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Acta Mechanica Sinica
Published in: Acta Mechanica Sinica 6/2016

30-09-2016 | Research Paper

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

Authors: Jiebin Liu, Jifu Zhou

Published in: Acta Mechanica Sinica | Issue 6/2016

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Abstract

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.
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Literature
1.
Mcanally, W.H., Friedrichs, C., Hamilton, D., et al.: Management of fluid mud in estuaries, bays, and lakes. I: present state of understanding on character and behavior. J. Hydraul. Eng. 133, 9–22 (2007)
2.
Mehta, A.J.: Understanding fluid mud in a dynamic environment. Geo Mar. Lett. 11, 113–118 (1991)CrossRef
3.
Parker, W.R., Kirby, R.: Time dependent properties of cohesive sediment relevant to sedimentation management-european experience. In: Estuarine Comparisons, Oregon, 573–589 (1982)
4.
Zhao, Z.: Transformation of waves over fluid mud beds. Mar. Sci. Bull. 12(1), 1–9 (1993) (in Chinese)
5.
Mehta, A.J.: On estuarine cohesive sediment suspension behavior. J. Geophys. Res. 94, 14303–14314 (1989)CrossRef
6.
Gade, H.G.: Effects of a nonrigid, impermeable bottom on plane surface waves in shallow water. J. Mar. Res. 16, 61–82 (1958)
7.
Dalrymple, R.A., Liu, P.L.F.: Waves over soft muds: a two-layer fluid model. J. Phys. Oceanogr. 8, 1121–1131 (1978)CrossRef
8.
Sakakiyama, T., Bijker, E.W.: Mass-transport velocity in mud layer due to progressive waves. J Waterw. Port Coast. Ocean Eng. 115, 614–633 (1989)CrossRef
9.
10.
Chiu-On, N.: Water waves over a muddy bed: a two-layer stokes’ boundary layer model. Coast. Eng. 40, 221–242 (2000)CrossRef
11.
Hu, Y., Guo, X., Lu, X., et al.: Idealized numerical simulation of breaking water wave propagating over a viscous mud layer. Phys. Fluids 24, 802–805 (2012)
12.
Keulegan, G.H.: Interfacial instability and mixing in stratified flows. J. Res. Natl. Bureau Stand. 43, 487–500 (1949)CrossRef
13.
Kundu, P.K., Cohen, I.M., Dowling, D.: Fluid Mechanics. Academic Press, New York (2012)MATH
14.
Betchov, R.: Stability of a shear layer between parallel streams. Phys. Fluids 6, 1391–1396 (1963)CrossRefMATH
15.
16.
17.
Liu, J., Zhou, J.: The instability of water–mud interface in viscous two-layer flow with large viscosity contrast. Theor. Appl. Mech. Lett. 4, 062007 (2014)
18.
19.
20.
21.
22.
Yiantsios, S.G., Higgins, B.G.: Linear stability of plane poiseuille flow of two superposed fluids. Phys. Fluids 31, 3225–3238 (1988)MathSciNetCrossRefMATH
23.
Hooper, A.P., Boyd, W.G.C.: Shear-flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. 179, 201–225 (1987)CrossRefMATH
24.
25.
Thorpe, S.A.: A method of producing a shear flow in stratified fluid. J. Fluid Mech. 32, 693–704 (1968)CrossRef
26.
Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge (2004)CrossRefMATH
27.
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Courier Dover Publications, Mineola (2013)MATH
28.
Boomkamp, P.: Classification of instabilities in parallel two-phase flow. Int. J. Multiph. Flow 22, 67–88 (1996)CrossRefMATH
29.
Trefethen, L.N.: Spectral Methods in Matlab. Society for Industrial & Applied Mathematics, Philadelphia (2000)CrossRefMATH
30.
Issa, R.I., Ahmadi-Befrui, B., Beshay, K.R., et al.: Solution of the implicitly discretised reacting flow equations by operator-splitting. J. Comput. Phys. 93, 388–410 (1991)
31.
32.
Youngs, D.L.: Time-dependent multi-material flow with large fluid distortion. Numer. Methods Fluid Dyn. 24, 273–285 (1982)MATH
33.
Valluri, P., Náraigh, L.Ó., Ding, H., et al.: Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 656, 458–480 (2010)
34.
Boeck, T., Li, J., López-Pagés, E., et al.: Ligament formation in sheared liquid-gas layers. Theoret. Comput. Fluid Dyn. 21, 59–76 (2007)CrossRefMATH
35.
Fringer, O.B.: Numerical simulations of breaking interfacial waves. [Ph.D. Thesis], Stanford University, America (2003)
Metadata
Title
Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers
Authors
Jiebin Liu
Jifu Zhou
Publication date
30-09-2016
Publisher
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Published in
Acta Mechanica Sinica / Issue 6/2016
Print ISSN: 0567-7718
Electronic ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-016-0599-6

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