Evolution and breakdown of Kelvin-Helmholtz billows in stratified compressible flows. Part I: Comparison of two- and three-dimensional flows

Journal of the Atmospheric Sciences

Volumn 53, Issue 22, 1996, Pages 3173-3191

  Fritts, David C ^a   Palmer, Teresa L ^a   Andreassen, Øyvind ^b   Lie, Ivar ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b NORWEGIAN DEFENCE RESEARCH ESTABLISHMENT FFI   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; FLUIDS STRATIFIED; INSTABILITY; THREE-DIMENSIONAL FLOW;

2D FLOW; 3D FLOW; ATMOSPHERIC FLOW; BILLOW; INSTABILITY; KELVIN-HELMHOLTZ WAVE; SHEAR FLOW; STRATIFIED FLOW;

EID: 0030390772     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0469(1996)053<3173:EABOKB>2.0.CO;2     Document Type: Review

References (78)

1. Acheson, D. J., 1990: Elementary Fluid Dynamics, Clarendon Press, 397 pp.
2. Andreassen, Ø., B. N. Andersen, and C. E. Wasberg, 1992: Gravity wave and convection interaction in the solar interior. Astr. Ap., 257, 763-769.
3. _, I. Lie, and C. E. Wasberg, 1994a: The spectral viscosity method applied to simulation of waves in a stratified atmosphere. J. Comput. Phys., 110, 257-273.
4. _, C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994b: Gravity wave breaking in two and three dimensions, 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res., 99, 8095-8108.
5. Atlas, D., J. I. Metcalf, J. H. Richter, and E. E. Gossard, 1970: The birth of CAT and microscale turbulence. J. Atmos. Sci., 27,903-913.
6. Bernal, L. P., and A. Roshko, 1986: Streamwise vortex structure in plane mixing layers. J. Fluid Mech., 170, 499-525.
7. Breidenthal, R., 1981: Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech., 109, 1-24.
8. Browand, F. K., and C. D. Winant, 1973: Laboratory observations of shear-layer instability in a stratified fluid. Bound.-Layer Meteor., 5, 67-77.
9. _, and T. Troutt, 1980: A note on spanwise structure in the two-dimensional mixing layer. J. Fluid Mech., 97, 771-781.
10. _, and _, 1985: The turbulent mixing layer: Geometry of large vortices. J. Fluid Mech., 158, 489-509.
11. Browning, K. A., 1971: Structure of the atmosphere in the vicinity of large-amplitude Kelvin-Helmholtz billows. Quart. J. Roy. Meteor. Soc., 97, 283-299.
12. _, and C. D. Watkins, 1970: Observations of clear air turbulence by high power radar. Nature, 227, 260-263.
13. Busse, F. H., and R. M. Clever, 1979: Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech., 91, 319-335.
14. Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, 1988: Spectral Methods in Fluid Dynamics. Springer, 567 pp.
15. Caulfield, C. P., and W. R. Peltier, 1994: Three dimensionalization of the stratified mixing layer. Phys. Fluids, 6, 3803-3805.
16. Clever, R. M., and F. H. Busse, 1992: Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech., 234, 511-527.
17. Corcos, G. M., and F. S. Sherman, 1976: Vorticity concentration and the dynamics of unstable free shear layers. J. Fluid Mech., 73, 241-246.
18. _, and S. J. Lin, 1984: The mixing layer: Deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech., 139, 67-95.
19. Coy, L., D. C. Fritts, and J. Weinstock, 1986: The Stokes drift due to vertically propagating internal gravity waves in a compressible atmosphere. J. Atmos. Sci., 43, 2636-2643.
20. Delisi, D. P., and G. M. Corcos, 1973: A study of internal waves in a wind tunnel. Bound.-Layer Meteor., 5, 121-137.
21. Drazin, P. G., 1958: The stability of a shear layer in an unbounded heterogeneous inviscid fluid. J. Fluid Mech., 4, 214-224.
22. _, 1970: Kelvin-Helmholtz instability of finite amplitude. J. Fluid Mech., 42, 321-335.
