A model based on mass conservation properties is developed for shock-wave/boundarylayer interactions (SWBLIs), aimed at reconciling the observed great diversity in flow organization documented in the literature, induced by variations in interaction geometry and aerodynamic conditions. It is the basis for a scaling approach for the interaction length that is valid independent of the geometry of the flow (considering compression corners and incident-reflecting shock interactions). As part of the analysis, a scaling argument is proposed for the imposed pressure jump that depends principally on the free-stream Mach number and the flow deflection angle. Its interpretation as a separation criterion leads to a successful classification of the separation states for turbulent SWBLIs (attached, incipient or separated). In addition, the dependence of the interaction length on the Reynolds number and the Mach numbers is accounted for. A large compilation of available data provides support for the validity of the model. Some general properties on the state of the flow are derived, independent of the geometry of the flow and for a wide range of Mach numbers and Reynolds numbers.
In this paper we describe a new strategy for combining orientation adaptive filtering and edge preserving filtering. The filter adapts to the local orientation and avoids filtering across borders. The local orientation for steering the filter will be estimated in a fixed sized window which never contains two orientation fields. This can be achieved using generalized Kuwahara filtering. This filter selects from a set of fixed sized windows that contain the current pixel, the orientation of the window with the highest anisotropy. We compare our filter strategy with a multi-scale approach. We found that our filter strategy has a lower complexity and yields a constant improvement of the SNR.
Streamline patterns and their bifurcations in two-dimensional Navier-Stokes flow of an incompressible fluid near a non-simple degenerate critical point close to a stationary wall are investigated from the topological point of view by considering a Taylor expansion of the velocity field. Using a five-order normal form approach we obtain a much simplified system of differential equations for the streamlines. Careful analysis of the simplified system gives possible bifurcations for non-simple degeneracies of codimension three. Three heteroclinic connections from three on-wall separation points merge at an in-flow saddle point to produce two separation bubbles with opposite rotations which occur only near a non-simple degenerate critical point. The theory is applied to the patterns and bifurcations found numerically in the studies of Stokes flow in a double-lid-driven rectangular cavity.
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