Geodesic
Large-scale structures as gradient lines: The case of the Trkal flow
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 350-369 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $1/R$.
Mots-clés : large-scale structure, Trkal solution, gradient line.
Keywords: Navier–Stokes equation, Beltrami flow, tube of velocities, vorticity tube 
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     title = {Large-scale structures as gradient lines: {The~case} of {the~Trkal} flow},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a11/}
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A. S. Libin. Large-scale structures as gradient lines: The case of the Trkal flow. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 350-369. http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a11/

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