Calculation of the nonlinear energy transfer through the wave spectrum at the sea surface covered with broken ice

Polnikov, V. G.; Lavrenov, Igor V.

doi:10.1134/s0001437007030058

Cited by 22 publications

(41 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here it should be noted that the most important part of the KI-calculation algorithm is the method of estimating the contribution of integrable singularities in the integrand (the contribution of 'singular points'), resulting from integration of the frequency delta-function (Masuda 1980;Polnikov 1989). The different 25 approaches to this point represent the main differences in the algorithms mentioned (e.g., Masuda, 1980;Van Vledder, 2006;Polnikov, 1989;Lavrenov, 2003). Herewith, Polnikov (1989) have showed numerically that the contribution of the singular points determines crucially the conservation balance for the integral values E, N, M (Eqs,(3)(4)(5), and the accuracy of the KIestimate as a whole.…”

Section: N ( S( ) / )D Dmentioning

confidence: 99%

“…It is used by these authors and the Zakharov's group. The second one elaborated by Polnikov (1989), Lavrenov (2003), Komatsu and Masuda (1996), Gagnaire-Renou, et al, (2010), who use it. Evaluation of these methods was done in (Benoit, 2005).…”

Section: N ( S( ) / )D Dmentioning

confidence: 99%

“…Soon, Zakharov (1966) rederived KE (1) using the technique of the Hamiltonian formalism (see also, Zakharov et al 1992;Badulin et al, 2005). Since late 60s, the KE became a separate subject of studying (e.g., Zakharov and 20 Filonenko, 1966;Zakharov and Zaslavskii, 1982;Webb, 1978;Masuda, 1980;Hasselmann and Hasselmann, 1981;Hasselmann et al, 1985;Polnikov, 1989Polnikov, , 1990Polnikov, , 1996Polnikov, , 2007Resio and Perrie, 1991;Pushkarev et al, 2003;Badulin et al, 2005;Young and Van Vledder, 2003;Van Vledder, 2006;Badulin and Zakharov (2017); Geodjaev and Zakharov 2017;Zakhariov, 2017, and references therein). Among them, analytical results found by Zakharov and co-authors (see below) play the crucial role in these investigations.…”

Section: N ( S( ) / )D Dmentioning

confidence: 99%

“…The different 25 approaches to this point represent the main differences in the algorithms mentioned (e.g., Masuda, 1980;Van Vledder, 2006;Polnikov, 1989;Lavrenov, 2003). Herewith, Polnikov (1989) have showed numerically that the contribution of the singular points determines crucially the conservation balance for the integral values E, N, M (Eqs,(3)(4)(5), and the accuracy of the KIestimate as a whole.…”

Section: N ( S( ) / )D Dmentioning

confidence: 99%

“…It was expanded by 30 Polnikov (1989) via introducing classification for the two-dimensional spectral shapes, S( , )  . After that, Polnikov (1990) has performed a numerical solution of KE (1), where it was shown the fact of establishing the self-similar shape of wave (ω,θ), in the course of long-term evolution of nonlinear waves.…”

Section: N ( S( ) / )D Dmentioning

confidence: 99%

See 4 more Smart Citations

Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

Polnikov

Teng

2018

Preprint

View full text Add to dashboard Cite

Abstract. The kinetic equation for a gravity wave spectrum is solved numerically to study the high frequencies asymptotes 10 for the one-dimensional nonlinear energy transfer and the variability of spectrum parameters that accompany the long-term evolution of nonlinear waves. The cases of initial two-dimensional spectra S(ω,θ) of modified JONSWAP type with the frequency decay-law S(ω) ~ ω -n (for n = 6, 5, 4 and 3.5) and various initial functions of the angular distribution are considered. It is shown that at the first step of the kinetic equation solution, the nonlinear energy transfer asymptote has the power-like decay-law, Nl(ω) ~ ω -p , with values p ≤ n-1, valid in cases when n ≥ 5, and the difference, n-p, changes 15 significantly when n approaches 4. On time scales of evolution greater than several thousands of initial wave periods, in every case, a self-similar spectrum S sf (ω,θ) is established with the frequency decay-law of form S(ω) ~ ω -4 . Herein, the asymptote of nonlinear energy transfer becomes negative in value and decreases according to the same law (i.e., Nl(ω)~-ω -4 ).The peak frequency of the spectrum, ω p (t), migrates in time t to the low-frequency region such that the angular and frequency characteristics of the two-dimensional spectrum S sf (ω,θ) remain constant. However, these characteristics depend 20 on the degree of angular anisotropy of the initial spectrum. The solutions obtained are interpreted, and their connection with the analytical solutions of the kinetic equation by Zakharov and co-authors for gravity waves in water is discussed.

