Gravity Wave Instability Dynamics at High Reynolds Numbers. Part II: Turbulence Evolution, Structure, and Anisotropy

David C. Fritts NorthWest Research Associates, Colorado Research Associates Division, Boulder, Colorado

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Ling Wang NorthWest Research Associates, Colorado Research Associates Division, Boulder, Colorado

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Joe Werne NorthWest Research Associates, Colorado Research Associates Division, Boulder, Colorado

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Tom Lund NorthWest Research Associates, Colorado Research Associates Division, Boulder, Colorado

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Kam Wan NorthWest Research Associates, Colorado Research Associates Division, Boulder, Colorado

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Abstract

This paper examines the character, intermittency, and anisotropy of turbulence accompanying wave instability, breaking, and turbulence evolution and decay for gravity waves (GW) having a high intrinsic frequency, amplitudes above and below nominal convective instability, and a high Reynolds number. Wave breaking at both amplitudes leads to an extended inertial range of turbulence, with turbulence energies that maximize within ∼1 wave period of the onset of breaking. Turbulence sources include both shear and buoyancy, with shear being the major contributor. Turbulence displays considerable intermittency both within and across the phase of the breaking gravity wave and exhibits clear anisotropy throughout the evolution. Turbulence anisotropy is found at all spatial scales and all times but is most pronounced in the most statically stable phase of the GW and at late times as the turbulent flow restratifies.

Corresponding author address: David C. Fritts, NorthWest Research Associates, Colorado Research Associates Division, 3380 Mitchell Lane, Boulder, CO 80301. Email: dave@cora.nwra.com

Abstract

This paper examines the character, intermittency, and anisotropy of turbulence accompanying wave instability, breaking, and turbulence evolution and decay for gravity waves (GW) having a high intrinsic frequency, amplitudes above and below nominal convective instability, and a high Reynolds number. Wave breaking at both amplitudes leads to an extended inertial range of turbulence, with turbulence energies that maximize within ∼1 wave period of the onset of breaking. Turbulence sources include both shear and buoyancy, with shear being the major contributor. Turbulence displays considerable intermittency both within and across the phase of the breaking gravity wave and exhibits clear anisotropy throughout the evolution. Turbulence anisotropy is found at all spatial scales and all times but is most pronounced in the most statically stable phase of the GW and at late times as the turbulent flow restratifies.

Corresponding author address: David C. Fritts, NorthWest Research Associates, Colorado Research Associates Division, 3380 Mitchell Lane, Boulder, CO 80301. Email: dave@cora.nwra.com

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  • Andreassen, Ø, C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994: Gravity wave breaking in two and three dimensions. 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res., 99 , 80958108.

    • Search Google Scholar
    • Export Citation
  • Andreassen, Ø, Hvidsten, D. C. Fritts, and S. Arendt, 1998: Vorticity dynamics in a breaking gravity wave. Part 1. Initial instability evolution. J. Fluid Mech., 367 , 2746.

    • Search Google Scholar
    • Export Citation
  • Arendt, S., D. C. Fritts, and Ø Andreassen, 1997: The initial value problem for Kelvin vortex waves. J. Fluid Mech., 344 , 181212.

  • Arendt, S., D. C. Fritts, and Ø Andreassen, 1998: Kelvin twist waves in the transition to turbulence. Eur. J. Mech., 17B , 595604.

  • Brasseur, J., and C-H. Wei, 1994: Interscale dynamics and local isotropy in high Reynolds number turbulence within triadic interactions. Phys. Fluids, 6 , 842870.

    • Search Google Scholar
    • Export Citation
  • Brown, L. W. B., A. A. Antonia, and D. A. Shaw, 1987: Turbulent energy dissipation in a wake. J. Fluid Mech., 179 , 307326.

  • Champagne, F. H., 1978: The fine-scale structure of the turbulent velocity field. J. Fluid Mech., 86 , 67108.

