Shear instability of two-fluid parallel flow in a Hele-Shaw cell

Physics of Fluids

Volumn 9, Issue 11, 1997, Pages 3267-3274

  Gondret, P ^a   Rabaud, M ^a  

^a Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001232837     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869441     Document Type: Article

References (19)

1. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961).
2. J. W. Miles, "On the generation of surface waves by shear flow," J. Fluid Mech. 3, 185 (1957).
3. S. A. Thorpe, "Experiment on the instability of stratified shear flows: immiscible fluid," J. Fluid Mech. 39, 25 (1969).
4. O. Pouliquen, J.-M. Chomaz, and P. Huerre, "Propagating Holmboe waves at the interface between two immiscible fluids," J. Fluid Mech. 226, 277 (1994).
5. M. Rabaud and Y. Couder, "A shear-flow instability in a circular geometry," J. Fluid Mech. 136, 291 (1983).
6. P. Barthelet, F. Charru, and J. Fabre, "Experimental study of interfacial long wave in a two-layer shear flow," J. Fluid Mech. 303, 25 (1995).
7. P. Gondret, N. Rakotomalala, M. Rabaud, D. Salin, and P. Watzky, "Viscous parallel flows in finite aspect ratio Hele-Shaw cell: Analytical and numerical results," Phys. Fluids 9, 1841 (1997).
8. H. J. S. Hele Shaw, "On the motion of a viscous fluid between two parallel plates," Nature (London) 58, 34 (1898).
9. H. Darcy, Les fontaines publiques de la ville de Dijon: distribution d'eau et filtrage des eaux (Victor Dalmont, Paris, 1856).
10. J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
11. S. Orszag, "Accurate solution of the Orr-Sommerfel stability equation," J. Fluid Mech. 50, 689 (1971).
12. T. Tatsumi and T. Yoshimura, "Stability of the laminar flow in a rectangular duct," J. Fluid Mech. 212, 437 (1990).
13. C. S. Yih, "Instability due to viscous stratification," J. Fuid Mech. 27, 337 (1967).
14. T. J. Hanratty, "Interfacial instabilities caused by air flow over a thin liquid layer," in Waves on Fluid Interfaces (Academic, New York, 1983).
15. J. R. D. Francis, "Wave motions and the aerodynamics drag on a free oil surface, "Philos. Mag. 45, 694 (1954).
16. M. Zeybek and Y. C. Yortsos, "Long waves in parallel flow in Hele-Shaw cells," Phys. Rev. Lett. 67, 1430 (1991).
17. M. Zeybek and Y. C. Yortsos, "Parallel flow in Hele-Shaw cells," J. Fluid Mech. 241, 421 (1992).
18. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1932), p. 582.
19. S. B. Savage and K. Hutter, "The motion of a finite mass of granular materials down a rough incline," J. Fluid Mech. 199, 177 (1989).