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Updated: Jul 4, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Lagrangian statistical theory of fully developed hydrodynamical turbulence
K P Zybin1, V A Sirota, A S Ilyin
1119991 P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia. zybin@lpi.ru
Abstract:
The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are for the first time derived based on the Navier-Stokes equation. For time tau much smaller than the correlation time, the structure functions are shown to obey the scaling relations K_{n}(tau) proportional, varianttau;{zeta_{n}}. The scaling exponents zeta_{n} are calculated analytically without any fitting parameters. The obtained values are in amazing agreement with the experimental results of the Bodenschatz group. A new relation connecting the Lagrangian structure functions of different orders analogously to the extended self-similarity ansatz is found.
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