• Achatz, U., 2007a: Modal and nonmodal perturbations of monochromatic high-frequency gravity waves: Primary nonlinear dynamics. J. Atnos. Sci., 64 , 19771994.

    • Search Google Scholar
    • Export Citation
  • Achatz, U., 2007b: Gravity-wave breaking: Linear and primary nonlinear dynamics. Adv. Space Res., 40 , 719733.

  • Bacmeister, J. T., S. D. Eckermann, P. A. Newman, L. Lait, K. R. Chan, M. Loewenstein, M. H. Proffitt, and B. L. Gary, 1996: Stratospheric horizontal wavenumber spectra of winds, potential temperature and atmospheric tracers observed by high-altitude aircraft. J. Geophys. Res., 101 , 94419470.

    • Search Google Scholar
    • Export Citation
  • Bolgiano, R., 1959: Turbulence spectra in a stably stratified atmosphere. J. Geophys. Res., 64 , 22262229.

  • Bühler, O., M. E. McIntyre, and J. F. Scinocca, 1999: On shear-generated gravity waves that reach the mesosphere. Part I: Wave generation. J. Atmos. Sci., 56 , 37493763.

    • Search Google Scholar
    • Export Citation
  • Carreras, B. A., and Coauthors, 2000: Intermittency of plasma data: Multifractal analysis. Phys. Plasmas, 8 , 32783287.

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28 , 10871095.

  • Cho, J. Y. N., and E. Lindborg, 2001: Horizontal velocity structure functions in the upper troposphere and lower stratosphere. Part I. Observations. J. Geophys. Res., 106 , 1022310232.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y. N., B. E. Anderson, J. D. W. Barrick, and K. L. Thornhill, 2001: Aircraft observations of boundary layer turbulence: Intermittency and the cascade of energy and passive scalar variance. J. Geophys. Res., 106 , 3246932479.

    • Search Google Scholar
    • Export Citation
  • Davis, A., A. Marshak, W. Wiscombe, and R. Cahalan, 1994: Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated. J. Geophys. Res., 99 , 80558072.

    • Search Google Scholar
    • Export Citation
  • Dewan, E. M., 1979: Stratospheric wave spectra resembling turbulence. Science, 204 , 832835.

  • Dewan, E. M., 1997: Saturated-cascade similitude theory of gravity wave spectra. J. Geophys. Res., 102 , D25. 2979929817.

  • Frisch, U., 1991: From global scaling, à la Kolmogorov, to local multifractal in fully developed turbulence. Proc. Roy. Soc. London, A434 , 8999.

    • 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
  • Fua, D., G. Chimonas, F. Einaudi, and O. Zeman, 1982: An analysis of wave-turbulence interaction. J. Atmos. Sci., 39 , 24502463.

  • Gage, K. S., and G. D. Nastrom, 1986: Theoretical interpretation of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft during GASP. J. Atmos. Sci., 43 , 729740.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., and W. Munk, 1972: Space–time scales of internal waves. Geophys. Fluid Dyn., 3 , 225264.

  • Garrett, C., and W. Munk, 1975: Space–time scales of internal waves: A progress report. J. Geophys. Res., 80 , 291297.

  • Kerr, R. M., M. Meneguzzi, and T. Gotoh, 2001: An inertial range crossover in structure functions. Phys. Fluids, 13 , 19851994.

  • Koch, S. E., and Coauthors, 2005: Turbulence and gravity waves within an upper-level front. J. Atmos. Sci., 62 , 38853908.

  • Kolmogorov, A., 1941: Dissipation of energy in the locally isotropic turbulence (English translation 1991). Proc. Roy. Soc. London, A434 , 1517.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1967: Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10 , 14171423.

  • Kraichnan, R. H., 1971: Inertial range transfer in two- and three-dimensional turbulence. J. Fluid Mech., 47 , 525535.

  • Lane, T. P., J. D. Doyle, R. Plougonven, M. A. Shapiro, and R. D. Sharman, 2004: Observations and numerical simulations of inertia-gravity waves and shearing instabilities in the vicinity of a jet stream. J. Atmos. Sci., 61 , 26922706.

    • Search Google Scholar
    • Export Citation
  • Lesieur, M., 1993: Turbulence in Fluids. 2nd ed. Kluwer Academic, 412 pp.

  • Lilly, D. K., 1983: Stratified turbulence and mesoscale variability of the atmosphere. J. Atmos. Sci., 40 , 749761.

  • Lilly, D. K., 1989: Two-dimensional turbulence generated by energy sources at two scales. J. Atmos. Sci., 46 , 20262030.

  • Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech., 388 , 259288.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., and J. Y. N. Cho, 2001: Horizontal velocity structure functions in the upper troposphere and lower stratosphere, 2, Theoretical considerations. J. Geophys. Res., 106 , 1023310242.

    • Search Google Scholar
    • Export Citation
  • Lombard, P. N., and J. R. Riley, 1996: Instability and breakdown of internal gravity waves. I. Linear stability analysis. Phys. Fluids, 8 , 32713287.

    • Search Google Scholar
    • Export Citation
  • Lu, C., S. Koch, and N. Wang, 2005a: Determination of temporal and spatial characteristics of gravity waves using cross-spectral analysis and wavelet transformation. J. Geophys. Res., 110 .D01109, doi:10.1029/2004JD004906.

    • Search Google Scholar
    • Export Citation
  • Lu, C., S. Koch, and N. Wang, 2005b: Stokes parameter analysis of a packet of turbulence-generating gravity waves. J. Geophys. Res., 110 .D20105, doi:10.1029/2004JD005736.

