Modal and nonmodal perturbations of monochromatic high-frequency gravity waves: Primary nonlinear dynamics

Journal of the Atmospheric Sciences

Volumn 64, Issue 6, 2007, Pages 1977-1994

  Achatz, Ulrich ^a  

^a UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; DIRECT NUMERICAL SIMULATION; DYNAMICS; PERTURBATION TECHNIQUES; TURBULENCE; UPPER ATMOSPHERE; VISCOSITY;

BOUSSINESQ FLUID; PHASE PROPAGATION; WAVE BREAKING;

GRAVITY WAVES;

DIFFUSION; DIRECT NUMERICAL SIMULATION; DYNAMICS; GRAVITY WAVES; PERTURBATION TECHNIQUES; TURBULENCE; UPPER ATMOSPHERE; VISCOSITY;

ATMOSPHERIC DYNAMICS; BOUSSINESQ EQUATION; DIFFUSION; GRAVITY WAVE; MESOSPHERE; TURBULENCE; VISCOSITY; WAVE BREAKING; WAVE PROPAGATION; WAVE VELOCITY; WAVE-WAVE INTERACTION;

EID: 34347404935     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/JAS3940.1     Document Type: Article

References (42)

1. Achatz, U., 2005: On the role of optimal perturbations in the instability of monochromatic gravity waves. Phys. Fluids, 17, 094107, doi:10.1063/1.2046709.
2. Achatz, U., 2007: The primary nonlinear dynamics of modal and non-modal perturbations of monochromatic inertia-gravity waves. J. Atmos. Sci., 64, 74-95.
3. Achatz, U., and G. Schmitz, 2006a: Shear and static instability of inertia-gravity wave packets: Short-term modal and nonmodal growth. J. Atmos. Sci., 63, 397-413.
4. Achatz, U., and G. Schmitz, 2006b: Optimal growth in inertia-gravity wave packets: Energetics, long-term development, and three-dimensional structure. J. Atmos. Sci., 63, 414-434.
5. Andreassen, Ø., C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994: Gravity wave breaking in two and three dimensions. 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res., 99, 8095-8108.
6. Becker, E., and G. Schmitz, 2002: Energy deposition and turbulent dissipation owing to gravity waves in the mesosphere. J. Atmos. Sci., 59, 54-68.
7. Boberg, L., and U. Brosa, 1988: Onset of turbulence in a pipe. Z. Naturforschung, 43A, 697-726.
8. Drazin, P. G., 1977: On the instability of an internal gravity wave. Proc. Roy. Soc. London Ser. A, 356, 411-432.
9. Farrell, B. F., 1988a: Optimal excitation of neutral rossby waves. J. Atmos. Sci., 45, 163-172.
10. Farrell, B. F., 1988b: Optimal excitation of perturbations in viscous shear flow. Phys. Fluids, 31, 2093-2102.
11. Ferziger, J. H., 1996: Large eddy simulation. Simulation and Modeling of Turbulent Flows, T. B. Gatski, M. Y. Hussaini, and J. L. Lumley, Eds., Oxford University Press, 109-154.
12. Fritts, D. C., and M. J. Alexander, 2003: Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys., 41, 1003, doi:10.1029/2001RG000106.
13. Fritts, D. C., 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, 8109-8124.
14. Fritts, D. C., C. Bizon, J. A. Werne, and C. K. Meyer, 2003: Layering accompanying turbulence generation due to shear instability and gravity-wave breaking. J. Geophys. Res., 108, 8452, doi:10.1029/2002JD002406.
15. Fritts, D. C., S. L. Vadas, K. Wan, and J. A. Werne, 2006: Mean and variable forcing of the middle atmosphere by gravity waves. J. Atmos. Terr. Phys., 68, 247-265.
16. Garcia, R. R., and S. Solomon, 1985: The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere. J. Geophys. Res., 90, 3850-3868,
17. Germano, M., U. Piomelli, P. Moin, and W. H. Cabot, 1991: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 3, 1760-1765.
18. Hines, C. O., 1960: Internal atmospheric gravity waves at ionospheric heights. Can. J. Phys., 38, 1441-1481.
