Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T07:32:10.740Z Has data issue: false hasContentIssue false
  • English
  • Français

The decay of turbulence in thermally stratified flow

Published online by Cambridge University Press:  26 April 2006

J. H. Lienhard V  and
C. W. Van Atta
J. H. Lienhard V
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
C. W. Van Atta
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California at San Diego, La Jolla, CA 92093 USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The decay of grid-generated turbulence in the presence of strong thermal stratification is studied in a continuously stratified, open-loop wind tunnel at Brunt–Väisälä frequencies up to 2.5s−1. The data include one-point statistical measurements through moments of fourth order and associated power- and cross-spectra. Cross-channel phase measurements are used to analyse the scales of correlation of velocity and temperature. The present data are considerably more coherent than previous salt-stratified data, and the structural form of stratified turbulence is thus more clearly manifested. No internal wave effects are observed at any stage of the decay. Stratified turbulence is found to be a two-scale process dominated by buoyancy forces at large scales of motion and dissipative effects at small scales. The two-scale structure is used to develop universal buoyancy scalings for the decay of the vertical heat flux, the scalar variance, and the molecular dissipation rates, and, in particular, for the vertical velocity decay. Velocity and temperature spectra satisfy universal equilibrium scaling at high wavenumbers, but show buoyancy effects at small wavenumbers. The flow remains isotropic at high wavenumbers over the entire range of turbulent decay studied. Cospectral and phase data are used to validate the two-scale model of the turbulence. The flow may show large-scale restratification while active turbulence persists at smaller scales, so that the vanishing of the vertical transport does not represent extinction of turbulent motion. Additionally, an original universal equilibrium scaling is developed for the cross-spectrum. Lengthscale evolution is measured, and the overturning and buoyancy lengthscales (associated with potential and kinetic energy, respectively) are found to characterize flow development. The role of the Prandtl number is assessed by comparison to previous works, and the Prandtl number is found to have a significant influence upon stratified turbulence evolution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 210 , January 1990 , pp. 57 - 112
Copyright
© 1990 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. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. J. Fluid Mech. 5, 113–133.Google Scholar
Britter, R. E., Hunt, J. C., Marsh, G. L. & Snyder, W. S. 1983 The effect of stable stratification on turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27–44.Google Scholar
Corrsin, S. 1951a On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.Google Scholar
Corrsin, S. 1951b The decay of isotropic temperature fluctuations in an isotropic turbulence. J. Aeronaut. Sci. 18, 417–423.Google Scholar
Corrsin, S. 1952 Heat transfer in isotropic turbulence. J. Appl. Phys. 23, 113–118.Google Scholar
Deissler, R. G. 1962 Turbulence in the presence of a vertical body force and temperature gradient. J. Geophys. Res. 67, 3049–3062.Google Scholar
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13–31.Google Scholar
Dunn, D. W. & Reid, W. H. 1958 Heat transfer in isotropic turbulence during the final period of decay. NACA TN-4186.Google Scholar
Gargett, A. E. 1985 Evolution of scalar spectra with the decay of turbulence in a stratified fluid. J. Fluid Mech. 159, 379–407.Google Scholar
George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155–191.Google Scholar
Gibson, C. H. 1980 Fossil temperature, salinity, and vorticity in the ocean. In Marine Turbulence (ed. J. C. T. Nihoul), p. 221. Elsevier.
Gibson, C. H. 1982 On the scaling of vertical temperature spectra. J. Geophys. Res. 87, 8031.Google Scholar
Helland, K. N. & Van Atta, C. W. 1978 The ‘Hurst phenomenon’ in grid turbulence. J. Fluid Mech. 85, 573–589.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1986 The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 299–338.Google Scholar
Lange, R. E. 1982 An experimental study of turbulence behind towed biplanar grids in a salt-stratified fluid. J. Phys. Oceanogr. 12, 1506.Google Scholar
Lienhard V, J. H. 1988 The decay of turbulence in thermally stratified flow. Doctoral dissertation, University of California, San Diego
Lienhard V, J. H. & Van Atta, C. W. 1989 Thermally stratifying a wind tunnel for buoyancy influenced flows. Exps Fluids (in the press).Google Scholar
Lin, T. J. & Veenhuizen, S. D. 1975 Measurements of the decay of grid-generated turbulence in a stratified fluid. Flow Research Note no. 85.
Métais, O. 1987 Turbulence submitted to stable density stratification and statistical theory. Sixth Symp. Turbulent Shear Flows September 7-9. Toulouse.
Métais, O. & Herring, J. R. 1989 Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202, 117–148.Google Scholar
Montgomery, R. D. 1974 An experimental study of grid turbulence in a thermally-stratified flow. Doctoral Dissertation, University of Michigan.
Obukhov, A. M. 1949 Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR, Ser. Geogr. i Geofiz. 13, 58–69.Google Scholar
Riley, J. J., Metcalff, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids In Nonlinear Properties of Internal Waves. AIP Conference Proc. vol. 76, pp. 79–112. American Institute of Physics.
Sanderson, R. C., Hill, J. C. & Herring, J. R. 1987 Transient behavior of a stably stratified homogeneous fluid. In Advances in Turbulence (ed. G. Comte-Bellot & J. Mathieu), p. 184. Springer.
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323–346.Google Scholar
Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S. 1980 Temperature fluctuations and scales in grid-generated turbulence. J. Fluid Mech. 100, 597–621.Google Scholar
Stewart, R. W. 1969 Turbulence and waves in a stratified atmosphere. Radio Sci. 4, 1269–1278.Google Scholar
Stillinger, D. C. 1981 An experimental study of the transition of grid turbulence to internal waves in a salt-stratified water channel. Doctoral dissertation, University of California, San Diego
Stillinger, D. C., Head, M. J., Helland, K. N. & Van Atta, C. W. 1983a A closed-loop gravity-driven water channel for density-stratified shear flows. J. Fluid Mech. 131, 73–89.Google Scholar
Stillinger, D. C., Helland, K. N. & Van Atta, C. W. 1983b Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 73–89.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 331–347.Google Scholar
Venkataramani, K. S. & Chevray, R. 1978 Statistical features of heat transfer in grid-generated turbulence: constant-gradient case. J. Fluid Mech. 86, 513–543.Google Scholar
Wiskind, H. K. 1962 A uniform gradient transport experiment. J. Geophys. Res. 67, 3033–3048.Google Scholar
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233–261.Google Scholar