ANGEO Annales Geophysicae ANGEO 1432-0576 Copernicus GmbH Göttingen, Germany 10.5194/angeo-27-4105-2009 On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere Chunchuzov I. P. 1 Obukhov Institute of Atmospheric Physics, 119017 Moscow, 3 Pyzhevskii Per., Russia 02 11 2009 27 11 4105 4124 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.ann-geophys.net/27/4105/2009/angeo-27-4105-2009.html The full text article is available as a PDF file from http://www.ann-geophys.net/27/4105/2009/angeo-27-4105-2009.pdf

The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.

 References Allen, K. A. and Joseph, R. I.: A canonical statistical theory of oceanic internal waves, J. Fluid Mech., 204, 185–228, 1989. Allen, S. J. and Vincent, R. A.: Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations, J. Geophys. Res., 100, 1327–1350, 1995. Bendat, J. S. and Piersol, A. G.: Measurement and analysis of random data, John Wiley & Sons, Inc., New York, 408 pp., 1967. Böhme, T., Hauf, T., and Lehnmann, V.: Investigation of short-period gravity waves with the Lindenberg 482 MHz tropospheric wind profiler, Q. J. Roy. Meteorol. Soc., 130, 2933–2952, 2004. Broutman, D., Grimshaw, R. H. J., and Eckermann, S. D.: On internal waves in a Lagrangian reference frame, J. Atmos. Sci., 61, 1308–1313, 2004. Chunchuzov, I. P.: The spectrum of high-frequency internal waves in the atmospheric waveguide, J. Atmos. Sci., 53, 1798–1814, 1996. Chunchuzov, I. P.: On the role of nonlinearity in the formation of the spectrum of atmospheric gravity waves, Izv. Atmos. Oceanic. Phys., 37(4), 466–469, 2001 (Engl. Transl.). Chunchuzov, I. P.: On the high-wavenumber form of the Eulerian internal wave spectrum in the atmosphere, J. Atmos. Sci., 59, 1753–1772, 2002. Chunchuzov, I. P., Kulichlov, S. N., Otrezov, A. I., Perepelkin, V. G., Kallistratova, M. A., Tovchigrechko, V. N., Kadygrov, E. N., and Kuznetsov, R. D.: Acoustic study of mesoscale fluctuations in the wind velocity in stable atmospheric boundary layer, Izv. Atmos. Oceanic Phys., 41(6), 693–712, 2006 (Engl. Transl.). Chunchuzov, I.: Nonlinear shaping mechanism for the spectrum of acoustic-gravity waves in the atmosphere, in: Proc. 18-th Int. Symp. On Nonlinear Acoustics, (ISNA 18), Stockholm, Sweden, 385–388, 7–10 July 2008. Craik, A. D. D.: Wave interactions and fluid flows, Cambridge University Press, 1985. Dalaudier, F., Sidi, C., Crochet, M., and Vernin, J.: Direct evidence of "sheets" in the atmospheric temperature field, J. Atmos. Sci., 51(2), 237–248, 1994. Dewan, E.: Saturated-cascade similitude theory of gravity wave spectra, J. Geophys. Res., 102(D25), 29799–29827, 1997. Eckermann, S. D.: Isentropic advection by gravity waves: quasi-universal M<sup>&minus;3</sup> vertical wavenumber spectra near the onset of instability, Geophys. Res. Lett., 26, 201–204, 1999. Fritts D. C. and Alexander, M. J.: Gravity wave dynamics and effects in the middle atmosphere, Rev. Geophys., 41(1), 1003, doi:10.1029/2001RG000106, 2003. Gossard, E. E. and Hooke, W. H.: Waves in the atmosphere, Elsevier, Amsterdam, 456 pp., 1975. Gurrett, C. J. R. and Munk, W. H.: Space-time scales of internal waves: a progress report, J. Geophys. Res., 80, 291–297, 1975. Gurvich, A. S. and Chunchuzov, I. P.: Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations, J. Geophys. Res., 108(D5), 4166, doi:10.1029/2002JD002281, 2003. Gurvich, A. and Chunchuzov, I.: Estimates of characteristic scales in the spectrum of internal waves in the stratosphere obtained from space observations of stellar scintillations, J. Geophys. Res., 110, D03114, doi:10.1029/2004JD005199, 2005. Gurvich, A. S. and Chunchuzov, I. P.: Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere, Ann. Geophys., 26, 2037–2042, 2008. Hines, C. O.: The saturation of gravity waves in the middle atmosphere. Part II: Development of Doppler-spread theory, J. Atmos Sci., 48, 1360–1379, 1991. Hines, C. O.: Theory of the Eulerian tail in the spectra of atmospheric and oceanic internal gravity waves, J. Fluid. Mech., 448, 289–313, 2001. Klaassen, G. P. and Sonmor, L. J.: Does kinematic advection by superimposed waves provide an explanation for quasi-universal gravity-wave spectra?, Geophys. Res. Lett., 33, L23802, doi:10.1029/2006GL027388, 2006. Klaassen, G.: Testing Lagrangian Theories of Internal Wave Spectra. Part I: Varying the Amplitude and Wavenumbers, J. Atmos. Sci., 66(5), 1077–1100, 2009. Lamb, H.: Hydrodynamics, 6th ed., Cambridge University Press, 1932. Lighthill, J.: Waves in Fluids, Cambridge University Press, 504 pp., 1978. Lindborg, E.: The energy cascade in a strongly stratified fluid, J. Fluid Mech., 550, 207–242, 2006. McComas, C. H. and Bretherton, F. P.: Resonant interaction of oceanic internal waves, J. Geophys. Res., 82, 1397–1412, 1977. McLandress, C.: Sensitivity Studies using the Hines and Fritts gravity wave drag parameterizations, Gravity Wave Processes, Their Parameterization in Global Climate Models, edited by: Hamilton, K., Springer Verlag Berlin, 245–257, 1997. Ostashev, V. E., Chucnhuzov, I. P., and Wilson, D. K.: Sound propagation through and scattering by internal gravity waves in a stably stratified atmosphere, J. Acoust. Soc. Am., 118(6), 3420–3429, 2005. Pinkel, R.: Advection, Phase Distortion, and the Frequency Spectrum of Finescale Fields in the Sea, J. Phys. Oceanogr., 38, 291–313, 2008. Phillips, O. M.: Theoretical and experimental study of the gravity wave interactions, in: Proceed. of the Royal Society: A discussion on nonlinear theory of wave propagation in dispersive systems, organized by M. J. Lighthill, London, Series A Math. And Phys. Sciences, 299, 104–120, 1967. Rudenko, O. V. and Soluyan, S. I.: Theoreticheskie osnovy nelineinoi akustiki, Engl. Transl., New York: Consultants Bureau, 274 pp., 1977. Sica, R. J. and Russell, A. T.: How many waves are in the gravity wave spectrum, Geophys. Res. Lett., 26, 3617–3620, 1999. Weinstock, J.: Effect of gravity waves on turbulence decay in stratified fluids, J. Fluid Mech., 140, 11–26, 1985. Whiteway, J. A., Carswell, A. I., and Ward, W. E.: Mesospheric temperature inversions with overlying nearly adiabatic lapse rate: An indication of a well-mixed turbulent layer, Geophys. Res. Lett., 22(10), 1201–1294, 1995. Zarembo, L. K. and Krasilnikov, V. A.: Introduction to nonlinear acoustics, 520 pp., Nauka, Moscow, 1966.