Extended self-similarity works for the Burgers equation and why

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 Reyno...

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Bibliographic Details
Published in:Journal of fluid mechanics 2010-04, Vol.649, p.275-285
Main Authors: CHAKRABORTY, SAGAR, FRISCH, URIEL, RAY, SAMRIDDHI SANKAR
Format: Article
Language:English
Subjects:
Exact sciences and technology
Flow velocity
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
High-reynolds-number turbulence
Physics
Reynolds number
Turbulence
Turbulence simulation and modeling
Turbulent flow
Turbulent flows, convection, and heat transfer
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112010000595