Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H(p) of passive scalar advected by two kinds of random velocity above are determined for structure function up to p = 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H(p)'s obtained by the multi-dimensional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity