Towards a structure-based turbulence model

The author is developing a new type of turbulence model in which a new one-point quantity, the eddy structure tensor, carries information about the two-point structure of the turbulence. The model was motivated by the observation that conventional one-point turbulence models based only on the turbulent stresses do not predict the rapid changes in state that are found when anisotropic homogeneous turbulence is subjected to mean rotation, and hence are fundamentally incorrect for rotation. The model appears to give topologically correct predictions for the changes in stress state and structure state under all types of rapid distortions of homogeneous turbulence, which is something no other type of one-point model can do at this time. The definitions, model elements, and provisional model constants for homogeneous turbulence are given in these author’s working notes so that others may explore the model. The author is indebted to John Lumley for many inspirations and insights that underlie this work.