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The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions. (English) Zbl 0781.76047

A family of explicit exactly solvable examples is developed which demonstrates the effects of large-scale intermittency at any positive time through simple formulae for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection- diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulae for the quantum-harmonic oscillator. These explicit formulae also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.

MSC:

76F10 Shear flows and turbulence
76R50 Diffusion
76M35 Stochastic analysis applied to problems in fluid mechanics
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