Isotropic Turbulent Mixing under a Second-Order Chemical Reaction

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Abstract
The decay of a dynamically passive reactant in a stationary isotropic turbulent velocity field is investigated using the direct-interaction and (modified) quasi-normal closures. The reactant undergoes an isothermal second-order chemical reaction of single species. The dynamical behavior can be characterized approximately by the ratio of the Damkohler to the Peclet numbers. For slow reactions, only the convective mixing action is important and the closures can be applied without restrictions just as in the turbulent mixing case. For the closures to yield consistent results with fast reactions, the initial mean concentration must be at least twice the initial rms fluctuations. Then the effect of reactive nonlinear interaction is so meager that the two modes of closure make little difference. Otherwise, application of the closure schemes which evoke initial Gaussian conditions is unwarranted and thus presents a convergence difficulty. Simple decay expressions of the mean concentration and rms fluctuations are obtained for the asymptotic range of slow and fast reactions.