Turbulent boundary layer equations

Alexey Cheskidov

doi:10.1016/S1631-073X(02)02275-6

Turbulent boundary layer equations
[Équations de la couche limite turbulente]

Alexey Cheskidov ¹

¹ Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405, USA

Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 423-427.

Résumé
Abstract

Nous considérons le problème de la couche limite pour l'α-modèle des équations de Navier–Stokes, obtenant d'abord une généralisation des équations de Prandtl. Notre hypothèse est que les solutions de ces équations représentent l'écoulement moyen dans une partie de la couche limite turbulente. Nous étudions, analytiquement et numériquement, ces solutions pour la plaque plane semi-infinie. Les solutions numériques donnent une très bonne approximation des certaines données expérimentales dans la couche limite turbulente.

We study a boundary layer problem for the Navier–Stokes-alpha model obtaining a generalization of the Prandtl equations which we conjecture to represent the averaged flow in a turbulent boundary layer. We study the equations for the semi-infinite plate, both theoretically and numerically. Solutions agree with some experimental data in a part of the turbulent boundary layer.

Reçu le : 2002-01-14
Accepté le : 2002-01-14
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02275-6

Affiliations des auteurs :

Alexey Cheskidov ¹

¹ Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405, USA

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Alexey Cheskidov. Turbulent boundary layer equations. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 423-427. doi : 10.1016/S1631-073X(02)02275-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02275-6/

Bibliographie
Cité par

[1] Blasius, Grenzschiehten in Flüssigkeiten mit kleiner Reibung, Dissertation, Leipzig, 1907

[2] R. Camassa; D.D. Holm A completely integrable dispersive shallow water equations with peaked solutions, Phys. Rev. Lett., Volume 71 (1993), pp. 1661-1664

[3] S. Chen; C. Foias; D.D. Holm; E. Olson; E.S. Titi; S. Wynne The Camassa–Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett., Volume 81 (1998), pp. 5338-5341

[4] S. Chen; C. Foias; D.D. Holm; E. Olson; E.S. Titi; S. Wynne A connection between the Camassa–Holm equations and turbulence flows in pipes and channels, Phys. Fluids, Volume 11 (1999), pp. 2343-2353

[5] S. Chen; C. Foias; D.D. Holm; E. Olson; E.S. Titi; S. Wynne The Camassa–Holm equations and turbulence in pipes and channels, Physica D, Volume 133 (1999), pp. 49-65

[6] A. Cheskidov, Boundary layer for the Navier–Stokes-alpha model of fluid turbulence (to be submitted)

[7] D.D. Holm; J.E. Marsden; T.S. Ratiu Euler–Poincaré models of ideal fluids with nonlinear dispersion, Phys. Rev. Lett., Volume 80 (1998), pp. 4173-4176

Jing Tian; Bingsheng Zhang Solution to Navier-Stokes equations for turbulent channel flows, Electronic Journal of Differential Equations, Volume 2020 (2020) no. 01-132, p. 05 | DOI:10.58997/ejde.2020.05
Bilal El Ouaragli; Mohamed Najib Zaghloul; Hajar El Talibi; Roberta Somma Tectono-sedimentary evolution of the Miocene Oued Dayr Formation (Ghomaride Complex, Internal Domain of the Maghrebian Rif Belt, Morocco), Arabian Journal of Geosciences, Volume 9 (2016) no. 15 | DOI:10.1007/s12517-016-2663-8
Ciprian Foias; Jing Tian; Bingsheng Zhang On the emergence of the Navier-Stokes-α model for turbulent channel flows, Journal of Mathematical Physics, Volume 57 (2016) no. 8 | DOI:10.1063/1.4960750
Ciprian G. Gal; T. Medjo Approximation of the trajectory attractor for a 3D model of incompressible two-phase-flows, Communications on Pure and Applied Analysis, Volume 13 (2014) no. 6, p. 2229 | DOI:10.3934/cpaa.2014.13.2229
T. Medjo A non-autonomous 3D Lagrangian averaged Navier-Stokes- $α$ model with oscillating external force and its global attractor, Communications on Pure and Applied Analysis, Volume 10 (2010) no. 2, p. 415 | DOI:10.3934/cpaa.2011.10.415
Mohamed Najib Zaghloul; Angelida Di Staso; Rachid Hlila; Vincenzo Perrone; Sonia Perrotta The Oued Dayr Formation: first evidence of a new Miocene late-orogenic cycle on the Ghomaride complex (Internal Domains of the Rifian Maghrebian Chain, Morocco), Geodinamica Acta, Volume 23 (2010) no. 4, p. 185 | DOI:10.3166/ga.23.185-194
Eric Olson; Edriss S. Titi Viscosity versus vorticity stretching: Global well-posedness for a family of Navier–Stokes-alpha-like models, Nonlinear Analysis: Theory, Methods Applications, Volume 66 (2007) no. 11, p. 2427 | DOI:10.1016/j.na.2006.03.030
A. Cheskidov Theoretical skin-friction law in a turbulent boundary layer, Physics Letters A, Volume 341 (2005) no. 5-6, p. 487 | DOI:10.1016/j.physleta.2005.04.099
Alexey Cheskidov; Darryl D. Holm; Eric Olson; Edriss S. Titi On a Leray–α model of turbulence, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 461 (2005) no. 2055, p. 629 | DOI:10.1098/rspa.2004.1373

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