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Titolo: VORTICITY ALIGNMENT RESULTS FOR THE 3DIMENSIONAL EULER AND NAVIERSTOKES EQUATIONS
Autore: GALANTI B; GIBBON JD; HERITAGE M;
 Indirizzi:
 WEIZMANN INST SCI,DEPT CHEM PHYS IL76100 REHOVOT ISRAEL UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED,DEPT MATH LONDON SW7 2BZ ENGLAND
 Titolo Testata:
 Nonlinearity
fascicolo: 6,
volume: 10,
anno: 1997,
pagine: 1675  1694
 SICI:
 09517715(1997)10:6<1675:VARFT3>2.0.ZU;2J
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 HOMOGENEOUS ISOTROPIC TURBULENCE; FULLYDEVELOPED TURBULENCE; 3DIMENSIONAL TURBULENCE; SCALAR GRADIENT; VORTEX TUBES; STRAIN RATE; FLOWS; INTERMITTENCY; DYNAMICS; SINGULARITY;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 CompuMath Citation Index
 CompuMath Citation Index
 Science Citation Index Expanded
 Science Citation Index Expanded
 Citazioni:
 56
 Recensione:
 Indirizzi per estratti:



 Citazione:
 B. Galanti et al., "VORTICITY ALIGNMENT RESULTS FOR THE 3DIMENSIONAL EULER AND NAVIERSTOKES EQUATIONS", Nonlinearity, 10(6), 1997, pp. 16751694
Abstract
We address the problem in NavierStokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasionedimensional tubes and quasitwodimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibbon, who observed that the vorticity vector omega aligns with the intermediate eigenvector of the strainmatrix S. we study this problem in the context of both the threedimensional Euler and NavierStokes equations using the variables alpha = <(xi)over cap>. S<(xi)over cap> and chi = <(xi)over cap> x S<(xi)over cap> where <(xi)over cap> = w/omega. This introduces the dynamic angle phi(x,t) = arctan(chi/alpha), which lies between omega and S omega. For the Euler equations a closed set of differential equations for alpha and chi is derived in terms of the Hessian matrix of the pressure P = (p,ij). For the NavierStokes equations. the Burgers vortex and shearlayer solutions turn out to be the Lagrangian fixedpaint solutions of the equivalent (alpha, chi) equations with a corresponding angle phi = 0. Under certain assumptions for more general Rows it is shown that there is an attracting fixed point of the (alpha, chi) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgerslike structures.
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Documento generato il 24/11/20 alle ore 14:25:37