Majda, Andrew J. The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions. (English) Zbl 0781.76047 Phys. Fluids, A 5, No. 8, 1963-1970 (1993). 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. Cited in 1 ReviewCited in 26 Documents MSC: 76F10 Shear flows and turbulence 76R50 Diffusion 76M35 Stochastic analysis applied to problems in fluid mechanics Keywords:Gaussian probability distribution functions; large-scale intermittency; advection-diffusion; quantum mechanical analogy; higher-order statistics; limiting probability distribution function PDFBibTeX XMLCite \textit{A. J. Majda}, Phys. Fluids, A 5, No. 8, 1963--1970 (1993; Zbl 0781.76047) Full Text: DOI References: [1] DOI: 10.1103/PhysRevLett.61.74 · doi:10.1103/PhysRevLett.61.74 [2] DOI: 10.1017/S0022112089001643 · doi:10.1017/S0022112089001643 [3] DOI: 10.1103/PhysRevLett.67.3507 · doi:10.1103/PhysRevLett.67.3507 [4] DOI: 10.1017/S0022112092004361 · Zbl 0825.76272 · doi:10.1017/S0022112092004361 [5] DOI: 10.1103/PhysRevLett.64.2370 · doi:10.1103/PhysRevLett.64.2370 [6] DOI: 10.1103/PhysRevLett.67.3519 · doi:10.1103/PhysRevLett.67.3519 [7] DOI: 10.1063/1.866832 · doi:10.1063/1.866832 [8] DOI: 10.1007/BF01089164 · Zbl 0724.76035 · doi:10.1007/BF01089164 [9] DOI: 10.1103/PhysRevLett.63.2657 · doi:10.1103/PhysRevLett.63.2657 [10] DOI: 10.1017/S0022112091003439 · Zbl 0729.76508 · doi:10.1017/S0022112091003439 [11] DOI: 10.1103/PhysRevLett.66.2984 · doi:10.1103/PhysRevLett.66.2984 [12] DOI: 10.1103/PhysRevLett.63.1962 · doi:10.1103/PhysRevLett.63.1962 [13] DOI: 10.1016/0010-2180(76)90035-3 · doi:10.1016/0010-2180(76)90035-3 [14] DOI: 10.1007/BF02161420 · Zbl 0703.76042 · doi:10.1007/BF02161420 [15] DOI: 10.1007/BF02099212 · Zbl 0754.76046 · doi:10.1007/BF02099212 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.