Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

Abstract

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer–Ohkitani–Yamada (GOY) shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She–Leveque velocity field, introduced by She, et al. We observe that extended self-similarity scaling exponents H(p)/H(2) of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.