23. _, and L. N. Howard, 1966: Hydrodynamic stability of parallel flow of inviscid fluid. Adv. Appl. Mech., 9, 1-89.
24. _, and W. H. Reid, 1993: Hydrodynamic Stability. Cambridge University Press, 527 pp.
25. Fritts, D. C., 1982: Shear excitation of atmospheric gravity waves. J. Atmos. Sci., 39, 1936-1952.
26. _, 1984: Shear excitation of atmospheric gravity waves. Part II: Nonlinear radiation from a free shear layer. J. Atmos. Sci., 41, 524-537.
27. _, J. R. Isler, and Ø. Andreassen, 1994: Gravity wave breaking in two and three dimensions, 2. Three dimensional evolution and instability structure. J. Geophys. Res., 99, 8109-8123.
28. Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.
29. Gossard, E. E., J. H. Richter, and D. Atlas, 1970: Internal waves in the atmosphere from high-resolution radar measurements. J. Geophys. Res., 75, 3523-3536.
30. Hardy, K. R., R. J. Reed, and G. K. Mather, 1973: Radar, instrumented aircraft, and meteorological measurements of developing Kelvin-Helmholtz billows. Quart. J. Roy. Meteor. Soc., 99, 279-293.
31. Haurwitz, B., and B. Fogle, 1969: Waveforms in noctilucent clouds. Deep-Sea Res., 16, 85-95.
32. Helmholtz, H., 1868: On discontinuous movements of fluids (translated from German by F. Guthrie.) Philos. Mag., 36, 337-346.
33. Howard, L. N., 1961: Note on a paper of John W. Miles. J. Fluid Mech., 10, 509-512.
34. Isler, J. R., D. C. Fritts, and Ø. Andreassen, 1994: Gravity wave breaking in two and three dimensions, 3. Vortex breakdown and transition to isotropy. J. Geophys. Res., 99, 8125-8137.
35. Jimenez, J., 1983: A spanwise structure in the plane shear layer. J. Fluid Mech., 132, 319-336.
36. Kelly, R. E., and S. A. Maslowe, 1970: The nonlinear critical layer in a slightly stratified shear flow. Stud. Appl. Math., 49, 301-326.
37. Kelvin, W., 1971: The influence of wind on waves in water supposed frictionless. Philos. Mag., 42, 368-374.
38. Klaassen, G. P., and W. R. Peltier, 1985a: The evolution of finite amplitude Kelvin-Helmholtz billows in two spatial dimensions. J. Atmos. Sci., 42, 1321-1339.
39. _, and _, 1985b: The onset of turbulence in finite amplitude Kelvin-Helmholtz billows. J. Fluid Mech., 155, 1-35.
40. _, and _, 1991: The influence of stratification on secondary instability in free shear layers. J. Fluid Mech., 227, 71-106.
41. Koop, C. G., and F. K. Browand, 1979: Instability and turbulence in stratified fluid with shear. J. Fluid Mech., 93, 135-159.
42. Landau, L. D., and E. M. Lifshitz, 1959: Fluid Dynamics. Pergamon Press, 536 pp.
43. Lasheras, J. C., and H. Choi, 1988: Three-dimensional instability of a plane free shear layer: An experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech., 189, 53-86.
44. _, J. S. Cho, and T. Maxworthy, 1986: On the origin and evolution of streamwise vortical structures in a plane, free shear layer. J. Fluid Mech., 172, 231-258.
45. Lie, I., 1994: Multidomain solution of advection problems with Chebyshev spectral collocation techniques. J. Sci. Comput., 9, 39-64.
46. Lopez, J. M., and C. J. Bulbeck, 1993: Behavior of streamwise rib vortices in a three-dimensional mixing layer. Phys. Fluids A. 5, 1694-1702.
47. Ludlam, F. H., 1967: Billow clouds and their relation to clear air turbulence. Quart. J. Roy. Meteor. Soc., 93, 419-435.
48. Maslowe, S. A., 1972: The generation of clear air turbulence by non-linear waves. Stud. Appl. Math., 51, 1-16.
49. _, 1973: Finite-amplitude Kelvin-Helmholtz billow. Bound.-Layer Meteor., 5, 43-52.
50. Metcalfe, R. W., S. A. Orszag, M. E. Brachet, S. Menon, and J. J. Riley, 1987: Secondary instability of a temporally growing mixing layer. J. Fluid Mech., 184, 207-243.
51. Miles, J. W., 1961: On the stability of heterogeneous shear flows. J. Fluid Mech., 10, 496-508.
