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The evolution of grid-generated turbulence in a stably stratified fluid

  • E. C. Itsweire (a1), K. N. Helland (a1) and C. W. Van Atta (a1)

Abstract

The spatial decay and structural evolution of grid-generated turbulence under the effect of buoyancy was studied in a ten-layer, salt-stratified water channel. The various density gradients were chosen such that the initial overturning turbulent scale was slightly smaller than any of the respective buoyancy scales. The observed general evolution of the flow from homogeneous turbulence to a composite of fossil turbulence or quasi-two-dimensional turbulence and internal wavefield is in good agreement with the predictions of Gibson (1980) and the lengthscale model of Stillinger, Helland & Van Atta (1983). The effect of the initial size of the turbulent lengthscale compared with the buoyancy scale on the decay and evolution of the turbulence is investigated and the observed influence on the rate of decay of both longitudinal and vertical velocity fluctuations pointed out by Van Atta, Helland & Itsweire (1984) is shown to be related to the magnitude of the initial internal wavefield at the grid. An attempt is made to remove the wave-component kinetic energy from the vertical-velocity-fluctuation data of Stillinger, Helland & Van Atta (1983) in order to obtain the true decay of the turbulent fluctuations. The evolution of the resulting fluctuations is similar to that of the present large-grid data and several towed-grid experiments. The rate of destruction of the density fluctuations (active-scalar dissipation rate) is estimated from the evolution equation for the potential energy, and the deduced Cox numbers are compared with those obtained from oceanic microstructure measurements. The classical Kolmogorov and Batchelor scalings appear to collapse the velocity and density spectra better than the buoyancy scaling proposed by Gargett, Osborn & Nasmyth (1984). The rise of the velocity spectra at low wavenumbers found by Stillinger, Helland & Van Atta (1983) is shown to be related to internal waves.

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Batchblor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539.
Britter, R. E., Hunt, J. C. R., Marsh, G. L. & Snyder, W. H. 1983 The effect of stable stratification on turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27.
Caldwell, D. R. 1983 Oceanic turbulence: big bangs or continuous creation?. J. Geophys. Res. 88, 7543.
Castaldini, M., Helland, K. N. & Malvestuto, V. 1980 Hot-film anemometry in aqueous NaCl solutions. Intl J. Heat Mass Transfer 24, 133.
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13.
Dillon, T. M. 1982 Vertical overturns: a comparison of the Thorpe and Ozmidov scales. J. Geophys. Res. 87, 9601.
Dillon, T. M. 1984 The energetics of overturning structures: implications for the theory of fossil turbulence. J. Phys. Oceanogr. 14, 541.
Dillon, T. M. & Caldwell, D. R. 1980 The Batchelor spectrum and dissipation in the upper ocean. J. Geophys. Res. 85, 1910.
Ellison, T. H. 1957 Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2, 456.
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.
Gargett, A. E., Osborn, T. R. & Nasmyth, P. W. 1984 Local isotropy and the decay of turbulence. J. Fluid Mech. 144, 231.
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. 1982a Alternative interpretations for microstructure patches in the thermocline. J. Phys. Oceanogr. 12, 374.
Gibson, C. H. 1982b On the scaling of vertical temperature spectra. J. Geophys. Res. 87, 8031.
Gregg, M. C. 1980 Microstructure patches in the thermocline. J. Phys. Oceanogr. 10, 915.
Gregg, M. C. 1984 Persistent turbulent mixing and near-inertial internal waves. In Proc. 2nd ‘Aha Huliko'a Hawaiian Winter Workshop.
Head, M. J. 1983 The use of miniature four-electrode conductivity probes for high resolution measurement of turbulent density or temperature variations in salt-stratified water flows. Ph.D. thesis, University of California, San Diego.
Högstböm, A. S. & Högström, U. 1975 Spectral gap in surface layer measurements. J. Atmoa. Sci. 32, 340.
Itsweire, E. C. 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764.
Lange, R. E. 1982 An experimental study of turbulence behind towed biplanar grids in a salt-stratified fluid. J. Phys. Oceanog. 12, 1506.
Lesieur, M. & Herring, J. R. 1985 Diffusion of a passive scalar in two-dimensional turbulence. J. Fluid Mech. 161, 79.
Lilly, D. K., Waco, D. W. & Adelfang, S. I. 1974 Stratospheric mixing estimated from high-altitude turbulence measurements. J. Appl. Met. 13, 488.
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids. Ann. Rev. Fluid Mech. 11, 317.
Lin, J. T. & Veenhuizen, S. D. 1975 Measurements of the decay of grid-generated turbulence in a stratified fluid. Flow Research Note no. 85.
Mcewan, A. D. 1983 The kinematics of stratified mixing through internal wavebreaking J. Fluid Mech. 128, 47.
Montgomery, R. D. 1974 An experimental study of grid turbulence in a thermally stratified flow. Ph.D. thesis, University of Michigan.
Oakey, N. S. 1982 Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr. 12, 256.
Osborn, T. R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83.
Ozmidov, R. V. 1965 On the turbulent exchange in a stably stratified ocean. Atmos. Ocean. Phys. 8, 853.
Riley, J. J., Metcalf, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In Non-linear Properties of Internal Waves (ed. B. West). AIP Conf. Proc. no. 76.
Rohr, J. J., Itsweire, E. C. & van Atta, C. W. 1984 Mixing efficiency in stably-stratified decaying turbulence. J. Geophys. Astrophys. Fluid Dyn. 29, 221.
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and the heat flux in grid turbulence. J. Fluid Mech. 128, 323.
Stewart, R. W. 1969 Turbulence and waves in a stratified atmosphere. Radio Sci. 4, 1289.
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. 1983 The interpretation of statistics from hot-film anemometers used in salt water flows of variable temperature and density. J. Phys. E: Sci. Instrum. 15, 1322
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.
Stillinger, D. C., Helland, K. N. & van Atta, C. W. 1983a Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91.
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. J. Fluid Mech. 104, 311.
Thorpe, S. A. 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. A 286, 125.
van Atta, C. W., Helland, K. N. & Itsweire, E. C. 1984 The influence of stable stratification on spatially decaying vertically homogeneous turbulence. In Proc. IUTAM Symposium on Turbulence and Chaotic Phenomena in Fluids, Sept. 1983, Kyoto, Japan (ed. T. Tatsumi), p. 519. North Holland.
Woods, J. D. 1968 Wave induced shear instability in the summer thermocline. J. Fluid Mech. 32, 791.
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The evolution of grid-generated turbulence in a stably stratified fluid

  • E. C. Itsweire (a1), K. N. Helland (a1) and C. W. Van Atta (a1)

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