The conditional dissipation rate of an initially binary scalar in homogeneous turbulence

It is shown that a necessary and sufficient condition for the scalar dissipation rate, conditioned on scalar value φ, to be independent of φ is that the one-point scalar probability distribution function (pdf) is Gaussian. It is then shown that the amplitude mapping closure yields a closed-form, separable expression for the φ dependence of the conditional dissipation rate in the case of an initial double-delta scalar pdf. If the initial binary scalar field is located at φ=±1, the solution is exp{ − 2[erf−1(φ)]2}, a result that is strongly supported by earlier direct numerical simulations.