Linear stability of equatorial zonal flows

Journal of Physical Oceanography

Volumn 26, Issue 4, 1996, Pages 601-621

  Proehl, Jeffrey A ^a  

^a DARTMOUTH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATORIAL ZONAL FLOW; FLOW MODELLING; INSTABILITY; WAVE OVER-REFLECTION;

EID: 0029903834     PISSN: 00223670     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0485(1996)026<0601:LSOEZF>2.0.CO;2     Document Type: Article

References (58)

1. Acheson, D. J., 1976: On over-reflexion. J. Fluid Mech., 77, 433-472.
2. Andrews, D. G., and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 2031-2048.
3. _, and _, 1978: Generalized Eliassen-Palm and Charney-Drazin theorems for waves on axisymmetric mean flows in compressible atmospheres. J. Atmos. Sci., 35, 175-185.
4. _, J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.
5. Booker, J. R., and F. P. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27, 513-539.
6. Boyd, J. P., 1976: The noninteraction of waves with the zonally averaged on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum. J. Atmos. Sci., 33, 2285-2291.
7. Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc., 92, 325-334.
8. Cox, M. D., 1980: Generation and propagation of 30-day waves in a numerical model of the Pacific. J. Phys. Oceanogr., 10, 1168-1186.
9. Cullum, J., and R. A. Willoughby, 1986: A practical procedure for computing eigenvalues for large sparse nonsymmetric matricies. Large Scale Eigenvalue Problems. J. Cullum and R. A. Willoughby, Eds., 193-240.
10. Dickinson, R. E., and F. J. Clare, 1973: Numerical study of the unstable modes of a hyperbolic-tangent barotropic shear flow. J. Atmos. Sci., 30, 1035-1049.
11. Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 33-52.
12. Firing, E., C. Fenander, and J. Miller, 1981: Profiling current meter measurements from the NORPAX Hawaii-to-Tahiti Shuttle Experiment. Data Rep. 39, H16-81-2, Hawaii Inst. of Geophys., University of Hawaii, Honolulu, 146 pp.
13. Fukamachi, Y., 1992: Instability of density fronts in layer and continuously stratified models. Ph.D. dissertation, Nova University, 116 pp.
14. Geisler, J. E., and R. E. Dickinson, 1974: Numerical study of an interacting Rossby wave and barotropic zonal flow near a critical level. J. Atmos. Sci., 31, 946-955.
15. Harvey, R. R., and W. C. Patzert, 1976: Deep current measurements suggest long waves in the equatorial Pacific. Science, 193, 883-884.
16. Hayashi, Y. Y., and W. R. Young, 1987: Stable and unstable shear modes of rotating parallel flows in shallow water. J. Fluid Mech., 184, 477-504.
17. Holm, D. D., and B. D. Long, 1989: Lyapunov stability of ideal stratified fluid equilibria in hydrostatic balance. Nonlinearity, 2, 23-35.
18. Howard, L. N., and P. G. Drazin, 1964: On the instability of parallel flow of inviscid fluid in a rotating system with variable Coriolis parameter. Stud. Appl. Math., 43, 83-99.
19. Jones, W. L., 1967: Propagation of internal gravity waves in fluids with shear flow and rotation. J. Fluid Mech., 30, 439-448.
20. _, 1968: Reflexion and stability of waves in stably stratified fluids with shear flow: A numerical study. J. Fluid Mech., 34, 609-624.
21. Legeckis, R., 1977: Long waves in the eastern equatorial Pacific Ocean: A view from a geostationary satellite. Science, 197, 1179-1181.
22. Lindzen, R. S., 1974: Stability of a Helmholtz velocity profile in a continuously stratified, infinite Boussinesq fluid - Applications to clear air turbulence. J. Atmos. Sci., 31, 1507-1514.
23. _, 1988: Instability of plane parallel shear flow. Pure Appl. Geophys., 126(1), 103-121.
24. _, and K. K. Tung, 1978. Wave over-reflection and shear instability. J. Atmos. Sci., 35, 1626-1632.
25. _, and A. J. Rosenthal, 1983: Instabilities in a stratified fluid having one critical level. Part III: Kelvin-Helmholtz instabilities as over-reflected waves. J. Atmos. Sci., 40, 530-542.
26. _, and J. W. Barker, 1985: Instability and wave over-reflection in stably stratified shear flow. J. Fluid Mech., 151, 189-217.
27. _, B. Farrell, and K. K. Tung, 1980: The concept of wave over-reflection and its application to baroclinic instability. J. Atmos. Sci., 37, 44-63.
