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On the stability of a falling liquid curtain. (English) Zbl 1015.76027
Summary: We investigate the stability of a falling liquid curtain. The sheet of liquid is assumed to be two-dimensional, driven by gravity and influenced by a compressible cushion of air enclosed on one side of the curtain. The linear stability problem is formulated in the form of integro-differential eigenvalue problem. Although experimental efforts have consistently reported a peak in the low-frequency range of the spectrum, the linear stability results do not show instabilities at these frequencies. However, a multimodal approach combined with a projection onto low-frequency modes reveals a dominant and robust instability feature that is in good agreement with experimental measurements. This instability manifests itself as a wave packet, consisting of a linear superposition of linear global modes, that travels down the curtain and causes a strong pressure signal in the enclosed air cushion.

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
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