\(\mathcal {M}_1(1)\) : Single Scalar in Homogeneous Turbulence

The CCK method is applied to the dynamics of a single, bounded scalar field in homogenous turbulence. Conditions are established for the image of a Gaussian to emerge as Cdf. Mapping equations for this case of a single scalar are derived and extended to two scalar fields to compute two-point correlations. Mapping equations are derived and closure models are discussed and illustrated with numerical results. Mapping methods for characteristic functions as image of Gaussian functions are developed and numerical examples are provided.