TY - GEN

T1 - On an alternative explanation of anomalous scaling and how inertial is the inertial range

AU - Kholmyansky, M.

AU - Tsinober, A.

N1 - Publisher Copyright:
© 2009, Springer-Verlag Berlin Heidelberg.

PY - 2009

Y1 - 2009

N2 - There are a variety of models of higher statistics that have meager or nonexistent deductive support from the Navier-Stokes equations but can be made to give good fits to experimental measurements [1]. These include ‘explanations’ of what is called anomalous scaling, observed experimentally for higher-order structure functions of velocity and temperature increments, such that their scaling exponents, are nonlinear concave functions of the order p. Starting with refined similarity hypotheses by Kolmogorov and Oboukhov, numerous phenomenological models have been proposed to describe these deviations. The dominant of these models has been the multifractal formalism, others claimed the Reynolds number dependence as responsible. The common in all these approaches is the basic, widely accepted premise that in the inertial range, the viscosity plays in principle no role [2] so that nonlinear dependence of the algebraic scaling exponents on the moment order p is a manifestation of the inertial-range intermittency [3] with the inertial range defined as (with being the Kolmogorov and L - some integral scale). Thus the issue is directly related to what is called inertial (sub)range and how inertial it is.

AB - There are a variety of models of higher statistics that have meager or nonexistent deductive support from the Navier-Stokes equations but can be made to give good fits to experimental measurements [1]. These include ‘explanations’ of what is called anomalous scaling, observed experimentally for higher-order structure functions of velocity and temperature increments, such that their scaling exponents, are nonlinear concave functions of the order p. Starting with refined similarity hypotheses by Kolmogorov and Oboukhov, numerous phenomenological models have been proposed to describe these deviations. The dominant of these models has been the multifractal formalism, others claimed the Reynolds number dependence as responsible. The common in all these approaches is the basic, widely accepted premise that in the inertial range, the viscosity plays in principle no role [2] so that nonlinear dependence of the algebraic scaling exponents on the moment order p is a manifestation of the inertial-range intermittency [3] with the inertial range defined as (with being the Kolmogorov and L - some integral scale). Thus the issue is directly related to what is called inertial (sub)range and how inertial it is.

UR - http://www.scopus.com/inward/record.url?scp=85123317723&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03085-7_173

DO - 10.1007/978-3-642-03085-7_173

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AN - SCOPUS:85123317723

SN - 9783642030840

T3 - Springer Proceedings in Physics

SP - 715

EP - 718

BT - Advances in Turbulence XII - Proceedings of the 12th EUROMECH European Turbulence Conference, 2009

A2 - Eckhardt, Bruno

PB - Springer Science and Business Media Deutschland GmbH

T2 - 12th EUROMECH European Turbulence Conference, ETC12 2009

Y2 - 7 September 2009 through 10 September 2009

ER -