Abstract
We propose an approach to study the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by ‘Statistically Preserved Structures’ which are associated with statistical conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations, and it demonstrates that the scaling exponents of these nonlinear models are indeed anomalous. In order to adress the universality of these nonlinear model we study the statistical properties of a semi-infinite chain of passive vectors advecting each other and study the scaling exponents at the fixed point of this chain.
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References
Frisch U (1995) Turbulence, Cambridge University Press
Bohr T, Jensen MH, Paladin G, Vulpiani A (1998) Dynamical systems approach to turbulence, Cambridge University Press
Biferale L (2003) Ann Rev Fluid Mech 35:441–468
Gledzer EB (1973) Dokl Akad Nauk SSSR 20:1046–1048
Yamada M, Ohkitani K (1987) J Phys Soc Jpn 56:4210–4213
Jensen MH, Paladin G, Vulpiani A (1991) Phys Rev A 43:798–805
Pissarenko D, Biferale L, Courvoisier D, Frisch U, Vergassola M (1993) Phys. Fluids A 5:2533–2538
Procaccia I, Gat O, Zeitak R (1995) Phys Rev E 51:1148–1154
L’vov VS, Podivilov E, Pomyalov A, Procaccia I, Vandembroucq D (1998) Phys Rev E 58:1811–1822
Benzi R, Biferale L, Parisi G (1993) Physica D 65:163–171
Benzi R, Biferale L, Toschi F (2001) Eur Phys J B 24:125–133
Benzi R, Biferale L, Sbragaglia M, Toschi F (2004) Phys Rev E 68:046304
Angheluta L, Benzi R, Biferale L, Procaccia I, Toschi F (2006) Phys Rev Lett 97:160601
Ditlevsen P (1996) Phys Rev E 54:985–988
Biferale L, Pierotti D, Toschi F (1998) Phys Rev E 57:R2515–R2518
Falkovich G, Gawedzki K, Vergassola M (2001) Rev Mod Phys 73:913–975
Arad I, Biferale L, Celani A, Procaccia I, Vergassola M (2001) Phys Rev Lett 87:164502
Cohen Y, Gilbert T, Procaccia I (2002) Phys Rev E 65:026314
Benzi R, Levant B, Procaccia I, Titi E (2007) Nonlinearity 20:1431
Arad I, Procaccia I (2001) Phys Rev E 63:056302
Celani A, Vergassola M (2001) Phys Rev Lett 86:424–427
Cohen Y, Pomyalov A, Procaccia I (2003) Phys Rev E 68:036303
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Procaccia, I., Benzi, R., Biferale, L. (2008). On Intermittency in Shell Models and in Turbulent Flows. In: Kaneda, Y. (eds) IUTAM Symposium on Computational Physics and New Perspectives in Turbulence. IUTAM Bookseries, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6472-2_5
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DOI: https://doi.org/10.1007/978-1-4020-6472-2_5
Publisher Name: Springer, Dordrecht
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