On the stability of a falling liquid curtain

Peter J. Schmid (1, 2) , D.S. Henningson (3)

1 LadHyX - Laboratoire d'hydrodynamique
2 University of Washington [Seattle]
3 Department of Mechanics, Royal Institute of Technology, S-10044 Stockholm, Sweden

The stability of a falling liquid curtain is investigated. The sheet of liquid is assumed 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 an 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.

Domains: Fluid mechanics [physics.class-ph]; Fluids mechanics [physics.class-ph]

Peter J. Schmid, D.S. Henningson. On the stability of a falling liquid curtain. Journal of Fluid Mechanics, 2002, 463 (july), pp.163-171. ⟨10.1017/s002211200200873x⟩. ⟨hal-01024914⟩