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Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid

Published online by Cambridge University Press:  20 April 2006

D. C. Stillinger ,
K. N. Helland  and
C. W. Van Atta
D. C. Stillinger
Affiliation:
Institute for Pure and Applied Physical Sciences and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093
K. N. Helland
Affiliation:
Institute for Pure and Applied Physical Sciences and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093
C. W. Van Atta
Affiliation:
Institute for Pure and Applied Physical Sciences and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093
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Abstract

The evolution of unsheared grid-generated turbulence in a stably stratified fluid was investigated in a closed-loop salt-stratified water channel. Simultaneous single-point measurements of the horizontal and vertical velocity and density fluctuations were obtained, including turbulent mass fluxes central in understanding the energetics of the fluctuating motion. When the buoyancy lengthscale was initially substantially larger than the largest turbulent scales, the initial behaviour of the velocity and density fields was similar to that in the non-stratified case. With further downstream development, the buoyancy lengthscale decreased while the turbulence scale grew. Deviations from neutral behaviour occurred when these two lengthscales became of the same order, after the initially larger inertial forces associated with the initial kinetic energy had become weaker and buoyancy forces became important.

Buoyancy forces produced anisotropy in the largest scales first, preventing them from overturning, while smaller-scale isotropic turbulent motions remained embedded within the larger-scale wave motions. These small-scale motions exhibited classical turbulent behaviour and scaled universally with Kolmogorov length and velocity scales. Eventually even the smallest scales of the decaying turbulence were affected by buoyancy, all isotropic motions disappeared, and Kolmogorov scaling failed. The turbulent vertical mass flux decreased to zero for this condition, indicating that the original turbulent field had been completely converted to random internal wave motions.

The transition from a fully turbulent state to one of internal waves occurred rapidly in a time less than the characteristic time of the turbulence based on the largest-scale eddies found in the flow at transition. The dissipation rate for complete transition to a wave field was found to be of the order of εt = 24.5νN2, where ν is the kinematic viscosity and N the Brunt-Väisälä frequency. This is in fairly good agreement with the value 30νN2 predicted by Gibson (1980, 1981).

The present experiments have determined quantitative limits on the range of active turbulent scales in homogeneous stratified turbulence, in terms of an upper limit near the buoyancy lengthscale and a lower limit determined by viscosity in the usual way. This description has been used here to help explain and assimilate the results from the earlier stratified grid-turbulence experiments of Lin & Veenhuizen (1975) and Dickey & Mellor (1980). While some of the features of the present observations may be qualitatively seen in the numerical simulations of the problem of Riley, Metcalfe & Weissman (1981), there are fundamental differences, probably due in part to large differences in initial lengthscale ratios and in the limited range of scales attainable in numerical simulations. The present experiments may serve as a useful test case for future modelling and interpretation of the behaviour of turbulence in stratified flows observed in the oceans and atmosphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 131 , June 1983 , pp. 91 - 122
Copyright
© 1983 Cambridge University Press

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References

Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539.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.Google Scholar
Chen, W. 1970 Spectral energy transfer and higher order correlations in grid turbulence. Ph.D. thesis, University of California, San Diego.
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids J. Fluid Meck. 99, 13.Google Scholar
Dougherty, J. P. 1961 The anisotropy of turbulence at the meteor level J. Atmos. Terrest. Phys. 21, 210.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. 1981 Fossil turbulence and internal waves. In Non-linear Properties of Internal Waves (ed. B.West). AIP Conf. Proc. no. 76.Google Scholar
Gibson, C. H. 1982a Alternative interpretations for microstructure patches in the thermocline. J. Phys. Oceanogr. 12, 374.Google Scholar
Gibson, C. H. 1982b On the scaling of vertical temperature gradient spectra. J. Geophys. Res. 87, 8031.Google Scholar
Gregg, M. C. 1980 Microstructure patches in the thermocline J. Phys. Oceanogr. 10, 915.Google Scholar
Lange, R. E. 1974 Decay of turbulence in stratified salt water. Ph.D. thesis, University of California, San Diego.
Lin, T. J. & Veenhutzen, S. D. 1975 Measurements of the decay of grid-generated turbulence in a stratified fluid. Flow Research Note no. 85.Google Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows J. Fluid Mech. 10, 496.Google Scholar
Monin, A. S. & Obukhov, A. M. 1953 Dimensionless characteristics of turbulence in the surface layer of the atmosphere Dokl. Acad. Nauk SSSR 92, no. 2.Google Scholar
Montgomery, R. D. 1974 An experimental study of grid turbulence in a thermally-stratified flow. Ph.D. thesis, University of Michigan.
Nasmyth, P. W. 1970 Oceanic turbulence. Ph.D. thesis, University of British Columbia.
Obukhov, A. M. 1959 On the influence of the buoyancy force on the structure of the temperature field in a turbulent flow Dokl. Acad. Nauk SSSR 125, no. 6.Google Scholar
Ozmidov, R. V. 1965 On the turbulent exchange in a stably stratified ocean Atmos. Ocean Phys. 8, 853.Google Scholar
Pao, Y. H. 1973 Measurements of internal waves and turbulence in two-dimensional stratified shear flows Boundary-Layer Met. 5, 177.Google Scholar
Riley, J. J., Metcalf, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In Nonlinear Properties of Internal Waves (ed. B. J. West). AIP Conf. Proc. no. 76.
Stewart, R. W. 1969 Turbulence and waves in a stratified atmosphere Radio Sci. 4, 1289.Google Scholar
Stillinger, D. C. 1981 An experimental study of the transition of grid turbulence to internal waves in a salt-stratified water channel. Ph.D. thesis, University of California, San Diego.
Stillinger, D. C., Head, M. J., Helland, K. N. & VAN ATTA, C. W. 1983 A closed-loop gravity-driven water channel for density-stratified shear flows J. Fluid Mech. 131, 73–89.Google Scholar
Tao, M. 1971 Turbulent mixing of density stratified fluids. Ph.D. thesis, University of Iowa.
Wyngaard, J. C. 1968 Measurement of small scale turbulence structure with hot wires J. Sci. Instrum. 2, 1105.Google Scholar