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Extended self-similarity works for the Burgers equation and why

Published online by Cambridge University Press:  13 April 2010

SAGAR CHAKRABORTY ,
URIEL FRISCH  and
SAMRIDDHI SANKAR RAY
SAGAR CHAKRABORTY
Affiliation:
NBIA, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark Theoretical Sciences, SNBNCBS, Kolkata-98, India
URIEL FRISCH*
Affiliation:
UNS, CNRS, Laboratoire Cassiopée, OCA, B.P. 4229, 06304 Nice Cedex 4, France
SAMRIDDHI SANKAR RAY
Affiliation:
Department of Physics, Indian Institute of Science, Bangalore, India
*
†Email address for correspondence: uriel@obs-nice.fr
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Abstract

Extended self-similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier–Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the IR and UV end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 649 , 25 April 2010 , pp. 275 - 285
Copyright
Copyright © Cambridge University Press 2010

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