Ocean swell within the kinetic equation for water waves

Badulin, Sergei I.; Захаров, В. Е.

doi:10.5194/npg-24-237-2017

Cited by 20 publications

(21 citation statements)

References 52 publications

(102 reference statements)

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“…Substituting parameters derived from fetch laws (Equation 15), the so-called "magic" universal relationship between fetch law exponents is recovered (Badulin & Zakharov, 2017;Zakharov, 2010):…”

Section: Effect Of Non-linear Interactionsmentioning

confidence: 99%

2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

2021

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An efficient and ready-to-use statistical description of the surface gravity wavefield, especially its directional energy characteristics, is often needed for many engineering and scientific applications, in particular, for short-term forecasting of surface waves generated by Tropical Cyclones (TC). Full sophisticated spectral wave models certainly have the capability to provide detailed wave information. Moon et al., (2003) performed a comprehensive investigation of wind wavefield generated by TC Bonnie using WAVEWATCH III model (Tolman, 2009), buoy and aircraft Scanning Radar Altimeter (SRA) measurements. This study clearly demonstrated that using realistic wind forcing, the use of a high-resolution WAVEWATCH III model may yield successful simulations of surface wave fields in hurricane conditions. Yet, computer limitations and/or needs to consider ensembles of solutions also invite to develop more simplified solutions. For instance, practical models can help to rapidly anticipate and document the role of partial resonance effects to increase the effective fetch and duration of the wave-growth process in the main direction of the tropical and extra-tropical weather systems, that is, the wave trapping phe-

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Section: Effect Of Non-linear Interactionsmentioning

confidence: 99%

2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

2021

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“…Now we discuss the self‐similar solutions of the stationary inhomogeneous WKE, that is, the fetch‐limited scenario of wave evolution

\frac{2 g}{ω} \cos θ \frac{\partial ε}{\partial x} = S_{nl} .

The self‐similar solution has the following form

ε (ω, θ, t) = B^{5} x^{p + q} G (ζ, θ); ζ = B ω x^{q},

where p and q are connected by the magic relation

10 q = 2 p + 1 .

The function G satisfies the equation

\frac{2}{ζ} [(5 q - \frac{1}{2}) F + q ζ \frac{\partial F}{\partial ζ}] = S_{nl} .

Self‐similar solution exists for any q ≥ 1/12. The marginal case q = 1/12 describes a stationary inhomogeneous swell (Badulin & Zakharov, ). Energy in this case decays as t −1/12 .…”

Section: Self‐similar Solutions Of Wkementioning

confidence: 99%

“…In the next series of numeric experiments, we have studied the evolution of anisotropic swell (Badulin & Zakharov, ). As it was expected, we observed the formation of the self‐similar solution with the Zakharov and Filonenko () asymptotics.…”

Section: Numerical Modeling Of Swellmentioning

confidence: 99%

“…This self-similar solution describes the evolution of the swell. This was studied in detail by Badulin and Zakharov (2017). As far as Q = 0, this solution is described by the KZ spectrum (20).…”

Section: Let Us Definementioning

confidence: 99%

“…Self-similar solution exists for any q ≥ 1∕12. The marginal case q = 1∕12 describes a stationary inhomogeneous swell (Badulin & Zakharov, 2017). Energy in this case decays as t −1/12 .…”

Section: 1029/2018ea000471mentioning

confidence: 99%

See 2 more Smart Citations

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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