Most theoretical results about turbulent mixing have been obtained for ideal flows that are delta-correlated in time. As is often believed, those ideal flows are, with regard to mixing, very similar to real flows with a finite correlation time. However, recent results show that these two cases may differ considerably. In this article we study the effects of finite correlation time in a chaotic smooth statistically isotropic two-dimensional velocity field. As mixing is predominantly determined by the statistics of the stretching of material elements (e.g. lines “painted” onto a liquid), in this article we focus on the characteristics describing such stretching: finite-time Lyapunov exponents and the Lyapunov dimension. For these quantities, we derive analytical expressions as functions of the correlation time and the compressibility of the velocity field, and we investigate these expressions numerically. The results agree well with numerical results of other authors, and are useful for understanding several physical phenomena, e.g. patchiness of pollution spreading on an ocean and kinematic magnetic dynamos.
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