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Numerical Simulation of Breaking Gravity Waves below a Critical Level

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 26))

Abstract

The interaction of an internal gravity wave with a critical layer and the generation of turbulence are studied by three-dimensional numerical simulations. Based on a successful comparison of a two-dimensional version of the model with experimental observations (Thorpe, 1981), we discuss results obtained with two different models of viscosity. Although the variances of the turbulent quantities are nearly the same, a direct numerical simulation gives a smooth breaking with stable vortices. The motion remains two-dimensional. In a largeeddy simulation, the initial field is randomly disturbed and a turbulent viscosity (function of the local shear and Richardson number) is used. The breakdown of the convectively unstable regions occurs immediately after the appearance of convective instability, and small-scale three-dimensional turbulent motion is generated.

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References

  1. Booker, J. R. and Bretherton, F. P., The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27 (1967) 513–539.

    Article  ADS  MATH  Google Scholar 

  2. Delesi, D. P. and Dunkerton, T. J., Laboratory observations of gravity wave critical-layer flows. Pure Appl. Geophys. 130 (1989) 445–461.

    Article  ADS  Google Scholar 

  3. Koop, C. G. and McGee, B., Measurements of internal gravity waves in a continiously stratified shear flow. J. Fluid Mech. 172 (1986) 453–480.

    Article  ADS  Google Scholar 

  4. Krettenauer, K. and Schumann, U., Numerical simulation of turbulent convection over wavy terrain. J. Fluid Mech. 237 (1992) 261–299.

    Article  ADS  Google Scholar 

  5. Nappo, C. J. and Chimonas, G., Wave exchange between the ground surface and a boundary-layer critical level. J. Atmos. Sciences 49 (1992) 1075–1091.

    Article  ADS  Google Scholar 

  6. Nastrom, G. D. and Eaton, F. D., The coupling of gravity waves and turbulence at White Sands, New Mexico, from VHF radar observations. J. Appl. Meteorol. 32 (1993) 81–87.

    Article  ADS  Google Scholar 

  7. Mason, P.J. and Derbyshire, S. H., Large-eddy simulation of the stably stratified atmospheric boundary layer. Bound.-Layer Meteorol. 53 (1990) 117–162.

    Article  ADS  Google Scholar 

  8. Merrill, J. T. and Grant, J. R., A gravity wave — critical level encounter observed in the atmosphere. J. Geophys. Res. 84 (1979) 6315–6320.

    Article  ADS  Google Scholar 

  9. Pao, Y. and Goldburg, A. (eds.), Clear air turbulence and its detection. Plenum Press, New York, 1969.

    Google Scholar 

  10. Sato, K. and Woodman, R. F., Fine altitude resolution radar observations of stratospheric layers by the Arecibo 430 MHz radar. J. Atmos. Sciences 39 (1982) 2546–2552.

    Article  ADS  Google Scholar 

  11. Sidi, C., Waves-turbulence coupling. Coupling Processes in the Lower and Middle Atmosphere E. V. Thrane et al. (eds.), Kluwer Amsterdam (1993) 291–304.

    Chapter  Google Scholar 

  12. Thorpe, S. A., A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32 (1968) 693–704.

    Article  ADS  Google Scholar 

  13. Thorpe, S. A., An experimental study of critical layers. J. Fluid Mech. 103 (1981) 321–344.

    Article  ADS  Google Scholar 

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© 1994 Springer Science+Business Media Dordrecht

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Dörnbrack, A., Schumann, U. (1994). Numerical Simulation of Breaking Gravity Waves below a Critical Level. In: Voke, P.R., Kleiser, L., Chollet, JP. (eds) Direct and Large-Eddy Simulation I. Fluid Mechanics and Its Applications, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1000-6_17

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  • DOI: https://doi.org/10.1007/978-94-011-1000-6_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4434-9

  • Online ISBN: 978-94-011-1000-6

  • eBook Packages: Springer Book Archive

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