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A study of Taylor instability of superposed fluids

Eine Untersuchung der Taylor-Instabilität der Trennfläche zweier Medien

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Summary

A solution of hydrodynamic equations for the case of (Taylor) instability of the interface of two fluids of different but constant densities when accelerated from the heavier fluid to the lighter fluid is sought. After identifying the problem as one of singular perturbation, it is solved by the method of strained coordinates. A third order theory is presented. It is found that the ratio of the densities of the fluids has a significant effect on the stability or growth of the interface. Growth of the interface is found to depend also on the wave number and amplitude of initial disturbance. Stability criterion is calculated for different values of density ratio.

Zusammenfassung

Für eine sogenannte Taylor-Instabilität der Trennfläche zweier Medien wird eine Lösung der hydrodynamischen Gleichungen gegeben. Die beiden Flüssigkeiten besitzen hierbei unterschiedliche Dichte, und die Trennfläche wird vom dichteren zum dünneren Medium bewegt. Es liegt ein singuläres Störungsproblem vor, das dadurch gelöst wird, daß die Koordinaten in geeigneter Weise gestreckt werden. Es wird eine Theorie dritter Ordnung hergeleitet. Es ergibt sich, daß das Verhältnis der Dichten einen wesentlichen Einfluß auf die Stabilität der Trennfläche hat. Die Deformation der Trennfläche hängt von der Wellenzahl und der Amplitude der Anfangsstörungen ab. Das Stabilitätskriterium wird für verschiedene Dichteverhältnisse angegeben.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Madras, India

    T. Amaranath

  2. Department of Aeronautics, Indian Institute of Technology, Madras, India

    N. R. Rajappa

Authors
  1. T. Amaranath
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  2. N. R. Rajappa
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Amaranath, T., Rajappa, N.R. A study of Taylor instability of superposed fluids. Acta Mechanica 24, 87–97 (1976). https://doi.org/10.1007/BF01175759

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  • DOI: https://doi.org/10.1007/BF01175759

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