科研成果详情

We have developed a quantitative theory for the mixing of fluids induced by a random velocity field. The theory provides a quantitative prediction for the growth of the mixing region. There are three distinct regimes for the asymptotic scaling behavior of the mixing layer, depending on the asymptotic behavior of the random velocity field. The asymptotic diffusion is Fickian when the correlation function of the random field decays rapidly at large length scales. Otherwise the asymptotic diffusion is non-Fickian. The scaling behavior of the mixing layer driven by a general random velocity field is determined over all length scales. Our results show that, in general, the scaling exponent of the mixing layer is nonFickian on all finite length scales. In the Lagrangian picture, due to the non-linearity of the effective dynamical equation derived from the Taylor diffusion theory, the mixing layer is not a fractal even if the random velocity field is a fractal.