Lagrangian structure functions in fully-developed hydrodynamical turbulence

Abstract

The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are derived basing on the Navier-Stokes equations. For time $\tau$ much smaller than the correlation time, the structure functions are shown to obey the scaling relations $K_n(\tau )\propto {\tau }^{{\zeta }_n}$. The scaling exponents ${\zeta }_n$ are calculated analytically. The obtained values are in amazing agreement with the unique experimental results of the Bodenschatz group \cite{Bod2}. New notion -- the Lagrangian position structure functions $R_n(\tau )$ is introduced. All the $R_n$ of the order $n>3$ are shown to have a universal scaling.

References in corpus (5)

• Measurement of Particle Accelerations in Fully Developed Turbulence
• Statistics of 3-dimensional Lagrangian turbulence
• Analytic Calculation of the Anomalous Exponents in Turbulence: Using the Fusion Rules to Flush Out a Small Parameter
• On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence
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Cited by in corpus (8)

• Lagrangian views on turbulent mixing of passive scalars
• Fully developed turbulence and the multifractal conjecture
• Multi-Time Multi-Scale Correlation Functions in Hydrodynamic Turbulence
• Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence
• Turbulence and Scale Relativity
• Multi-time structure functions and the Lagrangian scaling of turbulence
• Lagrangian stochastic integrals of motion in isotropic random flows
• Eulerian and Lagrangian Statistics from high resolution Numerical Simulations of weakly compressible turbulence