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Titolo:
Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations
Autore:
Gibbon, JD; Fokas, AS; Doering, CR;
Indirizzi:
Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England Univ London Imperial Coll Sci Technol & Med London England SW7 2BZ gland Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA Univ Michigan Ann ArborMI USA 48109 , Dept Math, Ann Arbor, MI 48109 USA
Titolo Testata:
PHYSICA D
fascicolo: 4, volume: 132, anno: 1999,
pagine: 497 - 510
SICI:
0167-2789(19990820)132:4<497:DSVASO>2.0.ZU;2-G
Fonte:
ISI
Lingua:
ENG
Soggetto:
TURBULENCE; VORTEX; FLOW; STATISTICS; ALIGNMENT; EULER;
Keywords:
stretched vortices; burgers vortices; Lundgren's transformation; vortex tubes; passive scalar;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
33
Recensione:
Indirizzi per estratti:
Indirizzo: Gibbon, JD Univ London Imperial Coll Sci Technol & Med, Dept Math, Huxley Bldg, London SW7 2BZ, England Univ London Imperial Coll Sci Technol & Med Huxley Bldg London England SW7 2BZ
Citazione:
J.D. Gibbon et al., "Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations", PHYSICA D, 132(4), 1999, pp. 497-510

Abstract

A well known limitation with stretched vortex solutions of the 3D Navier-Stokes (and Euler) equations, such as those of Burgers type, is that they possess uni-directional vorticity which is stretched by a strain field that is decoupled from them. It is shown here that these drawbacks can be partially circumvented by considering a class of velocity fields of the type u = (u(1)(x, y, t), u(2)(x, y, t), gamma(x, y, t)z + W(x, y, t)) where u(1), u(2), y and W are functions of x, y and t but not z. It turns out that the equations for the third component of vorticity omega(3) and W decouple. More specifically, solutions of Burgers type can be constructed by introducing a strain field into u such that u = (-(gamma/2)x - (gamma/2)y, yz) + (-psi(y), psi(x), W). The strain rate, y (t), is solely a function of time and is related to the pressure via a Riccati equation (gamma) over dot + gamma(2) p(zz)(t) = 0. A constraint on p(zz)(t) is that it must be spatially uniform. The decoupling of omega(3) and W allows the equation for omega(3) to be mapped to the usual general 2D problem through the use of Lundgren's transformation, while that for W can be mapped to the equation of a 2D passive scalar. When omega(3) stretches then W compresses and vice versa. Various solutions for W are discussed and some 2 pi-periodic theta-dependent solutionsfor W are presented which take the form of a convergent power series in a similarity variable. Hence the vorticity omega = (r(-1) W-theta, -W-r, omega(3)) has nonzero components in the azimuthal and radial as well as the axial directions. For the Euler problem, the equation for W can sustain a vortex sheet type of solution where jumps in W occur when a passes through multiples of 2 pi. (C)1999 Elsevier Science B.V. All rights reserved.

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Documento generato il 24/11/20 alle ore 14:40:24