Extended self-similarity works for the Burgers equation and why

TY - JOUR

T1 - Extended self-similarity works for the Burgers equation and why

AU - Chakraborty, Sagar

AU - Frisch, U.

AU - Ray, SS

PY - 2010/4/25

Y1 - 2010/4/25

N2 - 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.

AB - 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.

U2 - 10.1017/S0022112010000595

DO - 10.1017/S0022112010000595

M3 - Journal article

SN - 0022-1120

VL - 649

SP - 275

EP - 285

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -