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

Ghosh, Sukhendu; Usha, Ranganathan; Govindarajan, Rama; Tammisola, Outi

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Sukhendu Ghosh

Ranganathan Usha

Rama Govindarajan

Outi Tammisola


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.

Journal Article Type Article
Acceptance Date May 11, 2016
Online Publication Date May 25, 2016
Publication Date Mar 31, 2017
Deposit Date May 12, 2016
Publicly Available Date May 25, 2016
Journal Meccanica
Print ISSN 0025-6455
Electronic ISSN 1572-9648
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 52
Issue 4-5
Pages 955-972
Keywords Free surface flow; Linear stability analysis; Inviscid instability; Wave interaction
Public URL
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Additional Information The final publication is available at Springer via


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