SCALAR INTERMITTENCY AND THE GROUND-STATE OF PERIODIC SCHRODINGER-EQUATIONS

Recent studies of a passive scalar diffusing in a rapidly fluctuating Gaussian distributed linear shear layer have demonstrated intermittenc y in the form of broad tails and non-symmetric limiting probability di stribution functions. In this paper the authors explore similar issues within the context of a large class of rapidly fluctuating bounded pe riodic shear layers. We compute the evolution of the moments by analog y to an N dimensional quantum mechanics problem. By direct comparison of an appropriate system of interacting and non-interacting quantum pa rticles, we illustrate that the role of interaction is to induce a low ering of the ground state energy, which implies that the scalar PDF wi ll have broader than Gaussian tails for all large, but finite times. W e demonstrate for the case of Gaussian random wave initial data involv ing a zero spatial mean, that the effect of this energy shift is to in duce diverging normalized flatness factors indicative of very broad ta ils. For the more general case with Gaussian random initial data invol ving a non-zero spatial mean, the distribution must approach that of a Gaussian at infinite times, as required by homogenization theory, but we show that the approach is highly non-uniform. In particular our ca lculation shows that the time required for the system to approach Gaus sian statistics grows like the square of the moment number. (C) 1997 A merican Institute of Physics.