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Growth and decay of turbulence in a stably stratified shear flow

Published online by Cambridge University Press:  21 April 2006

J. J. Rohr ,
E. C. Itsweire ,
K. N. Helland  and
C. W. Van Atta
J. J. Rohr
Affiliation:
Naval Ocean Systems Center, Code 634, San Diego, CA 92152, USA
E. C. Itsweire
Affiliation:
Chesapeake Bay Institute, The Johns Hopkins University, Baltimore, MD 21211, USA
K. N. Helland
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093, USA Data Ready, Suite 150 4647T, Highway 280 East, Birmingham, AL 35243, USA
C. W. Van Atta
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, CA 92093, USA
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Abstract

The behaviour of an evolving, stably stratified turbulent shear flow was investigated in a ten-layer, closed-loop, salt-stratified water channel. Simultaneous single-point measurements of the mean and fluctuating density and longitudinal and vertical velocities were made over a wide range of downstream positions. For strong stability, i.e. a mean gradient Richardson number Ri greater than a critical value of Ricr ≈ 0.25, there is no observed growth of turbulence and the buoyancy effects are similar to those in the unsheared experiments of Stillinger, Helland & Van Atta (1983) and Itsweire, Helland & Van Atta (1986). For values of Richardson number less than Ricr the turbulence grows at a rate depending on Ri and for large evolution times the ratio between the Ozmidov and turbulent lengthscale approaches a constant value which is also a function of Richardson number.

Normalized velocity and density power spectra for the present experiments conform to normalized spectra from previous moderate- to high-Reynolds-number studies. With increasing $\tau = (x/\overline{U}) (\partial \overline{U}/\partial z)$ or decreasing stability, the stratified shear spectra exhibit greater portions of the universal non-stratified spectrum curve. The shapes of the shear-stress and buoyancy-flux cospectra confirm that they act as sources and sinks for the velocity and density fluctuations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 77 - 111
Copyright
© 1988 Cambridge University Press

