Abstract
A numerical simulation of the nonlinear evolution of an upward propagating gravity wave shows that overturning is responsible for limiting the growth of the wave via cellular convection in the moving unstable phase of the wave. Convection provides a rapid stabilization of the stratification. Wave kinetic energy reaches a level of slow growth during the nonlinear growth of the wave, while wave available potential energy increases monotonically until convection begins, at which time it exceeds wave kinetic energy by a large amount. Wave transience is responsible for generating a substantial mean wind that persists in the region of wave breakdown. Because wave breakdown occurs during the transient buildup of the wave, wave amplitude varies with height approximately as if the wave had reached saturation, even prior to breakdown. Therefore, observations of limited wave growth with height may reflect the natural and gradual nonlinear evolution of upward propagating gravity waves before breakdown.
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References
Andrews, D. G., and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalization of the Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 2031–2046.
Boyd, J., 1976: The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum. J. Atmos. Sci., 33, 2285–2291.
Dunkerton, T. J., 1982a: Stochastic parameterization of gravity wave stresses. J. Atmos. Sci., 39, 1711–1725.
Dunkerton, T. J., 1982b: Wave transience in a compressible atmosphere. Part III: The saturation of internal gravity waves in the mesosphere. J. Atmos. Sci.,39, 1042–1051.
Eliassen, A. and E. Palm, 1961: On the transfer of energy in stationary mountain waves, Geofys. Publ., 22, No. 3, 1–13.
Fritts, D. C., 1984: Gravity wave saturation in the middle atmosphere: A review of theory and observations. Rev. Geophys. Space Phys., 22, 275–308.
Grimshaw, R., 1975: Nonlinear internal gravity waves and their interaction with the mean wind. J. Atmos. Sci., 32,1779–1793.
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.
Holton, J. R., 1983: The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. Atmos. Sci.,40, 2497–2507.
Klemp, J. B., and D. K. Lilly, 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci., 35, 78–107.
Lindzen, R. S., 1981: Turbulence and stress due to gravity wave and tidal breakdown. J.Geophys. Res., 86, 9707–9714.
Manson, A. H., J. B. Gregory, and D. G. Stephenson, 1974: Winds and wave motions to 110 km at mid-latitudes I. Partial reflection radiowave soundings 1972–73. J. Atmos. Sci.,31, 2207–2215.
Matsuno, T., 1982: A quasi-one-dimensional model of the middle atmospheric circulation interacting with internal gravity waves. J. Meteorol. Soc. Japan,60, 347–386.
Philbrick, C. R., F. J. Schmidelin, K. U. Grossman, G. Lang, D. Offerman, K. D. Baker, D. Krankowsky, and U. von Zahn, 1985: Density and temperature structure over northern Europe. J. Atmos. Terr. Phys., 47, 159–172.
Theon, J. S., W. Nordberg, L. B. Katchen, and J. J. Horvath, 1967: Some observations on the thermal behavior of the mesosphere. J. Atmos. Sci., 24,428–438.
Walterscheid, R. L., 1981: Inertio-gravity wave induced accelerations of mean flow having an imposed periodic component: Implications for tidal observations in the meteor region. J. Geophys. Res., 86, 9698–9706.
Walterscheid, R., 1984: Gravity wave attenuation and the evolution of the mean state following wave breakdown. In Dynamics of the Middle Atmosphere, ed. by J. R. Holton and T. Matsuno, pp. 19–43, Terra, Tokyo.
Walterscheid, R. L., and G. Schubert, 1990: Nonlinear evolution of an upward propagating wave: overturning, convection, transience and turbulence. J. Atmos. Sci.,47, 101–125
Weinstock, J., 1976: Nonlinear theory of acoustic-gravity waves, 1, Saturation and enhanced diffusion. J. Geophys. Res., 81,633–652.
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© 1993 Springer Science+Business Media Dordrecht
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Walterscheid, R.L., Schubert, G. (1993). Nonlinear Evolution of an Upward Propagating Gravity Wave: A Numerical Case Study. In: Thrane, E.V., Blix, T.A., Fritts, D.C. (eds) Coupling Processes in the Lower and Middle Atmosphere. NATO ASI Series, vol 387. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1594-0_14
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DOI: https://doi.org/10.1007/978-94-011-1594-0_14
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