On Holmboe's instability for smooth shear and density profiles

Physics of Fluids

Volumn 17, Issue 8, 2005, Pages 1-8

  Alexakis, Alexandros ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY LAYER FLOW; DENSITY OF LIQUIDS; MATHEMATICAL MODELS; NUMERICAL METHODS; STABILITY;

LINEAR STABILITY; RICHARDSON NUMBER; STRATIFIED SHEAR FLOW;

SHEAR FLOW;

SHEAR FLOW;

EID: 24144438280     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2001567     Document Type: Article

References (36)

1. R. Rosner, A. Alexakis, Y. Young, J. Truran, and W. Hillebrand, "On the C/O enrichment of novae ejecta," Astrophys. J. ASJOAB 0004-637X 10.1086/338327 562, L177 (2002).
2. L. Armi and D. M. Farmer, "The flow of Mediterranean water through the Strait of Gibraltar," Prog. Oceanogr. POCNA8 0079-6611 10.1016/ 0079-6611(88)90055-9 21, 1 (1988).
3. T. Oguz, E. Ozsoy, M. A. Latif, H. I. Sur, and U. Unluata, "Modeling of hydraulically controlled exchanged flow in the Bosphorous Strait," J. Phys. Oceanogr. JPYOBT 0022-3670 10.1175/ 1520-0485(1990)020<0945:MOHCEF>2.0.CO;2 20, 945 (1990).
4. F. E. Sargent and G. H. Jirka, "Experiments on saline wedge," J. Hydraul. Eng. JHEND8 0733-9429 113, 1307 (1987).
5. S. Yoshida, M. Ohtani, S. Nishida, and P. F. Linden, "Mixing processes in a highly stratified river," Physical Processes in Lakes and Oceans, edited by J. Imberger (American Geophysical Union, Washington, D.C., 1998).
6. H. Helmholtz, "Ueber discontinuirliche Flüssigkeitsbewegungen," Wissenschaftliche Abhandlungen 3, 146 (1868).
7. Lord Kelvin, "Influence of wind and capillarity on waves in water supposed frictionless," in Mathematical and Physical Papers IV, Hydrodynamics and General Dynamics (Cambridge University Press, Cambridge, 1910), p. 76.
8. L. N. Howard, "Neutral curves and stability boundaries in stratified shear flow," J. Fluid Mech. JFLSA7 0022-1120 16, 333 (1963).
9. L. N. Howard and P. G. Drazin, "Hydrodynamic stability of parallel flow of inviscid fluid," Adv. Appl. Mech. AAMCAY 0065-2156 9, 1 (1966).
10. L. N. Howard and S. A. Maslowe, "Stability of stratified shear flows," Boundary-Layer Meteorol. BLMEBR 0006-8314 4, 511 (1973).
11. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
12. J. Holmboe, "On the behavior of symmetric waves in stratified shear layers," Geophys. Publ. 24, 67 (1962).
13. C. P. Caulfield, "Multiple linear instability of layered stratified shear flow," J. Fluid Mech. JFLSA7 0022-1120 258, 255 (1994).
14. S. P. Haigh and G. A. Lawrence, "Symmetric and non-symmetric Holmboe instabilities in an inviscid flow," Phys. Fluids PHFLE6 1070-6631 10.1063/1.870009 11, 1459 (1999).
15. G. A. Lawrence, F. K. Browand, and L. G. Redecopp, "The stability of a sheared density interface," Phys. Fluids A PFADEB 0899-8213 10.1063/1.858175 3, 2360 (1991).
16. P. G. Baines and H. Mitsudera, "On the mechanism of shear flow instabilities," J. Fluid Mech. JFLSA7 0022-1120 276, 327 (1994).
17. S. P. Hazel, "Numerical studies of the stability of inviscid shear flows," J. Fluid Mech. JFLSA7 0022-1120 51, 3261 (1972).
