Deflection-Flipping Waves in a Symmetric Channel with Spatially Periodic Expansions and Contractions(Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid mechanics)
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Bifurcations of flow in a two-dimensional symmetric channel with suddenly expanded sections arranged periodically and its relaxation processes are investigated numerically. Linear stability analysis revealed that the flow is subject to both a symmetry-breaking pitchfork bifurcation leading to a steady deflection and a Hopf bifurcation leading to an oscillation similar to the Tollmien-Schlichting wave. We observed two kinds of propagating waves in the relaxation to another bistable steady state, one of which is a fast wave being convected passively and the other a slow wave flipping flow deflections. It was confirmed that the deflection-flipping wave propagates downstream without decaying due to a self-sustaining mechanism of instability.