Extended Self Similarity works for the Burgers equation and why

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 infrared and ultraviolet 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.

10 pages, 1 figure, submitted to J. Fluid Mech. (fasttrack)

References in corpus (3)

• A Borel transform method for locating singularities of Taylor and Fourier series
• Entire solutions of hydrodynamical equations with exponential dissipation
• Does multifractal theory of turbulence have logarithms in the scaling relations?

Cited by in corpus (22)

• Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
• Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model
• On the Vortex Dynamics in Fractal Fourier Turbulence
• Passive directors in turbulence
• Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence
• Nelkin scaling for the Burgers equation and the role of high-precision calculations
• Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
• Universality of scaling and multiscaling in turbulent symmetric binary fluids
• Statistical Properties of three-dimensional Hall Magnetohydrodynamics Turbulence
• Bridging Inertial and Dissipation Range Statistics in Rotating Turbulence
• Extended self-similarity of atmospheric boundary layer wind fields in mesoscale regime: Is it real?
• Onset of Intermittency and Multiscaling in Active Turbulence
• Similarities between the structure functions of thermal convection and hydrodynamic turbulence
• The Statistical Properties of Superfluid Turbulence in ${}^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model
• Dynamic Scaling in Rotating Turbulence: A Shell Model Study
• Poles, Shocks and Tygers: The Time-reversible Burgers equation
• Extended self-similarity in two-dimensional complex plasmas
• Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation
• Nonlinear phase synchronization and the role of spacing in shell models
• Puff turbulence in the limit of strong buoyancy