Modeling of self-excited wake oscillations by amplitude equations

Abstract The purpose of this overview is to show the utility of simple amplitude equations for the modeling of various vortex-shedding phenomena in bluff-body (cylinder) wakes. After a review of global modes that leads to the physical concept of local self-excited oscillators acting as “generators” of Karman vortices in the near wake, the characterization of the vortex street by a single Stuart-Landau oscillator is discussed. The success beyond expectation of this model as well as the problems associated with it are documented. Among them, we focus on the neglect of spatial structure in the simple temporal Stuart-Landau model. The role of spatial structure in the streamwise direction is highlighted by a short discussion of the effect of feedback control, while in the last part of the paper the model is extended to include the spanwise structure of vortex shedding, in particular the effect of the cylinder ends.

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