Navegar

Colección

Datos Estadísticas

Artículo

El editor permite incluir el artículo en su versión final en nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier-Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re≈3300, Taylor Reynolds number of Re≈790, and to a direct numerical simulation (DNS) of the Navier-Stokes equations. We derive the de Kármán-Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k-1 energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼k1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán-Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α. © 2008 American Institute of Physics.

Registro:

Documento: Artículo
Título:Three regularization models of the Navier-Stokes equations
Autor:Graham, J.P.; Holm, D.D.; Mininni, P.D.; Pouquet, A.
Filiación:National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, United States
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States
Departamento de Fesica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Approximation theory; Direct numerical simulation; Mathematical models; Navier Stokes equations; Reynolds number; Energy spectrum; Subfilter-scale physics; Subgrid-scale (SGS) models; Flow of fluids; Approximation theory; Direct numerical simulation; Flow of fluids; Mathematical models; Navier Stokes equations; Reynolds number
Año:2008
Volumen:20
Número:3
DOI: http://dx.doi.org/10.1063/1.2880275
Título revista:Physics of Fluids
Título revista abreviado:Phys. Fluids
ISSN:10706631
CODEN:PHFLE
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_10706631_v20_n3_p_Graham.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v20_n3_p_Graham

Referencias:

  • Frisch, U., (1995) Turbulence: The Legacy of A. N. Kolmogorov, , (Cambridge University Press, Cambridge)
  • Kolmogorov, A.N., "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers" (1941) Dokl. Akad. Nauk, 30, p. 299. , SSSRDANKAS0002-3264 Reprinted in Proc. R. Soc. London, Ser. APRLAAZ1364-502110.1098/rspa.1991.0075 434, 9 (1991)
  • Kolmogorov, A.N., "On degeneration (decay) of isotropic turbulence in an incompressible viscous liquid" (1941) Dokl. Akad. Nauk, 31, p. 538. , SSSRDANKAS0002-3264
  • Kolmogorov, A.N., "Dissipation of energy in locally isotropic turbulence," (1941) Dokl. Akad. Nauk, 32, p. 16. , SSSRDANKAS0002-3264 Reprinted in Proc. R. Soc. London, Ser. APRLAAZ1364-502110.1098/rspa.1991.0076 434, 15 (1991)
  • Meneveau, C., Katz, J., "Scale-invariance and turbulence models for large-eddy simulation," (2000) Annu. Rev. Fluid Mech., 32, p. 1. , ARVFA30066-418910.1146/annurev.fluid.32.1.1
  • Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K., Uno, A., "Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box," (2003) Phys. Fluids, 15, pp. L21. , PHFLE61070-663110.1063/1.1539855
  • Tsuji, Y., "Intermittency effect on energy spectrum in high-Reynolds number turbulence" (2004) Phys. Fluids, 16, pp. L43. , PHFLE61070-663110.1063/1.1689931
  • Alexakis, A., Mininni, P.D., Pouquet, A., "Imprint of large-scale flows on turbulence" (2005) Phys. Rev. Lett., 95, p. 264503. , PRLTAO0031-900710.1103/PhysRevLett.95.264503
  • Mininni, P.D., Pouquet, A.G., Montgomery, D.C., "Small-scale structures in three-dimensional magnetohydrodynamic turbulence" (2006) Phys. Rev. Lett., 97, p. 244503. , PRLTAO0031-900710.1103/PhysRevLett.97.244503
  • Chen, S., Holm, D.D., Margolin, L.G., Zhang, R., "Direct numerical simulations of the Navier-Stokes alpha model" (1999) Physica, 133, p. 66. , DPDNPDT0167-278910.1016/S0167-2789(99)00099-8
  • Geurts, B.J., Holm, D.D., "Leray simulation of turbulent shear layers," (2002) Advances in Turbulence IX: Proceedings of the Ninth European Turbulence Conference, p. 337. , in edited by J. P. Castro and P. E. Hancock (CIMNE, Barcelona)
  • Geurts, B.J., Holm, D.D., "Regularization modeling for large-eddy simulation," (2003) Phys. Fluids, 15, pp. L13. , PHFLE61070-663110.1063/1.1529180
  • Holm, D.D., Nadiga, B., "Modeling mesoscale turbulence in the barotropic double gyre circulation" (2003) J. Phys. Oceanogr., 33, p. 2355. , JPYOBT1520-048510.1175/1520-0485(2003)033<2355:MMTITB>2.0.CO;2
