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Super free fall
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DOI：10.1017/S0022112009992424.png)
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Abstract
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The free fall of a liquid mass through vertical tubes with a weakly increasing cross-section induces an acceleration of the upper liquid interface larger than gravity. The phenomenon is well described by a one-dimensional inviscid model. The super acceleration of the upper interface comes from the additional positive pressure gradient caused by the expanding geometry, which adds to the gravity body force. A perturbative expansion of this base solution further accounts for the interface shape and stability. In particular, the positive pressure gradient at the interface makes it unstable, forming a concentrated 'nipple' on top of the essentially flat base solution. We discuss the possible connexion of these findings with the problem of wave breaking in free surface flows.
Keywords:
free surface flows
stability Rayleigh-Taylor instability
tubes superacceleration
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