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STABILIZING EFFECT OF LONGITUDINAL WALL OSCILLATION ON 2D OR 3D WAVE IN THE PLANE POISEUILLE FLOW

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Stability of the 2D channel flow with longitudinal wall oscillation is investigated by the Floquet theory. Since this flow has time periodicity, the ordinary Orr-Sommerfeld equation cannot be applied. Thus, using a small disturbance, which is modal type but has time dependence in only amplitude, time-dependent Orr-Sommerfeld equation is derived and is applied for the Floquet analysis. From this analysis, the stable region is found in the parameter space in spite of the supercritical condition. Furthermore, this stabilizing effect is more remarkable for 2D disturbance than for 3D one. This means that, due to the longitudinal wall oscillation, 3D disturbance is dominant even though the flow is 2D.

Author(s):

Takashi Atobe    
Japan Aerospace Exploration Agency
Japan