TRANSIENT-BEHAVIOR OF MIXING INDUCED BY A RANDOM VELOCITY-FIELD

We present a new analysis for Corrsin's hypothesis. We show this hypothesis is the leading term contribution in a renormalization group perturbation expansion. We present the exact results of a nonlinear dynamic equation obtained from Corrsin's hypothesis. The macroscopic dispersion induced by a random velocity field on all timescales is studied. Due to the nonlinearity of the governing equation, the transient growth rate of the mixing layer is nonfractal even for a fractal velocity field. For a velocity field with, an exponentially decaying correlation function, the comparisons of the exact results under Corrsin's approximation with the results from the linear and quasi-linear theories are presented. The results from Corrsin's hypothesis show that for an exponentially decaying correlation function with variance sigma, the longitudinal asymptotic dispersion coefficient is proportional to sigma(2) for Small values of sigma and proportional to sigma for large values of sigma. This result is further confirmed by a mean field approximation.