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Inviscid instability of two-fluid free surface flow down an incline

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Abstract

The inviscid temporal stability analysis of two-fluid parallel shear flow with a free surface, down an incline, is studied. The velocity profiles are chosen as piecewise-linear with two limbs. The analysis reveals the existence of unstable inviscid modes, arising due to wave interaction between the free surface and the shear-jump interface. Surface tension decreases the maximum growth rate of the dominant disturbance. Interestingly, in some limits, surface tension destabilises extremely short waves in this flow. This can happen because of the interaction with the shear-jump interface. This flow may be compared with a corresponding viscous two-fluid flow. Though viscosity modifies the stability properties of the flow system both qualitatively and quantitatively, there is qualitative agreement between the viscous and inviscid stability analysis when the less viscous fluid is closer to the free surface.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    Sukhendu Ghosh & R. Usha

  2. TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Narsingi, 500075, Hyderabad, India

    Rama Govindarajan

  3. Department of Engineering, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    O. Tammisola

Authors
  1. Sukhendu Ghosh
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  2. R. Usha
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  3. Rama Govindarajan
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  4. O. Tammisola
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Correspondence to R. Usha.

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Ghosh, S., Usha, R., Govindarajan, R. et al. Inviscid instability of two-fluid free surface flow down an incline. Meccanica 52, 955–972 (2017). https://doi.org/10.1007/s11012-016-0455-6

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  • DOI: https://doi.org/10.1007/s11012-016-0455-6

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