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Titolo: Dynamically stretched vortices as solutions of the 3D NavierStokes 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:
 01672789(19990820)132:4<497:DSVASO>2.0.ZU;2G
 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 NavierStokes equations", PHYSICA D, 132(4), 1999, pp. 497510
Abstract
A well known limitation with stretched vortex solutions of the 3D NavierStokes (and Euler) equations, such as those of Burgers type, is that they possess unidirectional 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 piperiodic thetadependent solutionsfor W are presented which take the form of a convergent power series in a similarity variable. Hence the vorticity omega = (r(1) Wtheta, Wr, 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.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 24/11/20 alle ore 14:40:24