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Singularity dynamics in curvature collapse and jet eruption on a fluid surface

Nature volume 403, pages 401–404 (2000)Cite this article

Abstract

Finite-time singularities—local divergences in the amplitude or gradient of a physical observable at a particular time—occur in a diverse range of physical systems. Examples include singularities capable of damaging optical fibres and lasers in nonlinear optical systems1, and gravitational singularities2 associated with black holes. In fluid systems, the formation of finite-time singularities cause spray and air-bubble entrainment3, processes which influence air–sea interaction on a global scale4,5. Singularities driven by surface tension have been studied in the break-up of pendant drops6,7,8,9 and liquid sheets10,11,12. Here we report a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs. Inertial forces cause a collapse of the surface that leads to jet formation; our analysis, which includes surface tension effects, predicts that the surface profiles should be describable by a single universal exponent. These theoretical predictions correlate closely with our experimental measurements of a collapsing surface singularity. The solution can be generalized to apply to a broad class of singular phenomena.

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Figure 1: Surface wave collapses and resulting jets.
Figure 2: Comparison of theoretical and experimental surface profiles for 0.26 cm2 s-1 glycerin–water solution.
Figure 3: Surface depressions produced by surface waves of three different heights in 1.94 cm2 s-1 fluid.
Figure 4: Dependence of jet velocity on surface wave height for 1.94 cm2 s-1 fluid.

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Acknowledgements

We thank R. Rohde, M. Brenner, A. Bertozzi, J. Drake, T. Antonsen, E. Ott and J. Pyle for their input. D.P.L. is a Cottrell Scholar of the Research Corporation. This work was supported by the National Science Foundation.

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Authors and Affiliations

  1. Institute for Plasma Research and Department of Physics, The University of Maryland, College Park , 20742, Maryland, USA

    Benjamin W. Zeff, Benjamin Kleber & Daniel P. Lathrop

  2. The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Jay Fineberg

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  1. Benjamin W. Zeff
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  2. Benjamin Kleber
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  4. Daniel P. Lathrop
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Correspondence to Daniel P. Lathrop.

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Zeff, B., Kleber, B., Fineberg, J. et al. Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403, 401–404 (2000). https://doi.org/10.1038/35000151

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