show abstract

Section: N ( S( ) / )D Dmentioning

confidence: 99%

Section: N ( S( ) / )D Dmentioning

confidence: 99%

Section: N ( S( ) / )D Dmentioning

confidence: 99%

Section: N ( S( ) / )D Dmentioning

confidence: 99%

Section: N ( S( ) / )D Dmentioning

confidence: 99%

See 3 more Smart Citations

Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

Polnikov

Teng

2018

Preprint

View full text Add to dashboard Cite

show abstract

Observations of surface waves interacting with ice using stereo imaging

Campbell

Bechle

2014

JGR Oceans

View full text Add to dashboard Cite

A powerful Automated Trinocular Stereo Imaging System (ATSIS) is used to remotely measure waves interacting with three distinct ice types: brash, frazil, and pancake. ATSIS is improved with a phaseonly correlation matching algorithm and parallel computation to provide high spatial and temporal resolution 3-D profiles of the water/ice surface, from which the wavelength, frequency, and energy flux are calculated. Alongshore spatial frequency distributions show that pancake and frazil ices differentially attenuate at a greater rate for higher-frequency waves, causing a decrease in mean frequency. In contrast, wave propagation through brash ice causes a rapid increase in the dominant wave frequency, which may be caused by nonlinear energy transfer to higher frequencies due to collisions between the brash ice particles. Consistent to the results in frequency, the wavelengths in pancake and frazil ices increase but decrease in brash ice. The total wave energy fluxes decrease exponentially in both pancake and frazil ice, whereas the overall energy flux remain constant in the brash ice due to thin layer thickness. The spatial energy flux distributions also reveal that wave reflection occurs at the boundary of each ice layer, with reflection coefficient decaying exponentially away from the ice interface. Reflection is the strongest at the pancake/ice-free and frazil/brash interfaces and the weakest at the brash/ice-free interface. These high resolution observations measured by ATSIS demonstrate the spatially variable nature of waves propagating through ice.

show abstract

Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea

Rogers

Thomson

Shen

et al. 2016

J. Geophys. Res. Oceans

115

159

View full text Add to dashboard Cite

A model for wind‐generated surface gravity waves, WAVEWATCH III®, is used to analyze and interpret buoy measurements of wave spectra. The model is applied to a hindcast of a wave event in sea ice in the western Arctic, 11–14 October 2015, for which extensive buoy and ship‐borne measurements were made during a research cruise. The model, which uses a viscoelastic parameterization to represent the impact of sea ice on the waves, is found to have good skill—after calibration of the effective viscosity—for prediction of total energy, but over‐predicts dissipation of high frequency energy by the sea ice. This shortcoming motivates detailed analysis of the apparent dissipation rate. A new inversion method is applied to yield, for each buoy spectrum, the inferred dissipation rate as a function of wave frequency. For 102 of the measured wave spectra, visual observations of the sea ice were available from buoy‐mounted cameras, and ice categories (primarily for varying forms of pancake and frazil ice) are assigned to each based on the photographs. When comparing the inversion‐derived dissipation profiles against the independently derived ice categories, there is remarkable correspondence, with clear sorting of dissipation profiles into groups of similar ice type. These profiles are largely monotonic: they do not exhibit the “roll‐over” that has been found at high frequencies in some previous observational studies.

show abstract

Calculation of the nonlinear energy transfer through the wave spectrum at the sea surface covered with broken ice

Cited by 22 publications

References 5 publications

Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

Observations of surface waves interacting with ice using stereo imaging

Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea

Contact Info

Product

Resources

About