Dissipation Independence of the Inertial-Convective Range in a Passive Scalar Model

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Abstract
We establish by exact, nonperturbative methods a universality for the correlation functions in Kraichnan's “rapid-change” model of a passively advected scalar field. We show that the solutions for separated points in the convective range of scales are unique and independent of the particular mechanism of the scalar dissipation. Any nonuniversal dependences therefore must arise from the large length-scale features. The main step in the proof is to show that solutions of the model equations are unique when square integrable, even in the idealized case of zero diffusivity.