Skip to main content

Direct Numerical Simulation of Breaking Atmospheric Gravity Waves

  • Conference paper
  • First Online:

Abstract

We present the results of fully resolved direct numerical simulations of monochromatic gravity waves breaking in the middle atmosphere. The simulations are initialized with optimal perurbations of the gives waves. Given a wavelength of 3 km, the required grid sizes range up to 3.6 billion computational cells, depending on the necessary domain size and the turbulence intensity. Our results provide an insight into the mechanics of gravity wave breaking they will be of great value for the validation of lower order methods for the prediction of wave breaking.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Achatz, U.: On the role of optimal perturbations in the instability of monochromatic gravity waves. Phys. Fluids 17(9), 094107 (2005)

    Article  MathSciNet  Google Scholar 

  2. Achatz, U., Schmitz, G.: Optimal growth in inertia-gravity wave packets: energetics, long-term development, and three-dimensional structure. J. Atmos. Sci. 63, 414–434 (2006)

    Article  MathSciNet  Google Scholar 

  3. Baldwin, M.P., Gray, L.J., Dunkerton, T.J., Hamilton, K., Haynes, P.H., Randel, W.J., Holton, J.R., Alexander, M.J., Hirota, I., Horinouchi, T., Jones, D.B.A., Kinnersley, J.S., Marquardt, C., Sato, K., Takahashi, M.: The quasi-biennial oscillation. Rev. Geophys. 39, 179–229 (2001)

    Article  Google Scholar 

  4. Chun, H.-Y., Song, M.-D., Kim, J.-W., Baik, J.-J.: Effects of gravity wave drag induced by cumulus convection on the atmospheric general circulation. J. Atmos. Sci. 58(3), 302–319 (2001)

    Article  Google Scholar 

  5. Fritts, D.C., Alexander, M.J.: Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys. 41(1), 1–64 (2003)

    Article  MathSciNet  Google Scholar 

  6. Fruman, M.D., Achatz, U.: Secondary instabilities in breaking inertia-gravity waves. J. Atmos. Sci. 69, 303–322 (2012)

    Article  Google Scholar 

  7. Grimsdell, A.W., Alexander, M.J., May, P.T., Hoffmann, L.: Model study of waves generated by convection with direct validation via satellite. J. Atmos. Sci. 67(5), 1617–1631 (2010)

    Article  Google Scholar 

  8. Hines, C.O.: Dynamical heating of the upper atmosphere. J. Geophys. Res. 70(1), 177–183 (1965)

    Article  Google Scholar 

  9. Hines, C.O.: Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 1: basic formulation. J. Atmos. Sol.-Terr. Phys. 59(4), 371–386 (1997)

    Google Scholar 

  10. Kim, Y.-J., Eckermann, S.D., Chun, H.-Y.: An overview of the past, present and future of gravity–wave drag parametrization for numerical climate and weather prediction models. Atmosphere-Ocean 41(1), 65–98 (2003)

    Article  Google Scholar 

  11. Lindzen, R.S.: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res. 86, 9707–9714 (1981)

    Article  Google Scholar 

  12. McFarlane, N.A.: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci. 44, 1775–1800 (1987)

    Article  Google Scholar 

  13. McLandress, C.: On the importance of gravity waves in the middle atmosphere and their parameterization in general circulation models. J. Atmos. Sol.-Terr. Phy. 60(14), 1357–1383 (1998)

    Article  Google Scholar 

  14. O’Sullivan, D., Dunkerton, T.J.: Generation of inertia-gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci. 52(21), 3695–3716 (1995)

    Article  Google Scholar 

  15. Plougonven, R., Snyder, C.: Inertia gravity waves spontaneously generated by jets and fronts. Part I: different baroclinic life cycles. J. Atmos. Sci. 64(7), 2502–2520 (2007)

    Google Scholar 

  16. Remmler, S., Fruman, M.D., Hickel, S.: Direct numerical simulation of a breaking inertia-gravity wave. J. Fluid Mech. 722, 424–436 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shu, C.-W.: Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9(6), 1073–1084 (1988)

    Article  MATH  Google Scholar 

  18. Smith, R.B.: The influence of mountains on the atmosphere. Adv. Geophys. 21, 87–230 (1979)

    Article  Google Scholar 

  19. Vallis, G.K.: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, Cambridge (2006)

    Book  Google Scholar 

  20. van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

U. A. and S. H. thank Deutsche Forschungsgemeinschaft (German Research Foundation, DFG) for partial support through the MetStröm (Multiple Scales in Fluid Mechanics and Meteorology) Priority Research Program (SPP 1276), and through Grants HI 1273/1-2 and Ac71/4-2. Computational resources were provided by the HLRS Stuttgart under the grants TIGRA and DINSGRAW and by the CSC Frankfurt.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stefan Hickel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Remmler, S., Hickel, S., Fruman, M.D., Achatz, U. (2015). Direct Numerical Simulation of Breaking Atmospheric Gravity Waves. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ‘14. Springer, Cham. https://doi.org/10.1007/978-3-319-10810-0_39

Download citation

Publish with us

Policies and ethics