  • Coy, L., and D. C. Fritts, 1988: Gravity wave heat fluxes: A Lagrangian approach. J. Atmos. Sci., 45 , 17701780.

  • Durbin, P. A., and C. G. Speziale, 1991: Local anisotropy in strained turbulence at high Reynolds numbers. J. Fluids Eng., 113 , 707709.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., and T. J. Dunkerton, 1985: Fluxes of heat and constituents due to convectively unstable gravity waves. J. Atmos. Sci., 42 , 549556.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., and J. A. Werne, 2000: Turbulence dynamics and mixing due to gravity waves in the lower and middle atmosphere. Atmospheric Science across the Stratopause, Geophys. Monogr., Vol. 123, Amer. Geophys. Union, 143–159.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., and M. J. Alexander, 2003: Gravity dynamics and effects in the middle atmosphere. Rev. Geophys., 41 , 1003. doi:10.1029/2001RG000106.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., J. R. Isler, and Ø Andreassen, 1994: Gravity wave breaking in two and three dimensions. 2. Three-dimensional evolution and instability structure. J. Geophys. Res., 99 , 81098123.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., J. F. Garten, and Ø Andreassen, 1996: Wave breaking and transition to turbulence in stratified shear flows. J. Atmos. Sci., 53 , 10571085.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., S. Arendt, and Ø Andreassen, 1998: Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence. J. Fluid Mech., 367 , 4765.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., C. Bizon, J. A. Werne, and C. K. Meyer, 2003: Layering accompanying turbulence generation due to shear instability and gravity-wave breaking. J. Geophys. Res., 108 , 8452. doi:10.1029/2002JD002406.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., S. L. Vadas, K. Wan, and J. A. Werne, 2006: Mean and variable forcing of the middle atmosphere by gravity waves. J. Atmos. Sol.-Terr. Phys., 68 , 247265.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., L. Wang, J. Werne, T. Lund, and K. Wan, 2009: Gravity wave instability dynamics at high Reynolds numbers. Part I: Wave field evolution at large amplitudes and high frequencies. J. Atmos. Sci., 66 , 11261148.

    • Search Google Scholar
    • Export Citation
  • George, W. K., and H. J. Hussain, 1991: Locally axisymmetric turbulence. J. Fluid Mech., 233 , 123.

  • Gibson-Wilde, D. E., J. A. Werne, D. C. Fritts, and R. J. Hill, 2000: Direct numerical simulation of VHF radar measurements of turbulence in the mesosphere. Radio Sci., 35 , 783798.

    • Search Google Scholar
    • Export Citation
  • Hunt, J. C. R., O. M. Phillips, and D. Williams, 1991: Turbulence and stochastic processes: Kolmogorov’s ideas 50 years on. Proc. Roy. Soc. London, 434A , 1240.

    • Search Google Scholar
    • Export Citation
  • Jeong, J., and F. Hussain, 1995: On the identification of a vortex. J. Fluid Mech., 285 , 6994.

  • Kaneda, Y., and K. Yoshida, 2004: Small-scale anisotropy in stably stratified turbulence. New J. Phys., 6 , 116.

  • Kelvin, L., 1880: Vibrations of a columnar vortex. Philos. Mag., 10 , 155168.

  • Kolmogorov, A. N., 1941: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. URSS, 30 , 301305.

    • Search Google Scholar
    • Export Citation
  • Kolmogorov, A. N., 1962: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech., 13 , 8285.

    • Search Google Scholar
    • Export Citation
  • McIntyre, M. E., 1989: On dynamics and transport near the polar mesopause in summer. J. Geophys. Res., 94 , 1461714628.

  • Mestayer, P., 1982: Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J. Fluid Mech., 125 , 475503.

  • Muschinski, A., 1996: Possible effect of Kelvin–Helmholtz instability on VHF radar observations of the mean vertical wind. J. Appl. Meteor., 35 , 22102217.

    • Search Google Scholar
    • Export Citation
  • Obukhov, A. M., 1941: Spectrum of energy of turbulent flow. Dokl. Akad. Nauk SSSR, 32 , 22.

