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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 1, Pages 171–181
DOI: https://doi.org/10.4213/tmf1843
(Mi tmf1843)
 

This article is cited in 1 scientific paper (total in 1 paper)

Interaction of Vortical and Acoustic Waves: From General Equations to Integrable Cases

A. A. Perelomova, S. B. Leble

Technical University of Gdańsk
Full-text PDF (224 kB) Citations (1)
References:
Abstract: The equations of the $(2+1)$-dimensional boundary-layer perturbation split into eigenmodes: a vortex wave and two acoustic waves. We assume that the equations of state (Taylor series approximation) are arbitrary. We realize a mode definition via local-relation equations extracted from the linearization of the general system over the boundary-layer flow. Each such link determines an invariant subspace and the corresponding projector. We examine the nonlinear equation for a vortex wave using a special orthogonal coordinate system based on streamlines. The equations for the orthogonal curves are linked to the Laplace equations via Laplace and Moutard transformations. The nonlinearity determines the proper form of the interaction between vortical and acoustic boundary-layer perturbation fields fixed by projecting to a subspace of the Orr–Sommerfeld equation solutions for the Tollmienn–Schlichting (linear vortical) wave and by the corresponding procedure for the acoustic wave. We suggest a new mechanism for controlling the nonlinear resonance of the Tollmienn–Schlichting wave by sound via a four-wave interaction.
Keywords: fluid mechanics, boundary layer, projecting to eigenmodes, Tollmienn–Schlichting waves, Laplace transformation, Moutard transformation, acoustic waves, $N$-wave system.
English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 1, Pages 1030–1039
DOI: https://doi.org/10.1007/s11232-005-0131-9
Bibliographic databases:
Language: Russian
Citation: A. A. Perelomova, S. B. Leble, “Interaction of Vortical and Acoustic Waves: From General Equations to Integrable Cases”, TMF, 144:1 (2005), 171–181; Theoret. and Math. Phys., 144:1 (2005), 1030–1039
Citation in format AMSBIB
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\by A.~A.~Perelomova, S.~B.~Leble
\paper Interaction of Vortical and Acoustic Waves: From General Equations to Integrable Cases
\jour TMF
\yr 2005
\vol 144
\issue 1
\pages 171--181
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\crossref{https://doi.org/10.4213/tmf1843}
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\zmath{https://zbmath.org/?q=an:1178.76122}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2005TMP...144.1030P}
\elib{https://elibrary.ru/item.asp?id=17702868}
\transl
\jour Theoret. and Math. Phys.
\yr 2005
\vol 144
\issue 1
\pages 1030--1039
\crossref{https://doi.org/10.1007/s11232-005-0131-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000231408800019}
Linking options:
  • https://www.mathnet.ru/eng/tmf1843
  • https://doi.org/10.4213/tmf1843
  • https://www.mathnet.ru/eng/tmf/v144/i1/p171
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:420
    Full-text PDF :235
    References:72
    First page:1
     
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