18. W. D. Smyth and W. R. Peltier, "The transition between Kelvin-Helmholtz and Holmboe instability; An investigation of the over-reflection hypothesis," J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1989)046<3698:TTBKAH>2.0.CO;2 46, 3698 (1989).
19. W. D. Smyth and W. R. Peltier, "Three-dimensional primary instabilities of a stratified dissipative, parallel flow," Geophys. Astrophys. Fluid Dyn.GAFDD3 0309-1929 52, 249 (1990).
20. W. D. Smyth, G. P. Klaasen, and W. R. Peltier, "Finite amplitude Holmboe waves," Geophys. Astrophys. Fluid Dyn. GAFDD3 0309-1929 43, 181 (1988).
21. W. D. Smyth and W. R. Peltier, "Instability and transition in in finite amplitude Kelvin-Helmholtz and Holmboe waves," J. Fluid Mech. JFLSA7 0022-1120 228, 387 (1991).
22. B. R. Sutherland, C. P. Caulfield, and W. R. Peltier, "Internal gravity generation and hydrodynamic instability," J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1994)051<3261:IGWGAH>2.0.CO;2 51, 3261 (1994).
23. W. D. Smyth and K. B. Winters, "Turbulence and mixing in Holmboe waves," J. Phys. Oceanogr. JPYOBT 0022-3670 10.1175/ 1520-0485(2003)33<694:TAMIHW>2.0.CO;2 33, 694 (2003).
24. F. K. Browand and C. D. Winant, "Laboratory observations of shear layer instability in a stratified fluid," Boundary-Layer Meteorol. BLMEBR 0006-8314 5, 67 (1973).
25. C. G. Koop, "Instability and turbulence in a stratified shear layer," Tech. Rep. USCAE 134, Department of Aerospace Engineering, University of South California (1976).
26. O. Pouliquen, J. M. Chomaz, and P. Huerre, "Propagating Holmboe waves at the interface between two immiscible fluids," J. Fluid Mech. JFLSA7 0022-1120 266, 277 (1994).
27. D. Z. Zhu and G. A. Lawrence, "Holmboe's instability in exchange flows," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S002211200000286X 429, 391 (2001).
28. A. M. Hogg and G. N. Ivey, "The Kelvin-Helmholtz to Holmboe instability transition in stratified exchange flows," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112002003397 477, 339 (2003).
29. N. Yonemitsu, G. E. Swaters, N. Rajaratnam, and G. A. Lawrence, "Shear instabilities in arrested salt wedge flows," Dyn. Atmos. Oceans DAOCDC 0377-0265 10.1016/0377-0265(95)00444-0 24, 173 (1996).
30. W. H. H. Banks, P. G. Drazin, and M. B. Zaturska, "On the normal modes of parallel flow of inviscid stratified fluid," J. Fluid Mech. JFLSA7 0022-1120 75, 149 (1976).
31. L. N. Howard, "A note on a paper of John Miles," J. Fluid Mech. JFLSA7 0022-1120 10, 509 (1961).
32. J. Miles, "On the stability of heterogeneous shear flow Part 2," J. Fluid Mech. JFLSA7 0022-1120 16, 209 (1963).
33. A. Alexakis, Y. Young, and R. Rosner, "Shear instability of fluid interfaces: A linear analysis," Phys. Rev. E PLEEE8 1063-651X 65, 26313 (2002).
34. A. Alexakis, Y. Young, and R. Rosner, "Weakly non-linear analysis of wind driven gravity waves," J. Fluid Mech. JFLSA7 0022-1120 505, 171 (2004).
35. S. M. Churilov, "Stability analysis of stratified shear flows with a monotonic velocity profile without inflection points," Izv. Akad. Nauk, Fiz. Atmos. Okeana IAKOEG 1023-6317 40, 725 (2004).
36. W. H. Press, B. P. Flannery, S. A. Teukolosky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, 1987).