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References

Abarbanel H., Holm D., Marsden, J. & Ratiu T. 1984 Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys. Lett. 52, 26.Google Scholar
Batchelor G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113.Google Scholar
Caldwell D. R. 1983 Oceanic turbulence: big bangs or continuous creation? J. Geophys. Res. 88, 7543.Google Scholar
Champagne F. H., Harris, V. G. & Corrsin G. 1971 Experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81.Google Scholar
Corrsin S. 1951 On the spectrum of isotropic temperature fluctuation in an isotropic turbulence. J. Appl. Phys. 22, 469.Google Scholar
Dillon T. M. 1982 Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Geophys. Res. 187, 9601.Google Scholar
Dougherty J. P. 1961 The anisotropy of turbulence at the meteor level. J. Atmos. Terrest. Phys. 21, 210.Google Scholar
Elghobashi S., Gerz, T. & Schumann U. 1985 Direct simulation of a turbulent homogeneous shear flow with buoyancy. Fifth Symp. on Turbulent Shear Flows. Cornell University.
Ellison T. H. 1957 Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2, 456.Google Scholar
Gargett A. E. 1985 Evolution of scalar spectra with the decay of turbulence in a stratified fluid. J. Fluid Mech. 159, 379.Google Scholar
Gargett A. E., Osborn, T. R. & Nasmyth P. W. 1984 Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 144, 231.Google Scholar
Gibson C. H. 1968 Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 236.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. & Schwarz W. H. 1963 The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech. 16, 365.Google Scholar
Grant H. L., Stewart, R. W. & Moilliet A. 1962 Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241.Google Scholar
Gregg M. C. 1984 Persistent turbulent mixing and near-inertial internal waves. In Proc. Second ‘Aha Huliko'a Hawaiian Winter Workshop (ed. P. Muller & R. Pujalet), p. 1. Hawaii Institute of Geophysics.
Harris V. G., Graham, A. A. & Corrsin S. 1977 Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 81, 657.Google Scholar
Head M. J. 1983 The use of miniature four-electrode conductivity probes for high resolution measurements of turbulent density or temperature variations in salt-stratified water flows. Ph.D. thesis, University of California, San Diego.
Helland K. N., Lii, K. S. & Rosenblatt M. 1977 Bispectra of atmospheric and wind tunnel turbulence. In Proc. Symp. on Applications of Statistics (ed. P. R. Krishnaiah), vol. 2, p. 123. Academic.
Itsweire E. C. 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764.Google Scholar
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.Google Scholar
Ivey, G. N. & Corcos G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 1.Google Scholar
Karnik, U. & Tavoularis S. 1983 The asymptotic development of nearly homogeneous turbulent shear flow. In Tubulent Shear Flows 4 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), p. 14.18. Springer.
Karnik, U. & Tavoularis S. 1987 Generation and manipulation of uniform shear with the use of screens. Exp. Fluids 5, 247.Google Scholar
Komori S., Ueda H., Ogino, F. & Mizushina T. 1983 Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. 130, 13.Google Scholar
Koop, G. C. & Browand F. K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135.Google Scholar
Launder B. E. 1975 On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67, 569.Google Scholar
Lin, J.-T. & Pao Y.-H. 1979 Wakes in stratified fluids. Ann. Rev. Fluid Mech. 11, 317.Google Scholar
Linden P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3.Google Scholar
Lumley, J. L. & Panofsky H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Miles J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 68, 577.Google Scholar
Montgomery R. D. 1974 An experimental study of grid turbulence in a thermally-stratified flow. Ph.D. thesis, University of Michigan.
Mulhearn, P. J. & Luxton R. E. 1975 The development of turbulent structure in a uniform mean shear flow. J. Fluid Mech. 68, 577.Google Scholar
Obukhov A. M. 1949 Struktura temperaturnova polia v turbulentnom potoke. Izv. Akad. Nauk SSSR Ser. Geofiz. 3, 59.Google Scholar
Owen, D. R. & Zienkiewicz H. K. 1957 The production of uniform shear flow in a wind tunnel. J. Fluid Mech. 2, 521.Google Scholar
Ozmidov R. V. 1965 On the turbulent exchange in a stably stratified ocean Izv. Acad. Sci. USSR Atmos. Ocean Phys. (Engl. Trans.) 1, 853.Google Scholar
Rohr J. J. 1985 An experimental study of evolving turbulence in uniform mean shear flows with and without stable stratification. Ph.D. thesis, University of California, San Diego.
Rohr J. J., Itsweire E. C., Helland, K. N. & Van Atta C. W. 1988 The investigation of the growth of turbulence in a uniform mean gradient shear flow. J. Fluid Mech. 187, 1.Google Scholar
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.Google Scholar
Rohr, J. J. & Van Atta C. W. 1987 Mixing efficiency in stably stratified growing turbulence. J. Geophys. Res. 92, 5481.Google Scholar
Rose W. G. 1966 Results of an attempt to generate a homogeneous turbulent shear flow. J. Fluid Mech. 25, 97.Google Scholar
Rose W. G. 1970 Interaction of grid turbulence with a uniform mean shear. J. Fluid Mech. 44, 767.Google Scholar
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. 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.Google Scholar
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.Google Scholar
Stillinger D. C., Helland, K. N. & Van Atta C. W. 1983 Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91.Google Scholar
Tavoularis S. 1985 Asymptotic laws for transversely homogeneous turbulent shear flows. Phys. Fluids 28, 999.Google Scholar
Tavoularis, S. & Corrsin S. 1981 Experiments in nearly homogeneous turbulent shear flows with a uniform mean temperature gradientPart 1. J. Fluid Mech. 104, 311.Google Scholar
Tennekes, M. & Lumley J. L. 1972 A First Course in Turbulence. Massachusetts Institute of Technology Press.
Thorpe S. A. 1977 Turbulence and mixing in a Scottish loch Phil. Trans. R. Soc. Lond. A 286, 125.Google Scholar
Webster C. G. A. 1964 An experimental study of turbulence in a density-stratified shear flow. J. Fluid Mech. 19, 221.Google Scholar