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

Tags

DTIC Thesaurus Topics

  • Dynamics
  • Equations
  • Physics
  • Reynolds Number
  • Shock
  • Shock Waves
  • Spectra
  • Stationary
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)