contribution into energy balance of wind-driven seas. Thus, the main conclusion about the dissipation taking place in short scales remains unchanged.…”

Section: Current State Of Wind Input Source Termsmentioning

confidence: 99%

Limited fetch revisited: Comparison of wind input terms, in surface wave modeling

Pushkarev

Захаров

2016

Ocean Modelling

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Results pertaining to numerical solutions of the Hasselmann kinetic equation (HE), for wind driven sea spectra, in the fetch limited geometry, are presented. Five versions of source functions, including the recently introduced ZRP model [1], have been studied, for the exact expression of S nl and high-frequency implicit dissipation, due to wave-breaking. Four of the five experiments were done in the absence of spectral peak dissipation for various S in terms. They demonstrated the dominance of quadruplet wave-wave interaction, in the energy balance, and the formation of self-similar regimes, of unlimited wave energy growth, along the fetch. Between them was the ZRP model, which strongly agreed with dozens of field observations performed in the seas and lakes, since 1947. The fifth, the W AM 3 wind input term experiment, used additional spectral peak dissipation and reproduced the results of a previous, similar, numerical simulation described in [2], but only supported the field experiments for moderate fetches, demonstrating a total energy saturation at half of that of the Pierson-Moscowits limit. The alternative framework for HE numerical simulation is proposed, along with a set of tests, allowing one to select physically-justified source terms.

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Evolution of one-dimensional wind-driven sea spectra

Cited by 9 publications

References 14 publications

On the Dissipation Rate of Ocean Waves due to White Capping

On the Dissipation Rate of Ocean Waves due to White Capping

Weak‐Turbulent Theory of Wind‐Driven Sea

Limited fetch revisited: Comparison of wind input terms, in surface wave modeling

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