A unified approach to the various formulations of the one-dimensional-turbulence model

The One-Dimensional Turbulence (ODT) model has been successfully applied as a stand-alone model for predicting turbulence statistics in both nonreacting and reacting flows. There are several formulations of the model in the literature, and most of the variable-density formulations do not clearly distinguish the governing equations from the numerical algorithm used to solve them, resulting in confusion about exactly what form of the governing equations are being solved in the various existing ODT formulations. This paper presents a derivation of the governing equations for the various forms of the ODT model in the literature, and presents some suggestions for possible improvement to the present formulations. In addition, eddy selection and implementation are discussed in the context of the various forms of the governing equations to illustrate differences between various approaches.