Abstract
Turbulence and stratification are common features of environmental flows, and their interactions lead to a myriad of flow phenomena of dynamical interest. These flow phenomena are described based on a dynamical framework provided by the equations of motion. Various broad categories of stratified turbulent flows are identified and their characteristics are briefly reviewed.
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Andre, J. C., De Moor, G. Lacarrere, P., Therry, G, Du Vachat, R. Modeling the 24 hour evolution of the mean and turbulent structures of the Planetary Boundary Layer. J. Atmos. Sci. 1978; 35:1861–1883.
Batchelor, G. K. The theory of homogeneous turbulence. Cambridge University Press, 1953.
Batchelor, G. K. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech., 1959; 5:113–133.
Batchelor, G. K., Townsend, A. A. Decay of isotropic turbulence in the final period. Proc. R. Soc. Lond. 1948; A194:527–543.
Boyer, D. L., Davies, P. A., Fernando, H. J. S., Zhang, X. Linearly stratified flow past a cylinder. Phil. Trans. R. Soc. London Ser A. 1989; 328:501–528.
De Silva, I. P. D., Fernando, H. J. S. Some aspects on mixing in a stratified turbulent patches. J. Fluid Mech. 1992; 240:601–625.
De Silva, I. P. D., Fernando, H. J. S. Experiments on collapsing turbulent regions in stratified fluids. J. Fluid Mech. 1998; 358:29–60.
De Silva, I. P. D., Fernando, H. J. S., Eaton, F., Hebert, D. Evolution of Kelvin-Helmholtz billows in nature and laboratory. Earth and Planetary Sci. Lett. 1996; 143:217–231.
Deardorff, J. W. A multi-limit mixed layer entrainment formulation. J. Phys. Oceanogr. 1983; 13:988–1002.
Dickey, T. D., Mellor, G. L. Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 1980; 99:13–31.
Fernando, H. J. S. Growth of a turbulent patch in a stratified fluid. J. Fluid Mech. 1988; 190:55–70.
Fernando, H. J. S. Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 1991; 23:455–493.
Fernando, H. J. S. Aspects of stratified turbulence. Proceedings GTP workshop, Boulder, Kluwer Academic Publishing 2000 (in Press).
Fernando, H. J. S., Hunt, J.C.R. Some aspects of turbulence and mixing in stably stratified fluids. Dyn. Atmos. Oceans 1996; 23:35–62.
Fincham, A. M., Maxworthy, T., Spedding, G. R. Energy dissipation and vortex structure in freely decaying stratified grid turbulence. Dyn. Atmos. Oceans 1996; 23(1–4):155–171.
Flor, J., Fernando, H. J. S., van Heijst, G. J. F. The evolution of an isolated turbulent region in a two-layer fluid. Phys. Fluids 1994; 6(1):287–296.
Fonseka, S. V., Fernando, H. J. S., van Heijst, G. J. F. Evolution of an isolated turbulent region in a stratified fluid. J. Geophys. Res. 1998; 103(C11):24857–24868.
Gargett, A. E., Osborn, T. R., Nasmyth, P. W. Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 1984; 144:231–280.
Gerz, T., Yamazaki, H. Direct numerical simulation of buoyancy-driven turbulence in stably stratified fluid J. Fluid Mech. 1993; 249:415–440.
Gibson, C. H. Fossil temperature, salinity, and vorticity turbulence in the ocean. In Marine Turbulence, J. Nihoul (ed.), Elsevier Publishing Co., Amsterdam, 1980.
Gibson, C. H. Fossil turbulence and intermittency in sampling oceanic mixing processes. J. Geophys. Res, 1987; 92(C5): 5383–5404.
Gibson, C. H. Laboratory, numerical, and oceanic fossil turbulence in rotating and stratified flows. J. Geophys. Res. 1991; 96:12549–12566.
Gregg, M. C. Diapycnal mixing in the thermocline: A review. J. Geophys. Res. 1987; 92(C5):5249–5286.
Hanazaki, H., Hunt, J. C. R. Linear processes in unsteady stably stratified turbulence. J. Fluid Mech. 1996; 318:303–337.
Harris, V. G., Graham, J. A., Corrsin, S. Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 1977; 81:657–687.
Hopfinger, E. J. Turbulence in stratified fluids: A Review. J. of Geophys. Res. 1987; 92(C5):5287–5303.
Huq, P., Britter, R. E. Turbulence evolution and mixing in a two-layer stably stratified fluid. J. Fluid Mech. 1995; 285:41–67.
Itsweire, E. C., Helland, K. N., van Atta, C. W. The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 1986; 162:299–338.
Ivey, G. N., Nokes, R.I. Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 1989; 204:479–500.
