One-point modelling of rapidly deformed homogeneous turbulence

Abstract

One-point turbulence models are important tools for engineering analysis. A good model should have a viscoelastic character, predicting turbulent stresses proportional to the mean strain rate for slow deformations and stresses determined by the amount of strain for rapid distortions. Our goal is to build a one-point turbulence model with this character, and this requires a one-point model for rapid distortions. Here it is shown that the turbulent stresses introduced by Osborne Reynolds do not, by themselves, provide an adequate tensorial base for one-point modelling of rapidly distorted turbulence because they do not carry critical information about the turbulence structure. The deficiency is shown to be most pronounced in flows subjected to strong mean rotation. Additional one-point tensors that do carry the missing information are introduced, and the complexities of a model that would have an adequate tensorial base are assessed. A new type of one-point structure-based turbulence model that overcomes the basic deficiency of Reynolds-stress transport models, but without the excessive complexity of multiple tensor variables, is then described. The ideas behind the rapid distortion version of this new model are presented, along with results for some special cases.