  • Cheskidov, A., Holm, D.D., Olson, E., Titi, E.S., "On a Leray-α model of turbulence," (2005) Proc. R. Soc. London, Ser., 461, p. 629. , APRLAAZ1364-502110.1098/rspa.2004.1373
  • Geurts, B.J., Holm, D.D., "Leray and LANS-α modelling of turbulent mixing," (2006) J. Turbul., 7, p. 1. , ZZZZZZ1468-5248
  • Leray, J., "Essai sur le mouvement d'un fluide visqueux emplissant l'espace" (1934) Acta Math., 63, p. 193. , ACMAA80001-596210.1007/BF02547354
  • Leonard, A., "Energy cascade in large-eddy simulations of turbulent fluid flows" (1974) Turbulent Diffusion in Environmental Pollution; Proceedings of the Second Symposium, 13, pp. 237-248. , 87 in Charlottesville, VA, 8-14 April 1973 (Academic, New York)
  • Clark, R.A., Ferziger, J.H., Reynolds, W.C., "Evaluation of subgrid-scale models using an accurately simulated turbulent flow" (1979) J. Fluid Mech., 91, p. 1. , JFLSA70022-112010.1017/S002211207900001X
  • Winckelmans, G.S., Wray, A.A., Vasilyev, O.V., Jeanmart, H., "Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term" (2001) Phys. Fluids, 13, p. 1385. , PHFLE61070-663110.1063/1.1360192
  • Carati, D., Winckelmans, G.S., Jeanmart, H., "On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation" (2001) J. Fluid Mech., 441, p. 119. , JFLSA70022-112010.1017/S0022112001004773
  • Cao, C., Holm, D.D., Titi, E.S., "On the Clark α model of turbulence: Global regularity and long-time dynamics" (2005) J. Turbul., 6, p. 19. , ZZZZZZ1468-5248
  • Holm, D.D., Marsden, J.E., Ratiu, T.S., "The Euler-Poincaré equations and semidirect products with applications to continuum theories" (1998) Adv. Math., 137, p. 1. , ADMTA40001-870810.1006/aima.1998.1721
  • Chen, S., Foias, C., Holm, D.D., Olson, E., Titi, E.S., Wynne, S., "Camassa-Holm equations as a closure model for turbulent channel and pipe flow" (1998) Phys. Rev. Lett., 81, p. 5338. , PRLTAO0031-900710.1103/PhysRevLett.81.5338
  • Chen, S., Foias, C., Holm, D.D., Olson, E., Titi, E.S., Wynne, S., "The Camassa-Holm equations and turbulence" (1999) Physica, 133, p. 49. , DPDNPDT0167-278910.1016/S0167-2789(99)00098-6
  • Chen, S., Foias, C., Holm, D.D., Olson, E., Titi, E.S., Wynne, S., "A connection between the Camassa-Holm equations and turbulent flows in channels and pipes," (1999) Phys. Fluids, 11, p. 2343. , PHFLE61070-663110.1063/1.870096
  • Holm, D.D., Marsden, J.E., Ratiu, T.S., "Euler-Poincaré models of ideal fluids with nonlinear dispersion" (1998) Phys. Rev. Lett., 80, p. 4173. , PRLTAO0031-900710.1103/PhysRevLett.80.4173
  • Holm, D.D., "Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics" (2002) Chaos, 12, p. 518. , CHAOEH1054-150010.1063/1.1460941
  • Holm, D.D., "Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics" (2002) Physica, 170, p. 253. , DPDNPDT0167-278910.1016/S0167-2789(02)00552-3
  • Foias, C., Holm, D.D., Titi, E.S., "The Navier-Stokes-alpha model of fluid turbulence," (2001) Physica, 152-153, p. 505. , DPDNPDT0167-2789
  • Montgomery, D.C., Pouquet, A., "An alternative interpretation for the Holm 'alpha model'" (2002) Phys. Fluids, 14, p. 3365. , PHFLE61070-663110.1063/1.1501542
  • Zhao, H., Mohseni, K., "A dynamic model for the Lagrangian-averaged Navier-Stokes-α equations" (2005) Phys. Fluids, 17, p. 5106. , PHFLE61070-663110.1063/1.1965166
  • Mohseni, K., Kosović, B., Shkoller, S., Marsden, J.E., "Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence," (2003) Phys. Fluids, 15, p. 524. , PHFLE61070-663110.1063/1.1533069
  • Geurts, B.J., Holm, D.D., "Alpha-modeling strategy for LES of turbulent mixing" (2002) Turbulent Flow Computation, p. 237. , in edited by D. Drikakis and B. J. Geurts (Kluwer Academic, London)
  • Pietarila Graham, J., Holm, D., Mininni, P., Pouquet, A., "Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes alpha model and their large-eddy-simulation potential" (2007) Phys. Rev., 76, p. 056310. , EPLEEE81063-651X10.1103/PhysRevE.76.056310
  • Meyers, J., Sagaut, P., Geurts, B.J., "Optimal model parameters for multi-objective large-eddy simulations" (2006) Phys. Fluids, 18, p. 5103. , PHFLE61070-663110.1063/1.2353402
