TURBULENT MIXING IN STRATIFIED FLUIDS

ion layer in the oceanic benthic boundary layer against the stratification of the lutocline, and the growth of the planetary boundary layer (PBL) due to the turbulent mixing at the tropopause. Such mixing processes are of importance in studying and controlling various biological activities and the dispersion of pollutants in the environment. Pertinent engineering situations include mixing at the thermocline due to the dis­ charge of buoyant jets from power plants [e.g. ocean thermal-energy con­ version (OTEC)]; water-qua lity control in stratified, multi port reservoirs; control of mixing during the operation of solar ponds; and mixing of methane gas in mine shafts. Mixing mechanisms in stratified fluids depend on the nature of the external forcing and the background

[1]  Lakshmi Kantha,et al.  On turbulent entrainment at a stable density interface , 1977, Journal of Fluid Mechanics.

[2]  T. Dillon,et al.  Zonal Momentum Balance at the Equator , 1989 .

[3]  G. M. Corcos,et al.  A numerical simulation of Kelvin-Helmholtz waves of finite amplitude , 1976, Journal of Fluid Mechanics.

[4]  E. Itsweire.  Measurements of vertical overturns in a stably stratified turbulent flow , 1984 .

[5]  A. E. Gill,et al.  A comparison of seasonal thermocline models with observation , 1976 .

[6]  Stephen Austen Thorpe,et al.  Turbulence and mixing in a Scottish Loch , 1977, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  R. A. Denton,et al.  Penetrative convection at low Pélet number , 1981, Journal of Fluid Mechanics.

[8]  R. R. Long,et al.  Mixed-Layer Growth in Stratified Fluids , 1985 .

[9]  Christopher N. K. Mooers,et al.  Observation and Simulation of Storm-Induced Mixed-Layer Deepening , 1978 .

[10]  Raymond T. Pollard,et al.  The deepening of the wind-Mixed layer , 1973 .

[11]  J. Atkinson,et al.  A diftusive limit tor entrainment , 1988 .

[12]  G. Ivey,et al.  Boundary mixing in a stratified fluid , 1982, Journal of Fluid Mechanics.

[13]  D. Carruthers,et al.  Waves in the Overlying inversion of the Convective Boundary Layer , 1987 .

[14]  Robert R. Long,et al.  A theory of mixing in a stably stratified fluid , 1977, Journal of Fluid Mechanics.

[15]  J. Hull,et al.  Ammonium sulfate solar pond: Obser vations from small-scale experiments , 1989 .

[16]  L. Kantha.  Turbulent Entrainment at a Buoyancy Interface Due to Convective Turbulence , 1980 .

[17]  S. Monismith,et al.  Differential mixing in a stratified fluid , 1988, Journal of Fluid Mechanics.

[18]  R. Folse,et al.  Measurements of the growth of a turbulently mixed layer in a linearly stratified fluid , 1981 .

[19]  J. Andre,et al.  Modeling the 24-Hour Evolution of the Mean and Turbulent Structures of the Planetary Boundary Layer , 1978 .

[20]  E. Hopfinger,et al.  Formation of thermoclines in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux , 1982, Journal of Fluid Mechanics.

[21]  D. Carruthers,et al.  Velocity fluctuations near an interface between a turbulent region and a stably stratified layer , 1986, Journal of Fluid Mechanics.

[22]  P. Müller,et al.  Wind Direction and Equilibrium Mixed Layer Depth: General Theory , 1985 .

[23]  J. Deardorff,et al.  On the use of an annulus to study mixed-layer entrainment , 1984, Journal of Fluid Mechanics.

[24]  J. Herring,et al.  Numerical simulations of freely evolving turbulence in stably stratified fluids , 1989, Journal of Fluid Mechanics.

[25]  C. Frankignoul.  Stability of finite amplitude internal waves in a shear flow , 1972 .

[26]  O. Phillips,et al.  An experiment on boundary mixing: mean circulation and transport rates , 1986, Journal of Fluid Mechanics.

[27]  D. B. Altman.  Critical layers in accelerating two-layer flows , 1988, Journal of Fluid Mechanics.

[28]  D. Caldwell.  Oceanic turbulence: Big bangs or continuous creation? , 1983 .

[29]  C. W. Atta,et al.  Growth and decay of turbulence in a stably stratified shear flow , 1988, Journal of Fluid Mechanics.

[30]  J. Herring,et al.  Numerical experiments in forced stably stratified turbulence , 1989, Journal of Fluid Mechanics.

[31]  C. Gibson.  Internal waves, fossil turbulence, and composite ocean microstructure spectra , 1986, Journal of Fluid Mechanics.

[32]  Paul Linden,et al.  The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment , 1973, Journal of Fluid Mechanics.

[33]  F. Browand,et al.  Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number , 1974, Journal of Fluid Mechanics.

