Abstract
A nonlocal turbulence transport theory is presented by means of a novel analysis of the Reynolds stress, inter alia involving the construct of a sample path space and a stochastic hypothesis. An analytical sampling rate model (satisfying exchange) and a nonlinear scaling relation (mapping the path space onto the boundary layer) lead to an integro-differential equation for the mixing of scalar densities, which represents fully-developed boundary-layer turbulence as a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The underlying near-wall behavior (i.e. for y +→0) of fluctuating velocities fully agrees with recent direct numerical simulations. The model involves a scaling exponent ɛ, with ɛ→∞ in the diffusion limit. For the (partly analytical) solution for the mean velocity profile, excellent agreement with the experimental data yields ɛ≈0.58. The significance of ɛ as a turbulence Cantor set dimension (in the logarithmic profile region, i.e. for y +→∞) is discussed.
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© 1997 Springer-Verlag
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Dekker, H., de Leeuw, G., van den Brink, A.M. (1997). Boundary-layer turbulence modeling and vorticity dynamics: I. A kangaroo-process mixing model of boundary-layer turbulence. In: Boratav, O., Eden, A., Erzan, A. (eds) Turbulence Modeling and Vortex Dynamics. Lecture Notes in Physics, vol 491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105039
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DOI: https://doi.org/10.1007/BFb0105039
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