Does multifractal theory of turbulence have logarithms in the scaling relations?

Abstract

The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present.

arXiv comment7 pages, 1 figure

References in corpus (4)

• Anisotropy in Turbulent Flows and in Turbulent Transport
• Kolmogorov turbulence in a random-force-driven Burgers equation: anomalous scaling and probability density functions
• Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?
• Does multifractal theory of turbulence have logarithms in the scaling relations?

Cited by in corpus (5)

• Twenty-five years of multifractals in fully developed turbulence: a tribute to Giovanni Paladin
• Probability Densities in Strong Turbulence
• Extended Self Similarity works for the Burgers equation and why
• Does multifractal theory of turbulence have logarithms in the scaling relations?
• The Onset of Intermittency in Stochastic Burgers Hydrodynamics