Dual Theory of Turbulent Mixing

We present an exact analytic solution for incompressible turbulent mixing described by 3D NS equations, with a passive scalar (concentration, temperature, or other scalar field) driven by the turbulent velocity field. Using our recent solution of decaying turbulence in terms of the Euler ensemble, we represent the correlation functions of a passive scalar as statistical averages over this ensemble. The statistical limit, corresponding to decaying turbulence, can be computed in quadrature. We find the decay spectrum and the scaling functions of the pair correlation and match them with physical and real experiments.