Turbulent mixing of a passive scalar

We review theory and experiment for the mixing of a passive scalar by a turbulent flow. If the scalar fluctuations are maintained steady by a uniform large scale gradient, the one-point distribution function of the scalar has exponential tails; a property readily explained in terms of the Lagrangian Green's function in path integral form. For higher order correlations and separations within the scaling regime of the turbulence itself, new anomalous exponents have been derived from the Hopf equation, expressing the stationarity of the correlation functions. We concentrate on the 3-point correlator whose scaling exponent is very different from Kolmogorov or mean field theory, and for which laboratory experiments can be compared with numerical solutions of the Hopf equation, and analytic theory based on representations of the group SL(2).

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