Turbulence model form errors in separated flows

In turbulence modeling, model form errors are introduced in the prediction of the Reynolds stresses through the Boussinesq hypothesis and other modeling choices, such as the specific form of the eddy viscosity. These linear eddy viscosity models have known points of failure in flows that feature significant complexity, such as separated flows. In this work, an implied models approach is used to better understand the sources and dynamics of model form error in separated flows through a priori analysis, focusing on the Boussinesq hypothesis using exact inputs for determining the eddy viscosity. In the implied models approach, a transport equation is derived for the model error through the transport equation implied by the model for the quantity of interest; that is, the Reynolds stresses in this work. A boundary layer over a flat plate with a statistically stationary separation bubble is analyzed and shown to have two error modes corresponding to the qualitative behavior of turbulent wall-bounded and turbulent free-shear model form errors. The wall-bounded mode is observed sufficiently upstream of the separation bubble, and the free-shear mode is observed near and within the separation bubble, with a superposition of these two modes observed in the intermediate regions. These results indicate on the one hand a complex picture of model error that changes through the flow but on the other hand a simple picture of model error that comprises elements of canonical flows. Therefore, calibration of turbulence models against simpler canonical flows can capture the main modes of model failure in more complex flows.