  • Pettersson-Reif, B. A., and Ø Andreassen, 2003: On local isotropy in stratified homogeneous turbulence. SIAM J. Appl. Math., 64 , 309321.

    • Search Google Scholar
    • Export Citation
  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

  • Praskovsky, A. A., 1992: Experimental verification of the Kolmogorov refined similarity hypothesis. Phys. Fluids, 4A , 25892591.

  • Praskovsky, A. A., and S. Oncley, 1994: Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers. Phys. Fluids, 6 , 27782784.

    • Search Google Scholar
    • Export Citation
  • Saddoughi, S. G., 1997: Local isotropy in complex turbulent boundary layers at high Reynolds number. J. Fluid Mech., 348 , 201245.

  • Saddoughi, S. G., and S. V. Veeravalli, 1994: Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech., 268 , 333372.

    • Search Google Scholar
    • Export Citation
  • Shen, X., and Z. Warhaft, 2000: The anisotropy of the small scale structure in high Reynolds number (Rl ∼1000) turbulent shear flow. Phys. Fluids, 12 , 29762989.

    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., 1999: Dissipation-range geometry and scalar spectra in sheared stratified turbulence. J. Fluid Mech., 401 , 209242.

  • Smyth, W. D., and J. N. Moum, 2000: Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids, 12 , 13431362.

  • Sreenivasan, K. R., 1991: On local isotropy of passive scalars in turbulent shear flows. Proc. Roy. Soc. London, 434A , 165182.

  • Thoroddsen, S. T., and C. W. Van Atta, 1992a: Experimental evidence supporting Kolmogorov’s refined similarity hypothesis. Phys. Fluids, 4A , 25922594.

    • Search Google Scholar
    • Export Citation
  • Thoroddsen, S. T., and C. W. Van Atta, 1992b: The influence of stable stratification on small-scale anisotropy and dissipation in turbulence. J. Geophys. Res., 97 , 36473658.

    • Search Google Scholar
    • Export Citation
  • Townsend, A. A., 1959: The uniform distortion of homogeneous turbulence. Quart. J. Mech. Appl. Math., 28 , 104127.

  • Uberoi, M. S., 1957: Equipartition of energy and local isotropy in turbulent flows. J. Appl. Phys., 28 , 11651170.

  • Van Atta, C., 1991: Local isotropy of the smallest scales of turbulent scalar and velocity fields. Proc. Roy. Soc. London, 434A , 139147.

    • Search Google Scholar
    • Export Citation
  • Werne, J. A., and D. C. Fritts, 1999: Stratified shear turbulence: Evolution and statistics. Geophys. Res. Lett., 26 , 439442.

  • Werne, J. A., and D. C. Fritts, 2000: Structure functions in stratified shear turbulence. 10th DoD HPC User Group Symp., Albequerque, NM, DoD High Performance Computing Modernization Program, 1–11.

    • Search Google Scholar
    • Export Citation
  • Werne, J. A., and D. C. Fritts, 2001: Anisotropy in a stratified shear layer. Phys. Chem. Earth, 26B , 263268.

  • Wroblewski, D., O. Cote, J. Hacker, T. L. Crawford, and R. J. Dobosy, 2003: Refractive turbulence in the upper troposphere and lower stratosphere: Analysis of aircraft measurements using structure functions. Preprints, 12th Symp. on Meteorological Observations and Instrumentation, Long Beach, CA, Amer. Meteor. Soc., 1.3. [Available online at http://ams.confex.com/ams/annual2003/techprogram/paper_58074.htm].

    • Search Google Scholar
    • Export Citation
  • Yeung, P. K., J. G. Brasseur, and Q. Wang, 1995: Dynamics of direct large-small scale couplings in coherently forced turbulence: Concurrent physical- and Fourier-space views. J. Fluid Mech., 283 , 4395.

    • Search Google Scholar
    • Export Citation
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