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Does multifractal theory of turbulence have logarithms in the scaling relations?

Published online by Cambridge University Press:  25 October 2005

U. FRISCH ,
M. MARTINS AFONSO ,
A. MAZZINO  and
V. YAKHOT
U. FRISCH
Affiliation:
CNRS, Lab. Cassiopée, Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
M. MARTINS AFONSO
Affiliation:
INFM – Dipartimento di Fisica, Università di Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
A. MAZZINO
Affiliation:
INFM – Dipartimento di Fisica, Università di Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
V. YAKHOT
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, 02215 Boston, USA
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Abstract

The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 542 , 10 November 2005 , pp. 97 - 103
Copyright
© 2005 Cambridge University Press

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