28. Lipps, F. B., 1963: Stability of jets in a divergent barotropic fluid. J. Atmos. Sci., 20, 120-129.
29. Long, B. D., 1987: On the stability of steady ideal fluid flow. Ocean Modelling (Unpublished manuscript), 73, 1-6.
30. Luther, D. S., and E. S. Johnson, 1990: Eddy energetics in the upper equatorial Pacific during the Hawaii-to-Tahiti shuttle experiment. J. Phys. Oceanogr., 20, 913-944.
31. 1/2-layer model. Progress in Oceanography, Vol. 29, Pergamon, 61-132.
32. McPhaden, M. J., and P. Ripa, 1990: Wave-mean flow interactions in the equatorial ocean. Annu. Rev. Fluid Mech., 22, 167-205.
33. _, J. A. Proehl, and L. M. Rothstein, 1986: The interaction of equatorial Kelvin waves with realistically sheared zonal currents. J. Phys. Oceanogr., 16, 1499-1515.
34. _, _, and _, 1987: On the structure of low-frequency equatorial waves. J. Phys. Oceanogr., 17, 1555-1559.
35. Miles, J. W., 1957: On the reflection of sound at an interface of relative motion. J. Acoust. Soc. Amer., 29, 226-228.
36. Nakamura, N., 1988: Scale selection of baroclinic instability - Effects of stratification and nongeostrophy. J. Atmos. Sci., 45, 3253-3267.
37. Philander, S. G. H., 1976: Instabilities of zonal equatorial currents. J. Geophys. Res., 81, 3725-3735.
38. _, 1978: Instabilities of zonal equatorial currents, 2. J. Geophys. Res., 83, 3679-3682.
39. Plumb, R. A., 1983: A new look at the energy cycle. J. Atmos. Sci., 40, 1669-1688.
40. Proehl, J. A., 1988: Equatorial wave-mean flow interaction: The long Rossby waves. Ph.D. dissertation, University of Washington, 185 pp.
41. _, 1990: Equatorial wave-mean flow interactions: The long Rossby waves. J. Phys. Oceanogr., 20, 274-294.
42. _, 1991: On the numerical dispersion of equatorial waves. J. Geophys. Res., 96, 16 929-16 934.
43. Qiao, L., and R. H. Weisberg, 1995: Tropical instability wave kinematics: Observations from the tropical instability wave experiment. J. Geophys. Res., 100, 8677-8694.
44. Ripa, P., 1983: General stability conditions for zonal flows in a one-layer model on a β-plane or the sphere. J. Fluid Mech., 126, 463-489.
45. _, 1986: Flow stability in equatorial oceans. Further Progress in Equatorial Oceanography: A Report of the U.S. TOGA Workshop on the Dynamics of the Equatorial Oceans., Honolulu, August 11-15, 1986. E. J. Katz and J. M. Witte, Eds., Nova University Press, 351-356.
46. _, 1989: Rays in the equatorial ocean. Trop. Ocean-Atmos. Newsltr., 48, 1-5.
47. _, 1990: Positive, negative and zero wave energy and the flow stability problem, in the Eulerian and Lagrangian descriptions. Pure Appl. Geophys., 133, 713-732.
48. _, 1991: General stability conditions for a multi-layer model. J. Fluid. Mech., 222, 119-137.
49. Rothstein, L. M., M. J. McPhaden, and J. A. Proehl, 1988: Wind forced wave-mean flow interactions in the equatorial waveguide. Part I: The Kelvin wave. J. Phys. Oceanogr., 18, 1435-1446.
50. Stone, P. H., 1966: On non-geostrophic baroclinic stability. J. Atmos. Sci., 23, 390-400.
51. _, 1970: On non-geostrophic baroclinic stability. Part II. J. Atmos. Sci., 27, 721-726.
52. Taft, B. A., B. M. Hickey, C. Wunsch, and D. J. Baker Jr., 1974: Equatorial undercurrent and deeper flows in the central Pacific. Deep-Sea. Res., 21, 403-430.
53. Tai, C. K., 1983: Over-reflection and instability. Dyn. Atmos. Oceans, 7, 147-165.
54. Takehiro, S. I., and Y. Y. Hayashi, 1992: Over-reflection and shear instability in a shallow water model. J. Fluid Mech., 236, 259-279.
55. Weisberg, R. H., 1986: Observations pertinent to instability waves in the equatorial oceans. Further Progress in Equatorial Oceanography: A Report of the U.S. TOGA Workshop on the Dynamics of the Equatorial Oceans., Honolulu, August 11-15, 1986, E. J. Katz and J. M. Witte, Eds., Nova University Press, 335-350.
56. _, and T. J. Weingartner, 1988: Instability waves in the equatorial Atlantic Ocean. J. Phys. Oceanogr., 18, 1641-1657.
57. _, A. M. Horigan, and C. Colin, 1979: Equatorially trapped Rossby-gravity wave propagation in the Gulf of Guinea. J. Mar. Res., 37, 67-87.
58. Wyrtki, K., and B. Kilonsky, 1984: Mean water and current structure during the Hawaii-to-Tahiti Shuttle Experiment. J. Phys. Oceanogr., 14, 242-254.