Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows

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The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are...

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Autor principal: Krstulovic, G.
Otros Autores: Mininni, P.D, Brachet, M.E, Pouquet, A.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2009
Acceso en línea:Registro en Scopus
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100 1 |a Krstulovic, G. 
245 1 0 |a Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows 
260 |c 2009 
270 1 0 |m Krstulovic, G.; Laboratoire de Physique Statistique, Ecole Normale Supérieure, Universités Paris VI et VII, 24 Rue Lhomond, 75231 Paris, France 
506 |2 openaire  |e Política editorial 
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504 |a Brissaud, A., Frisch, U., Leorat, J., Lesieur, M., Mazure, A., (1973) Phys. Fluids, 16, p. 1366. , 10.1063/1.1694520 
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504 |a Chen, Q.N., Chen, S.Y., Eyink, G.L., (2003) Phys. Fluids, 15, p. 361. , 10.1063/1.1533070 
504 |a Mininni, P.D., Alexakis, A., Pouquet, A., (2006) Phys. Rev. e, 74, p. 016303. , 10.1103/PhysRevE.74.016303 
504 |a Cichowlas, C., Bonaïti, P., Debbasch, F., Brachet, M.E., (2005) Phys. Rev. Lett., 95, p. 264502. , 10.1103/PhysRevLett.95.264502 
504 |a Frisch, U., Hasslacher, B., Pomeau, Y., (1986) Phys. Rev. Lett., 56, p. 1505. , 10.1103/PhysRevLett.56.1505 
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504 |a Nore, C., Abid, M., Brachet, M.E., (1997) Phys. Rev. Lett., 78, p. 3896. , 10.1103/PhysRevLett.78.3896 
504 |a Frisch, U., Kurien, S., Pandit, R., Pauls, W., Ray, S.S., Wirth, A., Zhu, J.Z., (2008) Phys. Rev. Lett., 101, p. 144501. , 10.1103/PhysRevLett.101.144501 
504 |a Krstulovic, G., Brachet, M.E., (2008) Physica D, 237, p. 2015. , 10.1016/j.physd.2007.11.008 
504 |a Gómez, D.O., Mininni, P.D., Dmitruk, P., (2005) Phys. Scr., 116, p. 123. , 10.1238/Physica.Topical.116a00123; 
504 |a Gómez, D.O., Mininni, P.D., Dmitruk, P., (2005) Adv. Space Res., 35, p. 889 
504 |a Gottlieb, D., Orszag, S.A., (1977) Numerical Analysis of Spectral Methods: Theory and Applications, , SIAM, Philadelphia 
504 |a Orszag, S.A., (1970) J. Fluid Mech., 41, p. 363. , 10.1017/S0022112070000642 
504 |a The Liouville equation requires a statistical ensemble of initial data however, by ergodicity, the small scales of a single initial condition do statistically equilibrate; Bos, W.J.T., Bertoglio, J.-P., (2006) Phys. Fluids, 18, p. 071701. , 10.1063/1.2219766 
504 |a André, J.C., Lesieur, M., (1977) J. Fluid Mech., 81, p. 187. , 10.1017/S0022112077001979 
504 |a Baerenzung, J., Politano, H., Ponty, Y., Pouquet, A., (2008) Phys. Rev. e, 77, p. 046303. , 10.1103/PhysRevE.77.046303 
504 |a Mininni, P.D., Pouquet, A., (2009) Phys. Rev. e, 79, p. 026304. , 10.1103/PhysRevE.79.026304; 
504 |a Baerenzung, J., Mininni, P.D., Pouquet, A., ; Lesieur, M., Schertzer, D., (1978) J. Mec., 17, p. 609 
520 3 |a The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are found using initial data concentrated at high wave numbers. Using low-wave-number initial conditions, the results of Cichowlas [Phys. Rev. Lett. 95, 264502 (2005)] are extended to helical flows. Similarities between the turbulent transient evolution of the ideal (time-reversible) system and viscous helical flows are found. Using an argument in the manner of Frisch [Phys. Rev. Lett. 101, 144501 (2008)], the excess of relative helicity found at small scales in the viscous run is related to the thermalization of the ideal flow. The observed differences in the behavior of truncated Euler and (constant viscosity) Navier-Stokes are qualitatively understood using the concept of eddy viscosity. The large scales of truncated Euler equations are then shown to follow quantitatively an effective Navier-Stokes dynamics based on a variable (scale dependent) eddy viscosity. © 2009 The American Physical Society.  |l eng 
593 |a Laboratoire de Physique Statistique, Ecole Normale Supérieure, Universités Paris VI et VII, 24 Rue Lhomond, 75231 Paris, France 
593 |a Departamento de Física, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina 
593 |a NCAR, P.O. Box 3000, Boulder, CO 80307-3000, United States 
690 1 0 |a EDDY VISCOSITY 
690 1 0 |a EULER FLOWS 
690 1 0 |a GALERKIN 
690 1 0 |a HELICAL FLOWS 
690 1 0 |a HELICITY 
690 1 0 |a HELICITY CASCADES 
690 1 0 |a HIGH WAVE NUMBER 
690 1 0 |a IDEAL FLOW 
690 1 0 |a INITIAL CONDITIONS 
690 1 0 |a LINEAR SCALING 
690 1 0 |a NAVIER STOKES 
690 1 0 |a SMALL SCALE 
690 1 0 |a THERMALIZATION 
690 1 0 |a TRANSIENT ENERGY 
690 1 0 |a TRANSIENT EVOLUTION 
690 1 0 |a WAVE NUMBERS 
690 1 0 |a DYNAMICS 
690 1 0 |a EULER EQUATIONS 
690 1 0 |a VISCOSITY 
690 1 0 |a NAVIER STOKES EQUATIONS 
700 1 |a Mininni, P.D. 
700 1 |a Brachet, M.E. 
700 1 |a Pouquet, A. 
773 0 |d 2009  |g v. 79  |k n. 5  |p Phys. Rev. E Stat. Nonlinear Soft Matter Phys.  |x 15393755  |t Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 
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856 4 0 |u https://doi.org/10.1103/PhysRevE.79.056304  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_15393755_v79_n5_p_Krstulovic  |y Handle 
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