Extended Self Similarity works for the Burgers equation and why
Chakraborty, S., Frisch, U. and Ray, S.S

Sunday 28 November 2010 by Ponty Yannick

 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.


 Chakraborty, S., Frisch, U. and Ray, S.S., "Extended Self Similarity works for the Burgers equation and why", Journal of Fluid Mechanics, 649, pp. 275-285 (2010)