The kinetic equation solutions and Kolmogorov spectra
The Hasselmann kinetic equation (KE) for stochastic nonlinear surface waves is studied numerically with the aim of searching for features of the Kolmogorov turbulence (KT). To this aim, solutions of the KE for the long-term wave-spectrum evolution are executed. As far as the total wave action N and...
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| creator | Polnikov, V G Qiao, F |
| description | The Hasselmann kinetic equation (KE) for stochastic nonlinear surface waves is studied numerically with the aim of searching for features of the Kolmogorov turbulence (KT). To this aim, solutions of the KE for the long-term wave-spectrum evolution are executed. As far as the total wave action N and wave energy E are not preserved simultaneously in the course of the KE solution, two versions of the numerical algorithm are used, preserving values of N or E in separate. In every case, the KE solutions result in formation of the self-similar spectrum shape, Ssf(ω), with the frequency tail Ssf(ω) ∼ ω-4, independently of the N- or E-fluxes generated by the nonlinear interactions. This urges us to state that the used KE does not obey to regulations of the KT. The reason of this fact resides in the mathematical feature of the kinetic integral, which, in any case of solving the KE, results in formation of the nonlinear energy-transfer tail of kind Nl(ω) ∼ - ω-4, what stabilizes the spectral tail in form SSf(ω) ∼ ω-4. |
| doi_str_mv | 10.1088/1755-1315/231/1/012043 |
| format | Article |
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To this aim, solutions of the KE for the long-term wave-spectrum evolution are executed. As far as the total wave action N and wave energy E are not preserved simultaneously in the course of the KE solution, two versions of the numerical algorithm are used, preserving values of N or E in separate. In every case, the KE solutions result in formation of the self-similar spectrum shape, Ssf(ω), with the frequency tail Ssf(ω) ∼ ω-4, independently of the N- or E-fluxes generated by the nonlinear interactions. This urges us to state that the used KE does not obey to regulations of the KT. The reason of this fact resides in the mathematical feature of the kinetic integral, which, in any case of solving the KE, results in formation of the nonlinear energy-transfer tail of kind Nl(ω) ∼ - ω-4, what stabilizes the spectral tail in form SSf(ω) ∼ ω-4.</description><identifier>ISSN: 1755-1307</identifier><identifier>ISSN: 1755-1315</identifier><identifier>EISSN: 1755-1315</identifier><identifier>DOI: 10.1088/1755-1315/231/1/012043</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Algorithms ; Fluxes ; Kinetic equations ; Numerical analysis ; Self-similarity ; Surface waves ; Tails ; Wave action ; Wave energy ; Wave power</subject><ispartof>IOP conference series. Earth and environmental science, 2019-02, Vol.231 (1), p.12043</ispartof><rights>Published under licence by IOP Publishing Ltd</rights><rights>2019. This work is published under http://creativecommons.org/licenses/by/3.0/ (the “License”). 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The reason of this fact resides in the mathematical feature of the kinetic integral, which, in any case of solving the KE, results in formation of the nonlinear energy-transfer tail of kind Nl(ω) ∼ - ω-4, what stabilizes the spectral tail in form SSf(ω) ∼ ω-4.</description><subject>Algorithms</subject><subject>Fluxes</subject><subject>Kinetic equations</subject><subject>Numerical analysis</subject><subject>Self-similarity</subject><subject>Surface waves</subject><subject>Tails</subject><subject>Wave action</subject><subject>Wave energy</subject><subject>Wave power</subject><issn>1755-1307</issn><issn>1755-1315</issn><issn>1755-1315</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><sourceid>BENPR</sourceid><recordid>eNqFkE9Lw0AQxRdRsFa_ggS8eImZ_ZvkKKVWseDBel42uxtNTbPpbiL47U2IVATB0zyY93vDPIQuMdxgyLIEp5zHmGKeEIoTnAAmwOgRmh0WxwcN6Sk6C2ELIFJG8xnimzcbvVeN7Sod2X2vuso1UXB1P4oQqcZEj67euVfn3UcUWqs7r87RSanqYC--5xy93C03i_t4_bR6WNyuY80g7WKTYQYiS7mmORRaGUFwIbjmKadGZMwQIAVQLjQlRBUCyoJyIgpRUgOEETpHV1Nu692-t6GTW9f7ZjgpCR9SCMvyfHCJyaW9C8HbUra-2in_KTHIsSI5fi_HJuRQkcRyqmgAyQRWrv1J_he6_gNaLp9_2WRrSvoFHL5zFQ</recordid><startdate>20190212</startdate><enddate>20190212</enddate><creator>Polnikov, V G</creator><creator>Qiao, F</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>PATMY</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PYCSY</scope></search><sort><creationdate>20190212</creationdate><title>The kinetic equation solutions and Kolmogorov spectra</title><author>Polnikov, V G ; Qiao, F</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c407t-d81406875c390bcad621b65c5753d684d202b0356c322ab60fb3526b6f3d02423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Fluxes</topic><topic>Kinetic equations</topic><topic>Numerical analysis</topic><topic>Self-similarity</topic><topic>Surface waves</topic><topic>Tails</topic><topic>Wave action</topic><topic>Wave energy</topic><topic>Wave power</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Polnikov, V G</creatorcontrib><creatorcontrib>Qiao, F</creatorcontrib><collection>Institute of Physics Open Access Journal Titles</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>Environmental Science Database</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Environmental Science Collection</collection><jtitle>IOP conference series. Earth and environmental science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Polnikov, V G</au><au>Qiao, F</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The kinetic equation solutions and Kolmogorov spectra</atitle><jtitle>IOP conference series. Earth and environmental science</jtitle><addtitle>IOP Conf. Ser.: Earth Environ. Sci</addtitle><date>2019-02-12</date><risdate>2019</risdate><volume>231</volume><issue>1</issue><spage>12043</spage><pages>12043-</pages><issn>1755-1307</issn><issn>1755-1315</issn><eissn>1755-1315</eissn><abstract>The Hasselmann kinetic equation (KE) for stochastic nonlinear surface waves is studied numerically with the aim of searching for features of the Kolmogorov turbulence (KT). To this aim, solutions of the KE for the long-term wave-spectrum evolution are executed. As far as the total wave action N and wave energy E are not preserved simultaneously in the course of the KE solution, two versions of the numerical algorithm are used, preserving values of N or E in separate. In every case, the KE solutions result in formation of the self-similar spectrum shape, Ssf(ω), with the frequency tail Ssf(ω) ∼ ω-4, independently of the N- or E-fluxes generated by the nonlinear interactions. This urges us to state that the used KE does not obey to regulations of the KT. The reason of this fact resides in the mathematical feature of the kinetic integral, which, in any case of solving the KE, results in formation of the nonlinear energy-transfer tail of kind Nl(ω) ∼ - ω-4, what stabilizes the spectral tail in form SSf(ω) ∼ ω-4.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1755-1315/231/1/012043</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms Fluxes Kinetic equations Numerical analysis Self-similarity Surface waves Tails Wave action Wave energy Wave power |
| title | The kinetic equation solutions and Kolmogorov spectra |
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