Realizability of dynamic subgrid-scale stress models via stochastic analysis

Large eddy simulations involving dynamic subgrid-scale stress models reveal questions regarding the formulation of dynamic stress models. The dynamic Smagorinsky model, for example, yields large fluctuations and can easily become unstable. An analysis explains the reasons for these problems: it is shown that the dynamic Smagorinsky model involves an incorrect scale dependence which may produce significant errors leading to instabilities. These problems are addressed by analyzing the implications of the realizability constraint, this means the constraint that an acceptable turbulence closure model be based on the statistics of a velocity field that is physically achievable or realizable. The realizable dynamic stress models obtained have strong theoretical support: these models are the result of a well based systematic development of stress models. From a practical point of view, the realizable dynamic stress models obtained have the advantage that they do not support the development of instabilities due to possibly huge model errors. It is also shown that the consideration of nonlinear dynamic stress models further improves the accuracy of simulations.