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Direct numerical simulation of a breaking inertia–gravity wave

  • S. Remmler (a1), M. D. Fruman (a2) and S. Hickel (a1)

Abstract

We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an $f$ -plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.

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Email address for correspondence: sh@tum.de

References

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Achatz, U. 2005 On the role of optimal perturbations in the instability of monochromatic gravity waves. Phys. Fluids 17 (9), 094107.
Achatz, U. 2007 The primary nonlinear dynamics of modal and nonmodal perturbations of monochromatic inertia gravity waves. J. Atmos. Sci. 64, 7495.
Achatz, U. & Schmitz, G. 2006a Optimal growth in inertia-gravity wave packets: energetics, long-term development, and three-dimensional structure. J. Atmos. Sci. 63, 414434.
Achatz, U. & Schmitz, G. 2006b Shear and static instability of inertia-gravity wave packets: short-term modal and nonmodal growth. J. Atmos. Sci. 63, 397413.
Afanasyev, Y. D. & Peltier, W. R. 2001 Numerical simulations of internal gravity wave breaking in the middle atmosphere: the influence of dispersion and three-dimensionalization. J. Atmos. Sci. 58, 132153.
Andreassen, Ø., Øyvind Hvidsten, P., Fritts, D. C. & Arendt, S. 1998 Vorticity dynamics in a breaking internal gravity wave. Part 1. Initial instability evolution. J. Fluid Mech. 367, 2746.
Andreassen, Ø, Wasberg, C. E., Fritts, D. C. & Isler, J. R. 1994 Gravity wave breaking in two and three dimensions 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res. 99, 80958108.
Blumen, W. & McGregor, C. D. 1976 Wave drag by three-dimensional mountain lee-waves in nonplanar shear flow. Tellus 28 (4), 287298.
Bretherton, F. P. 1969 Waves and turbulence in stably stratified fluids. Radio Sci. 4 (12), 12791287.
Chun, H.-Y. & Baik, J.-J. 1998 Momentum flux by thermally induced internal gravity waves and its approximation for large-scale models. J. Atmos. Sci. 55, 32993310.
Dörnbrack, A. 1998 Turbulent mixing by breaking gravity waves. J. Fluid Mech. 375, 113141.
Drazin, P. G. 1977 On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356 (1686), 411432.
Dunkerton, T. J. 1997a The role of gravity waves in the quasi-biennial oscillation. J. Geophys. Res. 102, 2605326076.
Dunkerton, T. J. 1997b Shear instability of internal inertia-gravity waves. J. Atmos. Sci. 54, 16281641.
Fritts, D. C. & Alexander, M. J. 2003 Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys. 41, 1003.
Fritts, D. C., Isler, J. R. & Andreassen, Ø. 1994 Gravity wave breaking in two and three dimensions 2. Three-dimensional evolution and instability structure. J. Geophys. Res. 99, 81098124.
Fritts, D. C., Wang, L., Werne, J., Lund, T. & Wan, K. 2009 Gravity wave instability dynamics at high Reynolds numbers. Parts I and II. J. Atmos. Sci. 66 (5), 11261171.
Fruman, M. D. & Achatz, U. 2012 Secondary instabilities in breaking inertia-gravity waves. J. Atmos. Sci. 69, 303322.
Holton, J. R. 1982 The role of gravity wave induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci. 39, 791799.
Houghton, J. T. 1978 The stratosphere and mesosphere. Q. J. R. Meteorol. Soc. 104 (439), 129.
Klostermeyer, J. 1982 On parametric instabilities of finite-amplitude internal gravity waves. J. Fluid Mech. 119, 367377.
Lelong, M.-P. & Dunkerton, T. J. 1998 Inertia-gravity wave breaking in three dimensions. Parts I and II. J. Atmos. Sci. 55, 24732501.
Lilly, D. K. 1972 Wave momentum flux – A GARP problem. Bull. Am. Meteorol. Soc. 53, 1723.
Lindzen, R. S. 1981 Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res. 86, 97079714.
McLandress, C. 1998 On the importance of gravity waves in the middle atmosphere and their parameterization in general circulation models. J. Atmos. Sol.-Terr. Phys. 60 (14), 13571383.
Mied, R. P. 1976 The occurrence of parametric instabilities in finite-amplitude internal gravity waves. J. Fluid Mech. 78 (4), 763784.
Nappo, C. J. 2002 An Introduction to Atmospheric Gravity Waves. Academic.
Remmler, S. & Hickel, S. 2012a Direct and large eddy simulation of stratified turbulence. Intl J. Heat Fluid Flow 35, 1324.
Remmler, S. & Hickel, S. 2012b Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation. Theor. Comput. Fluid Dyn. Published online: doi:10.1007/s00162-012-0259-9.
Sawyer, J. S. 1959 The introduction of the effects of topography into methods of numerical forecasting. Q. J. R. Meteorol. Soc. 85 (363), 3143.
Shu, C.-W. 1988 Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9 (6), 10731084.
Thorpe, S. A. 1977 Turbulence and mixing in a scottish loch. Phil. Trans. R. Soc. Lond. A 286 (1334), 125181.
Winters, K. B. & D’Asaro, E. A. 1994 Three-dimensional wave instability near a critical level. J. Fluid Mech. 272, 255284.
Yamazaki, Y., Ishihara, T. & Kaneda, Y. 2002 Effects of wavenumber truncation on high-resolution direct numerical simulation of turbulence. J. Phys. Soc. Japan 71, 777781.
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Direct numerical simulation of a breaking inertia–gravity wave

  • S. Remmler (a1), M. D. Fruman (a2) and S. Hickel (a1)

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