Stochastic Theory of Turbulence Mixing by Finite Eddies in the Turbulent Boundary Layer

Turbulence mixing is treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic hypothesis. The theory simplifies for mixing by exchange (strong-eddies) and is then applied to the boundary layer (involving scaling). This maps boundary layer turbulence onto a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The theory involves an exponent epsilon (with the significance of a Cantor set dimension if epsilon is less than 1). With expsilon approximately equal to 0.58 (epsilon approaches infinity in the diffusion limit) the ensuing mean velocity profile U-bar+ = f(y+) is in perfect agreement with experimental data. The near-wall (y approaches 0) velocity fluctuations agree with recent direct numerical simulations