Non-Gaussian Extension of the Sparse-Direct Interaction Perturbation

An extension of the Sparse Direct-Interaction Perturbation (SDIP) technique is investigated with the objective to predict the theoretical Obukhov-Corrsin constant consistently with experimental observation. This extension involves relaxing the assumption that, in the case of a turbulent passive scalar field, third-order correlations between Non-Direct-Interaction (NDI) fields are identitically zero. This is the leading order term in the traditional SDIP expansion. The theory of invariants and dimensional analysis provide a functional form of the retained third-order correlation, and integrability of its Fourier modes produces constraints on the remaining unknown parameters. To close the approximation, these unknown parameters are determined from direct numerical simulation of actively forced turbulent mixing. The resulting closure is then used to estimate the scalar spectral constant.