LAGRANGIAN-HISTORY STATISTICAL THEORY FOR BURGERS' EQUATION.
Abstract
The Lagrangian-history direct-interaction approximation for Burgers' equation yields a 1/(k sq) inertial-range spectrum and an infinite-Reynolds-number similarity solution which describes stationary, decaying sawtooth shock waves. This solution differs only by a numerical factor from an exact statistical solution of Burgers' equation into which almost all spatially periodic, zero-mean, infinite-Reynolds-number initial ensembles are expected to evolve. The different inertial-range predictions of the approximation for Burgers' equation and Navier-Stokes dynamics (where k to the -5/3 power results) are directly associated with the effects of pressure-induced accelerations on Langrangian correlation times. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1967
- Accession Number
- AD0653112
Entities
People
- Robert H. Kraichnan