52. Moser, R. D., and M. M. Rogers, 1993: The three-dimensional evolution of a plane mixing layer. J. Fluid Mech., 247, 275-320.
53. Nagata, M., and F. H. Busse, 1983: Three-dimensional tertiary motions in a plane shear layer. J. Fluid Mech., 135, 1-26.
54. Palmer, T. L., D. C. Fritts, Ø. Andreassen, and I. Lie, 1994: Three-dimensional evolution of Kelvin-Helmholtz billows in stratified compressible flow. Geophys. Res. Lett., 21, 2287-2290.
55. _, _, and _, 1996: Evolution and breakdown of Kelvin-Helmholtz billows in stratified compressible flows. Part II: Instability structure, evolution, and energies. J. Atmos. Sci., 53, 3192-3212.
56. Patnaik, P. C., F. S. Sherman, and G. M. Corcos, 1976: A numerical simulation of Kelvin-Helmholtz waves of finite amplitude. J. Fluid Mech., 73, 215-240.
57. Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.
58. Peltier, W. R., J. R. Halle, and T. L. Clark, 1979: The evolution of finite-amplitude Kelvin-Helmholtz billows. Geophys. Astrophys. Fluid Dyn., 10, 53-87.
59. Pierrehumbert, R. T., and S. E. Widnall, 1982: The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech., 114, 59-82.
60. Readings, C. J., D. Atlas, C. B. Emmanuel, Y.-H. Pao, and S. A. Thorpe, 1973: The formation and breakdown of Kelvin-Helmholtz billows. Bound.-Layer Meteor., 5, 233-240.
61. Richter, J. H., 1969: High-resolution tropospheric radar sounding. Radio Sci., 4, 1261-1268.
62. Rogers, M. M., and R. D. Moser, 1992: The three-dimensional evolution of a plane mixing layer: The Kelvin-Helmholtz rollup. J. Fluid Mech., 243, 183-226.
63. Schowalter, D. G., C. W. van Atta, and J. C. Lasheras, 1994: A study of streamwise vortex structure in a stratified shear layer. J. Fluid Mech., 281, 247-291.
64. Scinocca, J. F., 1995: The mixing of mass and momentum by Kelvin-Helmholtz billows. J. Atmos. Sci., 52, 2509-2530.
65. Scorer, R. S., 1969: Billow mechanics. Radio Sci., 4, 1299-1307.
66. Scotti, R. S., and G. M. Corcos, 1972: An experiment on the stability of small disturbances in a stratified free shear layer. J. Fluid Mech., 52, 499-528.
67. Sykes, R. I., and W. S. Lewellen, 1982: A numerical study of breaking Kelvin-Helmholtz billows using a Reynolds stress closure model. J. Atmos. Sci., 39, 1506-1520.
68. Tadmor, E., 1989: Convergence of spectral methods for nonlinear conservation laws. SIAM J. Numer. Anal., 26, 30-44.
69. Thorpe, S. A., 1968: A method of producing a shear flow in a stratified fluid. J. Fluid Mech., 32, 693-704.
70. _, 1971: Experiments on the instability of stratified shear flows: Miscible fluids. J. Fluid Mech., 46, 299-320.
71. _, 1973: Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech., 61, 731-751.
72. _, 1985: Laboratory observations of secondary structures in Kelvin-Helmholtz billows and consequences for ocean mixing. Geophys. Astrophys. Fluid Dyn., 34, 175-199.
73. _, 1987: Transitional phenomena and the development of turbulence in stratified fluids: A review. J. Geophys. Res., 92, 5231-5248.
74. Wasberg, C. E., and Ø. Andreassen, 1990: Pseudospectral methods with open boundary conditions for the study of atmospheric wave phenomena. Comput. Methods Appl. Mech. Eng., 80, 459-465.
75. Winters, K. B., and E. A. D'Asaro, 1994: 3D wave breaking near a critical level. J. Fluid Mech., 272, 255-284.
76. Witt, G., 1962: Height, structure, and displacements of noctilucent clouds. Tellus, 14, 1-12.
77. Woods, J. D., 1969: On Richardson's number as a criterion for laminar-turbulent transition in the ocean and atmosphere. Radio Sci., 4, 1289-1298.
78. _, and R. L. Wiley, 1972: Billow turbulence and ocean microstructure. Deep-Sea Res., 19, 87-121.