2022/08/19 by Katepalli R. Sreenivasan, Sreenivasan, Katepalli R., Victor Yakhot +1
Earth and Planetary Sciences · Environmental Science · Physics and Astronomy · #Applied Physics (physics.app-ph) #Climate variability and models #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Oceanographic and Atmospheric Processes #Solar and Space Plasma Dynamics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2208.09561
openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents ζn for large n, defined via structure functions of order n as Sn(r)=(δr u)n=A(n)r^ζn. We focus on longitudinal structure functions for δr u between two positions that are r apart in the same direction. In a previous paper (Phys. Rev. Fluids 6, 104604, 2021), we developed a theory for ζn, which agrees with measurements for all n for which reliable data are available, and shows saturation for large n. Here, we derive expressions for the probability density functions of δr u for four different states of turbulence, including the asymptotic fourth state corresponding to the saturation of exponents for large n. This saturation means that the scale separation is violated in favor of a strongly-coupled quasi-ordered flow structures, which take the form of long and thin (worm-like) structures of length L and thickness l=O(L/Re).