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

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

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.

Citation

Ghosh, S., Usha, R., Govindarajan, R., & Tammisola, O. (2017). Inviscid instability of two-fluid free surface flow down an incline. Meccanica, 52(4-5), 955-972. https://doi.org/10.1007/s11012-016-0455-6

• 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
• DOI: https://doi.org/10.1007/s11012-016-0455-6
• Keywords: Free surface flow; Linear stability analysis; Inviscid instability; Wave interaction
• Public URL: https://nottingham-repository.worktribe.com/output/795662
• Publisher URL: https://link.springer.com/article/10.1007/s11012-016-0455-6
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11012-016-0455-6