Journal of Fluid Mechanics

Papers

Extended self-similarity works for the Burgers equation and why

SAGAR CHAKRABORTYa1a2, URIEL FRISCHa3 c1 and SAMRIDDHI SANKAR RAYa4

a1 NBIA, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark

a2 Theoretical Sciences, SNBNCBS, Kolkata-98, India

a3 UNS, CNRS, Laboratoire Cassiopée, OCA, B.P. 4229, 06304 Nice Cedex 4, France

a4 Department of Physics, Indian Institute of Science, Bangalore, India

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.

(Received December 11 2009)

(Revised January 29 2010)

(Accepted January 31 2010)

Correspondence:

c1 Email address for correspondence: uriel@obs-nice.fr

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