Opportunities for use of exact statistical equations

Abstract

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.

accepted by Journal of Turbulence

References in corpus (7)

• Measurement of Particle Accelerations in Fully Developed Turbulence
• Exact Second-Order Structure-Function Relationships
• Equations relating structure functions of all orders
• Recovering Isotropic Statistics in Turbulence Simulations: The Kolmogorov 4/5th-Law
• Local 4/5-Law and Energy Dissipation Anomaly in Turbulence
• "Locally homogeneous turbulence" Is it an inconsistent framework?
• The Approach of Turbulence to the Locally Homogeneous Asymptote as Studied using Exact Structure-Function Equations

Cited by in corpus (8)

• Simultaneous 3D measurement of the translation and rotation of finite size particles and the flow field in a fully developed turbulent water flow
• Turbulent pair dispersion as a ballistic cascade phenomenology
• Where do small, weakly inertial particles go in a turbulent flow?
• Inertial effects on two-particle relative dispersion in turbulent flows
• Relative dispersion of particle pairs in turbulent channel flow
• Multi-particle Lagrangian statistics in homogeneous rotating turbulence
• Lagrangian irreversibility and energy exchanges in rotating-stratified turbulent flows
• Methods for measuring energy dissipation rate in anisotropic turbulence