LAGRANGIAN-HISTORY CLOSURE APPROXIMATION FOR TURBULENCE
Abstract
The direct-interaction approximation for turbulence is extended to predict the covariance and average Green's function of a generalized velocity. The latter is defined as the velocity measured at time r in the fluid element which passes through the point x at time t. The resulting formulas for triple moments involve integrals over the Eulerian time history of the fluid. The approximation is then altered so that the integrals are instead over Lagrangian histories, measured along the particle paths. The alteration is made necessary and is uniquely determined by requiring simultaneously the consistency properties that energy be conserved; that there exist formal inviscid equipartition solutions; and that the dynamics exhibit invariance under a class of random Galilean transformations. In the altered approximation, the relaxation times associated with energy transfer are Lagrangian memory times determined by the viscous and pressure forces. As a result, the approximation yields the Kolmogorov inertial- and dissipation-range laws. The corresponding approximation for convection of a passive scalar field yields some exact results of Taylor and yields Richardson's law for the relative diffusion of two particles.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1964
- Accession Number
- AD0603629
Entities
People
- Robert H. Kraichnan