Ivey, G. N., Imberger, J. On the nature of turbulence in a stratified fluid. 1: The energetics of mixing. J. Phys. Oceanogr. 1991; 21:650–658.
Jacobitz, F. G., Sarkar, S. On the shear number effects in stratified shear flow. Theor. Comp. Fluid Dyn. 1999; 13:171–188.
Kitaigorodskii, S. A. On the computation of the thickness of the wind mixing layer in the ocean. Bull. Acad. Sci. U.S.S.R. Geophys. Ser. 1960; 3:284–287.
Lienhard, J. K., van Atta, C. W. The decay of turbulence in thermally stratified flow. J. Fluid Mech. 1990; 210:57–112.
Lilly, D. K. Stratified turbulence and mesoscale variability of the atmosphere. Amer. Meteor. Soc. 1983; 40:749–761.
Lin, J.-T., Pao, Y. H. Wakes in stratified fluids, Ann. Rev. Fluid Mech. 1979; 11:317.
Lindborg, E. Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 1998; 388:259–288.
Liu, H.-T. Energetics of grid turbulence in a stably stratified fluid. J. Fluid Mech. 1995; 296:127–157.
Liu, Y. N., Maxworthy, T., Spedding, G. R. Collapse of a turbulent front in a stratified fluid, 1. Nominally two-dimensional evolution in a narrow tank. J. Geophys. Res. 1987; 92(5):5427–5433.
Lozovatsky, I. E., Fernando, H. J. S. Turbulent mixing on a shallow shelf, Submitted to J. Phys. Oceanogr. 2000.
Mahrt, L. Stratified atmospheric boundary layers and breakdown of models. Theor. Comp. Fluid Dynamics 1998; 11:263–279.
McEwan, A. D. The kinematics of stratified mixing through internal wave breaking. J. Fluid Mech. 1983; 128:47–57.
Mellor, G. L., Yamada, T. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 1974; 31:1791–1806.
Müller, P. Small-scale vortical motions. Proceedings of the Internal Gravity Waves and Small-Scale Turbulence Hawaiian Winter Workshop, (ed. P. Muller, and R. Pujalet). Hawaii Institute of Geophysics, Honolulu. 1984.
Pacanowski, R. C., Philander, S. G. H. Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr. 1981; 11:1442–1451.
Pearson, H. J., Linden, P. F. The final stage of decay of turbulence in stably stratified fluid. J. Fluid Mech. 1983; 134:195–203.
Piccirillo, P.S., van Atta, C.W. The evolution of a uniformly sheared thermally stratified turbulent flow. J. Fluid Mech. 1997; 334:61–86.
Rehmann, C. R., Koseff, J. R. A unified scaling theory for the mixing efficiency of decaying stratified turbulence. Submitted to J. Fluid Mech., 2000.
Riley, J. J., Lelong, M. P. Fluid motions in the presence of strong stable stratification. Ann. Rev. Fluid Mech. 2000; 32:613–657.
Riley, J. J., Metcalfe, R. W., Weissman, M. W. Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In: Nonlinear Properties of Internal Waves (ed: B.J. West). AIP Conf. Proc. 1981; 76:79–112.
Rohr, J. J., Itsweire, C., Helland, K. N., van Atta, C. W. Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 1988a; 195:77–111.
Rohr, J. J., Itsweire, C., Helland, K. N., van Atta, C. W. An investigation of growth of turbulence in a uniform-mean-shear flow. J. Fluid Mech. 1988b; 188:1–33.
Rouse, H., Dodu, J. Turbulent diffusion across a density discontinuity. Houille Blanche 1955; 10:522–532.
Sherman, F. S., Imberger, J., Corcos, G. M. Turbulence and mixing in stably stratified waters. Ann. Rev. Fluid Mech. 1978; 10:267–288.
Stillinger, D. C., Helland, K. N., van Atta, C. W. Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 1983; 131:91–122.
Strang, E. J., Fernando, H. J. S. Entrainment and mixing in stratified shear flows. J. Fluid Mech., Submitted, 2000.
Thorpe, S.A. Turbulence and mixing in a Scottish loch. Phil. Trans. Roy. Soc. London Ser. A. 1977; 286:125–181.
Townsend, A. A. Structure of Turbulent Shear Flow. Cambridge University Press, 1976.
Yoon, K., Warhaft, Z. The evolution of grid generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 1990; 215:601–638.
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Fernando, H.J.S. (2003). Turbulence in Stratified Fluids. In: Grimshaw, R. (eds) Environmental Stratified Flows. Topics in Environmental Fluid Mechanics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/0-306-48024-7_6
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DOI: https://doi.org/10.1007/0-306-48024-7_6
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