  • de Kármán, T., Howarth, L., "On the statistical theory of isotropic turbulence," (1938) Proc. R. Soc. London, Ser. A, 164, p. 192. , PRLAAZ1364-502110.1098/rspa.1938.0013
  • Holm, D.D., "Kármán Howarth theorem for the Lagrangian-averaged Navier Stokes alpha model of turbulence" (2002) J. Fluid Mech., 467, p. 205. , JFLSA70022-112010.1017/S002211200200160X
  • Kraichnan, R.H., "Inertial ranges in two-dimensional turbulence" (1967) Phys. Fluids, 10, p. 1417. , PFLDAS0031-917110.1063/1.1762301
  • van Reeuwijk, M., Jonker, H.J.J., Hanjali, K., "Incompressibility of the Leray-α model for wall-bounded flows" (2006) Phys. Fluids, 18, p. 018103. , PHFLE61070-663110.1063/1.2166459
  • Gómez, D.O., Mininni, P.D., Dmitruk, P., "Parallel simulations in turbulent MHD" (2005) Phys. Scr., 116, p. 123. , TPHSTER0281-184710.1238/Physica.Topical.116a00123
  • Gómez, D.O., Mininni, P.D., Dmitruk, P., "MHD simulations and astrophysical applications" (2005) Adv. Space Res., 35, p. 899. , ASRSDW0273-117710.1016/j.asr.2005.02.099
  • Taylor, G.I., Green, A.E., "Mechanism of the production of small eddies from large ones" (1937) Proc. R. Soc. London, Ser. A, 499. , PRLAAZ1364-5021158
  • Mininni, P.D., Ponty, Y., Montgomery, D.C., Pinton, J.-F., Politano, H., Pouquet, A., "Dynamo regimes with a nonhelical forcing" (2005) Astrophys. J., 626, p. 853. , ASJOAB0004-637X10.1086/429911
  • Brachet, M., "The geometry of small-scale structures in a Taylor-Green vortex" (1990) Academie Des Sciences Paris Comptes Rendus Serie Sciences Mathematiques, 311, p. 775
  • Ponty, Y., Mininni, P.D., Montgomery, D.C., Pinton, J.-F., Politano, H., Pouquet, A., "Numerical study of dynamo action at low magnetic Prandtl numbers" (2005) Phys. Rev. Lett., 94, p. 164502. , PRLTAO0031-900710.1103/PhysRevLett.94.164502
  • Sagaut, P., (2006) Large Eddy Simulation for Incompressible Flows, , 3rd ed. (Springer, Berlin)
  • Mininni, P.D., Alexakis, A., Pouquet, A., "Large-scale flow effects, energy transfer, and self-similarity on turbulence" (2006) Phys. Rev., 74, p. 016303. , EPLEEE81063-651X10.1103/PhysRevE.74.016303
  • Benzi, R., Ciliberto, S., Baudet, C., Ruiz Chavarria, G., Tripiccione, R., "Extended self-similarity in the dissipation range of fully developed turbulence" (1993) Europhys. Lett., 24, p. 275. , EULEEJ0295-507510.1209/0295-5075/24/4/007
  • Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., Succi, S., "Extended self-similarity in turbulent flows" (1993) Phys. Rev., 48, pp. R29. , EPLEEE81063-651X10.1103/PhysRevE.48.R29
  • Benzi, R., Biferale, L., Ciliberto, S., Struglia, M.V., Tripiccione, R., "Scaling property of turbulent flows" (1996) Phys. Rev., 53, pp. R3025. , EPLEEE81063-651X10.1103/PhysRevE.53.R3025
  • Laval, J.-P., Dubrulle, B., Nazarenko, S., "Nonlocality and intermittency in three-dimensional turbulence" (2001) Phys. Fluids, 13, p. 1995. , PHFLE61070-663110.1063/1.1373686
  • Dubrulle, B., Laval, J.-P., Nazarenko, S., Zaboronski, O., "A model for rapid stochastic distortions of small-scale turbulence" (2004) J. Fluid Mech., 520, p. 1. , JFLSA70022-112010.1017/S0022112004001417
  • She, Z., Leveque, E., "Universal scaling laws in fully developed turbulence" (1994) Phys. Rev. Lett., 72, p. 336. , PRLTAO0031-900710.1103/PhysRevLett.72.336

Citas:

---------- APA ----------
Graham, J.P., Holm, D.D., Mininni, P.D. & Pouquet, A. (2008) . Three regularization models of the Navier-Stokes equations. Physics of Fluids, 20(3).
http://dx.doi.org/10.1063/1.2880275
---------- CHICAGO ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. "Three regularization models of the Navier-Stokes equations" . Physics of Fluids 20, no. 3 (2008).
http://dx.doi.org/10.1063/1.2880275
---------- MLA ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. "Three regularization models of the Navier-Stokes equations" . Physics of Fluids, vol. 20, no. 3, 2008.
http://dx.doi.org/10.1063/1.2880275
---------- VANCOUVER ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. Three regularization models of the Navier-Stokes equations. Phys. Fluids. 2008;20(3).
http://dx.doi.org/10.1063/1.2880275