Turbulence Model Form Errors in a Statistically Stationary Separation Bubble

Model form error arises from physical assumptions made in constructing models either to reduce the physical complexity or to model physical processes that are not well understood. In turbulence modeling, specifically Reynolds stress modeling, model form errors result from 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 introduce complex strain, 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. 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. 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, which have previously been analyzed. These results indicate a complex picture of model error that changes through the flow but also that calibration of turbulence models against simpler canonical flows may capture the main modes of model failure.