Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T15:38:04.752Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of gravity waves on turbulence decay in stratified fluids

Published online by Cambridge University Press:  20 April 2006

J. Weinstock
J. Weinstock
Affiliation:
National Oceanic and Atmospheric Administration. Aeronomy Laboratory, Boulder, Colorado 80303
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical calculation is made of the decay of turbulence energy in the presence of coherent internal gravity waves of various intensities. The wave-turbulence interaction considered is energy production by wave shear. The production term (stress) is calculated by a second-order closure, with temperature fluctuations accounted for by buoyancy subrange theory. This formalism applies to large or small turbulence Froude number, both extremes of which are often encountered in experimental turbulence decay. The theoretical turbulence decay is shown to be a universal function of the wave shear (strain rate) and wave frequency provided that the energy is expressed in terms of the buoyancy wavenumber kB, and time is expressed in terms of N, the Brunt-Väisälä frequency. With the amplitude of wave shear characterized by a gradient Richardson number Ri0, the turbulence decay is found to undergo a sudden transition from rapid decay to a much slower oscillating decay when Ri0 is less than about 0.4. The transition time occurs at about t ≈ 2πN−1. If Ri0 exceeds 0.8 the rate of decay exceeds that of a neutral fluid. A transition in turbulence decay was observed in experiments by Dickey & Mellor (1980). It might explain the continued presence of turbulence in dynamically stable regions of oceans or atmosphere. The theory is compared in much detail with the Dickey & Mellor experiment. A briefer comparison is also made with other experiments, and with previous calculations of turbulence maintenance by steady mean shear. A simple explanation is proposed of why a transition is observed in a vertical grid experiment but not in horizontal grid experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 11 - 26
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539–566.Google Scholar
Boucher, R. J. 1974 Evaluation of clear air turbulence detection by ground based radars, special rawinsondes and aircraft, 1967–1971. AFCRL-TR-74-0489, Air Force Cambridge Research Lab., Hanscomb, MA.
Britter, R. E., Hunt, J. C. R., Marsh, C. L. & Snyder, W. H. 1983 The effects of stable stratification on turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27–44.Google Scholar
Caldwell, D. R., Dillon, T. M., Brubaker, J. M., Newberger, P. A. & Paulson, C. A. 1980 The scaling of vertical temperature gradient spectra. J. Geophys. Res. 85, 1917–1924.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of gridgenerated turbulence. J. Fluid Mech. 25, 667–687.Google Scholar
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 37–48.Google Scholar
Dutton, J. A. & Panofsky, H. A. 1970 Clear air turbulence: a mystery may be unfolding. Science 167, 937–944.CrossRefGoogle Scholar
Einaudi, F., Lalas, D. P. & Peron, G. E. 1978–1979 The role of gravity waves in the tropospheric processes. Pure Appl. Geophys. 117, 627–663.Google Scholar
Fua, D., Chimonas, G., Einaudi, F. & Zeman, O. 1982 An analysis of wave-turbulence interaction. J. Atmos. Sci. 39, 2450–2463.Google Scholar
Gargett, A. E., Hendricks, P. J., Sanford, T. B., Osborn, T. R. & Williams, A. J. 1981 A composite spectrum of vertical shear in the upper ocean. J. Phys. Oceanogr. 11, 1258–1271.Google Scholar
Klemp, J. B. & Lilly, D. K. 1975 The dynamics of wave-induced downslope winds. J. Atmos. Sci. 32, 320–339.Google Scholar
Lange, R. E. 1974 Decay of turbulence in stratified salt water. PhD thesis, University of California, San Diego.
Lilly, D. K., Waco, D. E. & Adlefang, S. I. 1974 Stratospheric mixing estimated from high altitude turbulence measurements. J. Appl. Meteor. 13, 488–493.Google Scholar
Lin, J. T. & Pao, Y. H. 1979 Waves in stratified fluids. Ann. Rev. Fluid Mech. 11, 317–388.Google Scholar
Lin, J. T. & Veenhuizen, S. D. 1974 Measurements of the decay of grid generated turbulence in a stably stratified fluid (abstract). Bull. Am. Phys. Soc. 19, 1142–1143.Google Scholar
Linden, P. F. 1980 Mixing across a density interface produced by grid turbulence. J. Fluid Mech. 100, 691–703.Google Scholar
Lumley, J. L. 1964 The spectrum of nearly inertial range turbulence in a stably stratified fluid. J. Atmos. Sci. 21, 99–102.Google Scholar
Lumley, J. L. & Newman, G. R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178.Google Scholar
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Mellor, G. L. & Yamada, T. 1974 A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, pp. 397–398. MIT Press.
Pao, Y. H. 1973 Measurements of internal waves and turbulence in two-dimensional stratified shear flows. Boundary-Layer Meteor. 5, 177–193.Google Scholar
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Phys. 8, 183–208.Google Scholar
Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. 1. Mitteilung. Z. Phys. 129, 547–572.Google Scholar
Rüster, R., Rottger, J. & Woodman, R. F. 1978 Radar measurements of waves in the lower troposphere. Geophys. Res. Lett. 5, 555–558.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Van Zandt, T. E., Green, J. L. & Clark, W. L. 1979 Buoyancy waves in the troposphere: Doppler radar observations and a theoretical model. Geophys. Res. Lett. 6, 429–432.Google Scholar
Weinstock, J. 1978a On the theory of turbulence in the buoyancy subrange of stably stratified flows. J. Atmos. Sci. 35, 634–649.Google Scholar
Weinstock, J. 1978b Vertical turbulent diffusion in a stably stratified fluid. J. Atmos. Sci. 35, 1022–1027.Google Scholar
Weinstock, J. 1981 Theory of the pressure-strain-rate correlation for Reynolds-stress turbulence closures. Part 1. Off-diagonal element. J. Fluid Mech. 105, 369–395.Google Scholar
Yamada, T. 1975 The critical Richardson number and the ratio of the eddy transport coefficients obtained from a turbulence closure model. J. Atmos. Sci. 32, 926–933.Google Scholar
Zimmerman, S. P. & Loving, N. V. 1975 Turbulence dissipation and diffusivities in the stratosphere using Richardson's technique. In. The Natural Stratosphere of 1974; CIAP Monograph 2, Dept. Transportation TST-75-51, pp. 6–93-6–103.