    • Search Google Scholar
    • Export Citation
  • Marroquin, A., and B. Stankov, 1991: Diagnostic studies of clear air turbulence in isentropic coordinates. Preprints, Fourth Int. Conf. on Aviation Weather Systems, Paris, France, Amer. Meteor. Soc., 262–266.

  • Marshak, A., A. Davis, W. Wiscombe, and R. Cahalan, 1997: Scale invariance in liquid water distributions in marine stratocumulus. Part II: Multifractal properties and intermittency issues. J. Atmos. Sci., 54 , 14231444.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1975: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2. MIT Press, 874 pp.

  • Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42 , 950960.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., K. S. Gage, and W. H. Jasperson, 1984: The atmospheric kinetic energy spectrum, 10–10 km. Nature, 310 , 3638.

  • Orszag, S. A., 1977: Fluid dynamics: Statistical theory of turbulence. Fluid Dynamics, R. Balian and J. L. Peube, Eds., Gordon and Breach Science, 237–374.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., and R. Ford, 2000: The nonlinear forcing of large-scale internal gravity waves by stratified shear instability. J. Atmos. Sci., 57 , 653672.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132 , 30193032.

  • Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33 .L12812, doi:10.1029/2006GL026429.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and W. W. Orlando, 2003: The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level model simulation. J. Atmos. Sci., 60 , 824835.

    • Search Google Scholar
    • Export Citation
  • Vinnichenko, N. K., N. Z. Pinus, S. M. Shmeter, and G. N. Shur, 1980: Turbulence in the Free Atmosphere. 2nd ed. Plenum, 310 pp.

  • Weinstock, J., 1986: Finite amplitude gravity waves: Harmonics, advective steepening, and saturation. J. Atmos. Sci., 43 , 688704.

  • Weinstock, J., 1987: The turbulence field generated by a linear gravity wave. J. Atmos. Sci., 44 , 410420.

  • Yu, C. X., M. Gilmore, W. A. Peebles, and T. L. Rhodes, 2003: Structure function analysis of long-range correlations in plasma turbulence. Phys. Plasmas, 10 , 27722779.

    • Search Google Scholar
    • Export Citation
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Interaction of Upper-Tropospheric Turbulence and Gravity Waves as Obtained from Spectral and Structure Function Analyses

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  • 1 NOAA/Earth System Research Laboratory, Boulder, Colorado
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Abstract

Spectral and structure function analyses of horizontal velocity fields observed in the upper troposphere and lower stratosphere during the Severe Clear Air Turbulence Collides with Air Traffic (SCATCAT) field program, conducted over the Pacific, were carried out in an effort to identify the scale interactions of turbulence and small-scale gravity waves. Because of the intermittent nature of turbulence, these analyses were conducted by clearly separating out the cases when turbulence did or did not occur in the data. In the presence of turbulence, transitional power spectra from k−2 to k−5/3 were found to be associated with gravity waves and turbulence, respectively. The second-order structure function analysis was able to translate these spectral slopes into r and r2/3 scaling, consistent with the Monin and Yaglom conversion law, in physical space, which presented clearer pictures of scale interactions between turbulence and gravity waves. The third-order structure function analysis indicated the existence of a narrow region of inverse energy cascade from the scales of turbulence up to the gravity waves scales. This inverse energy cascade region was linked to the occurrence of Kelvin–Helmholtz instability and other wave-amplifying mechanisms, which were conjectured to lead to the breaking of small-scale gravity waves and the ensuing generation of turbulence. The multifractal analyses revealed further scale breaks between gravity waves and turbulence. The roughness and intermittent properties were also calculated for turbulence and gravity waves, respectively. Based on these properties, turbulence and gravity waves in a bifractal parameter space were mapped. In this way, their physical and statistical attributes were clearly manifested and understood.

* Additional affiliation: Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

Corresponding author address: Chungu Lu, NOAA/Earth System Research Laboratory, Boulder, CO 80305. Email: chungu.lu@noaa.gov

Abstract

Spectral and structure function analyses of horizontal velocity fields observed in the upper troposphere and lower stratosphere during the Severe Clear Air Turbulence Collides with Air Traffic (SCATCAT) field program, conducted over the Pacific, were carried out in an effort to identify the scale interactions of turbulence and small-scale gravity waves. Because of the intermittent nature of turbulence, these analyses were conducted by clearly separating out the cases when turbulence did or did not occur in the data. In the presence of turbulence, transitional power spectra from k−2 to k−5/3 were found to be associated with gravity waves and turbulence, respectively. The second-order structure function analysis was able to translate these spectral slopes into r and r2/3 scaling, consistent with the Monin and Yaglom conversion law, in physical space, which presented clearer pictures of scale interactions between turbulence and gravity waves. The third-order structure function analysis indicated the existence of a narrow region of inverse energy cascade from the scales of turbulence up to the gravity waves scales. This inverse energy cascade region was linked to the occurrence of Kelvin–Helmholtz instability and other wave-amplifying mechanisms, which were conjectured to lead to the breaking of small-scale gravity waves and the ensuing generation of turbulence. The multifractal analyses revealed further scale breaks between gravity waves and turbulence. The roughness and intermittent properties were also calculated for turbulence and gravity waves, respectively. Based on these properties, turbulence and gravity waves in a bifractal parameter space were mapped. In this way, their physical and statistical attributes were clearly manifested and understood.

* Additional affiliation: Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

Corresponding author address: Chungu Lu, NOAA/Earth System Research Laboratory, Boulder, CO 80305. Email: chungu.lu@noaa.gov

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