19. Holton, J. R., 1982: The role of gravity wave induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci., 39, 791-799.
20. Holton, J. R., 1983: The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. Atmos. Sci., 40, 2497-2507.
21. Houghton, J. T., 1978: The stratosphere and mesosphere. Quart. J., Roy. Meteor. Soc., 104, 1-29.
22. Howard, L. N., 1961: Note on a paper of John W. Miles. J. Fluid Mech., 10, 509-512.
23. Isler, J. R., D. C. Fritts, Ø. Andreassen, and C. E. Wasberg, 1994: Gravity wave breaking in two and three dimensions. 3. Vortex breakdown and transition to isotropy. J. Geophys. Res., 99, 8125-8138.
24. Klaassen, G. P., and W. R. Peltier, 1985: The onset of turbulence in finite-amplitude Kelvin-Helmholtz billows. J. Fluid Mech., 155, 1-35.
25. Klostermeyer, J., 1991: Two- and three-dimensional parametric instabilities in finite amplitude internal gravity waves. Geophys. Astrophys. Fluid Dyn., 61, 1-25.
26. Lelong, M. P., and T. J. Dunkerton, 1998a: Inertia-gravity wave breaking in three dimensions. Part I: Convectively stable waves. J. Atmos. Sci., 55, 2473-2488.
27. Lelong, M. P., and T. J. Dunkerton, 1998b: Inertia-gravity wave breaking in three dimensions. Part II: Convectively unstable waves. J. Atmos. Sci., 55, 2489-2501.
28. Lilly, D. K., 1992: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A, 4, 633-635.
29. Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707-9714.
30. Lombard, P. N., and J. R. Riley, 1996a: Instability and breakdown of internal gravity waves. I. Linear stability analysis. Phys. Fluids, 8, 3271-3287.
31. Lombard, P. N., and J. R. Riley, 1996b: On the breakdown into turbulence of propagating internal waves. Dyn. Atmos. Oceans, 23, 345-355.
32. Lübken, F.-J., 1997: Seasonal variation of turbulent energy dissipation rates at high latitudes as determined by in situ measurements of neutral density fluctuations. J. Geophys. Res., 102, 13 441-13 456.
33. McComas, C. H., and F. P. Bretherton, 1977: Resonant interaction of oceanic internal waves. J. Geophys. Res., 82, 1397-1412.
34. Meneveau, C., T. S. Lund, and W. H. Cabot, 1996: A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech., 319, 353-385.
35. Mied, R. P., 1976: The occurrence of parametric instabilities in finite amplitude internal gravity waves. J. Fluid Mech., 78, 763-784.
36. Miles, J. W., 1961: On the stability of heterogeneous shear flows. J. Fluid Mech., 10, 496-508.
37. Müllemann, A., M. Rapp, and F.-J. Lübken, 2003: Morphology of turbulence in the polar summer mesopause region during the MIDAS/ SOLSTICE campaign 2001. Adv. Space Res., 31, 2069-2074.
38. Sonmor, L. J., and G. P. Klaassen, 1997: Toward a unified theory of gravity wave stability. J. Atmos. Sci., 54, 2655-2680.
39. Strelnikov, B., M. Rapp, and F.-J. Lübken, 2003: A new technique for the analysis of neutral air density fluctuations measured in situ in the middle atmosphere. Geophys. Res. Lett., 30, 2052, doi:10.1029/2003GL018271.
40. Trefethen, L. N., A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, 1993: Hydrodynamic stability without eigenvalues. Science, 261, 578-584.
41. Winters, K. B., and E. A. D'Asaro, 1994: Three-dimensional wave instability near a critical level, J. Fluid Mech., 272, 255-284.
42. Yau, K.-H., G. P. Klaassen, and L. J. Sonmor, 2004: Principal instabilities of large amplitude inertio-gravity waves. Phys. Fluids, 16, 936-951.