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Mathematical theory of turbulence

Book ·
OSTI ID:7260780
A mathematical discussion of turbulence emphasizing nonlinear stochastic phenomena is presented. The classical approach to turbulence is first discussed in conjunction with the semiempirical methods of Prandtl, Taylor, and von Karman. Eddy viscosity, the turbulent boundary layer, the law of the wall in turbulent channel flows; and velocity distributions in the transition region of the turbulent boundary layer are discussed in depth. Statistical theories of turbulence are then considered, elaborating on the fundamental stochastic formulations developed by von Karman, Howarth, and Taylor. Then Kolmogoroff's, Heisenberg's, Kraichnan's, and Kopf's theories of turbulence are introduced, applying Kraichnan's theory to the Burgers model equation in order to demonstrate the general features of the Direct Interaction Approximation using an average Green's function in the full Navier-Stokes equations. The treatment of ordinary turbulence using characteristic functionals as developed by Hopf is emphasized. Hopf's theory is extended to include a full derivation of the phi equation and two two orders of approximation to it. Finally, magnetohydrodynamic turbulence is treated using joint characteristic functionals and temperature dispersion in a weakly conducting turbulent fluid. 112 references.
OSTI ID:
7260780
Country of Publication:
United States
Language:
English