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TMF, 2010, Volume 165, Number 2, Pages 350–369 (Mi tmf6582)  

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

Large-scale structures as gradient lines: The case of the Trkal flow

A. S. Libin


Abstract: Based on expansion terms of the Beltrami-flow type, we use multiscale methods to effectively construct an asymptotic expansion at large Reynolds numbers $R$ for the long-wavelength perturbation of the nonstationary anisotropic helical solution of the force-free Navier–Stokes equation (the Trkal solution). We prove that the systematic asymptotic procedure can be implemented only in the case where the scaling parameter is $R^{1/2}$. Projections of quasistationary large-scale streamlines on a plane orthogonal to the anisotropy direction turn out to be the gradient lines of the energy density determined by the initial conditions for two modulated anisotropic Beltrami flows (modulated as a result of scaling) with the same eigenvalues of the curl operator. The three-dimensional streamlines and the curl lines, not coinciding, fill invariant vorticity tubes inside which the velocity and vorticity vectors are collinear up to terms of the order of $1/R$.

Keywords: large-scale structure, Navier–Stokes equation, Beltrami flow, Trkal solution, tube of velocities, vorticity tube, gradient line

DOI: https://doi.org/10.4213/tmf6582

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English version:
Theoretical and Mathematical Physics, 2010, 165:2, 1534–1551

Bibliographic databases:

Document Type: Article
Received: 22.01.2010
Revised: 16.04.2010

Citation: A. S. Libin, “Large-scale structures as gradient lines: The case of the Trkal flow”, TMF, 165:2 (2010), 350–369; Theoret. and Math. Phys., 165:2 (2010), 1534–1551

Citation in format AMSBIB
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\by A.~S.~Libin
\paper Large-scale structures as gradient lines: The~case of the~Trkal flow
\jour TMF
\yr 2010
\vol 165
\issue 2
\pages 350--369
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\transl
\jour Theoret. and Math. Phys.
\yr 2010
\vol 165
\issue 2
\pages 1534--1551
\crossref{https://doi.org/10.1007/s11232-010-0128-x}
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  • https://doi.org/10.4213/tmf6582
  • http://mi.mathnet.ru/eng/tmf/v165/i2/p350

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    Citing articles on Google Scholar: Russian citations, English citations
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    Errata

    This publication is cited in the following articles:
    1. Libin A., “Scale-invariant streamline equations and strings of singular vorticity for perturbed anisotropic solutions of the Navier–Stokes equation”, J. Exp. Theor. Phys., 115:6 (2012), 1128–1139  crossref  adsnasa  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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