Imperfect supercritical bifurcation in a three-dimensional turbulent wake

Abstract : The turbulent wake of a square-back body exhibits a strong bimodal behavior. The wake randomly undergoes symmetry-breaking reversals between two mirror asymmetric steady modes [reflectional symmetry-breaking (RSB) modes]. The characteristic time for reversals is about 2 or 3 orders of magnitude larger than the natural time for vortex shedding. Studying the effects of the proximity of a ground wall together with the Reynolds number, it is shown that the bimodal behavior is the result of an imperfect pitchfork bifurcation. The RSB modes correspond to the two stable bifurcated branches resulting from an instability of the stable symmetric wake. An attempt to stabilize the unstable symmetric wake is investigated using a passive control technique. Although the controlled wake still exhibits strong fluctuations, the bimodal behavior is suppressed and the drag reduced. This promising experiment indicates the possible existence of an unstable solution branch corresponding to a reflectional symmetry preserved (RSP) mode. This work is encouraging to develop a control strategy based on a stabilization of this RSP mode to reduce mean drag and lateral force fluctuations.
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Olivier Cadot, Antoine Evrard, Luc Pastur. Imperfect supercritical bifurcation in a three-dimensional turbulent wake. Physical Review Online Archive (PROLA), American Physical Society, 2015, pp.063005. ⟨10.1103/PhysRevE.91.063005⟩. ⟨hal-01164472⟩

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