[34]  E. Kit,et al.  Vertical Mixing Induced By Wind Anda Rotating Screen In A Stratified Fluidin A Channel , 1980 .

[35]  Jerrold E. Marsden,et al.  Richardson number criterion for the nonlinear stability of three-dimensional stratified flow , 1984 .

[36]  R. R. Long,et al.  Experiments on steady buoyancy transfer through turbulent fluid layers separated by density interfaces , 1988 .

[37]  S. Thorpe.  Laboratory observations of secondary structures in kelvin-helmhoitz billows and consequences for ocean mixing , 1985 .

[38]  J. Deardorff.  Stratocumulus-capped mixed layers derived from a three-dimensional model , 1980 .

[39]  R. Nokes.  On the entrainment rate across a density interface , 1988, Journal of Fluid Mechanics.

[40]  P. Linden.  Mixing across a density interface produced by grid turbulence , 1980, Journal of Fluid Mechanics.

[41]  J. Turner,et al.  Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows , 1986, Journal of Fluid Mechanics.

[42]  W. Peltier,et al.  The onset of turbulence in finite-amplitude Kelvin–Helmholtz billows , 1985, Journal of Fluid Mechanics.

[43]  F. Browand,et al.  The behavior of a turbulent front in a stratified fluid: Experiments with an oscillating grid , 1987 .

[44]  J. Price,et al.  On the scaling of stress-driven entrainment experiments , 1979, Journal of Fluid Mechanics.

[45]  J. Weinstock.  Effect of gravity waves on turbulence decay in stratified fluids , 1984, Journal of Fluid Mechanics.

[46]  Imad A. Hannoun,et al.  Turbulence structure near a sharp density interface , 1988, Journal of Fluid Mechanics.

[47]  C. Kranenburg,et al.  Wind-induced entrainment in a stably stratified fluid , 1984, Journal of Fluid Mechanics.

[48]  T. Utnes,et al.  Wind mixing of a stratified shear flow , 1986 .

[49]  S. Thorpe.  On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid , 1982, Journal of Fluid Mechanics.

[50]  E. Lavernia,et al.  An experimental investigation , 1992, Metallurgical and Materials Transactions A.

[51]  G. M. Corcos,et al.  Turbulence and Mixing in Stably Stratified Waters , 1978 .

[52]  A. Mcewan.  Internal mixing in stratified fluids , 1983, Journal of Fluid Mechanics.

[53]  F. Zangrando,et al.  Interfacial Mixing Caused by Turbulent Buoyant Jets , 1991 .

[54]  G. M. Corcos,et al.  Vorticity concentration and the dynamics of unstable free shear layers , 1976, Journal of Fluid Mechanics.

[55]  R. Britter,et al.  The effects of stable stratification on turbulent diffusion and the decay of grid turbulence , 1983, Journal of Fluid Mechanics.

[56]  Earl E. Gossard.  Radar Research on the Atmospheric Boundary Layer , 1990 .

[57]  A. Gargett,et al.  Local isotropy and the decay of turbulence in a stratified fluid , 1984, Journal of Fluid Mechanics.

[58]  Douglas K. Lilly,et al.  Laboratory investigation of non-steady penetrative convection , 1969, Journal of Fluid Mechanics.

[59]  C. W. Atta,et al.  Mixing efficiency in stably-stratified decaying turbulence , 1984 .

[60]  H. S. Fernando,et al.  Measurement of interfacial distortions at a stratified entrainment interface , 1990 .

[61]  C. Gibson.  Fossil Temperature, Salinity, and Vorticity Turbulence in the Ocean , 1980 .

[62]  Stephen G. Monismith,et al.  An experimental study of the upwelling response of stratified reservoirs to surface shear stress , 1986, Journal of Fluid Mechanics.

[63]  L. Padman,et al.  Richardson Number Statistics in the Seasonal Thermocline , 1985 .

[64]  S. A. Thorpe,et al.  Turbulence in stably stratified fluids: A review of laboratory experiments , 1973 .

[65]  T. Gerz,et al.  Direct numerical simulation of stratified homogeneous turbulent shear flows , 1989, Journal of Fluid Mechanics.

[66]  C. W. Atta,et al.  Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid , 1983, Journal of Fluid Mechanics.

[67]  K. Bryan,et al.  Formation of the thermocline step structure by large‐amplitude internal gravity waves , 1969 .

[68]  P. Ridd,et al.  Fluidization of mud in estuaries , 1988 .

[69]  C. Eriksen.  Implications of Ocean Bottom Reflection for Internal Wave Spectra and Mixing , 1985 .

[70]  L. Howard,et al.  Stability of stratified shear flows , 1973 .

[71]  K. N. Helland,et al.  The evolution of grid-generated turbulence in a stably stratified fluid , 1986, Journal of Fluid Mechanics.

[72]  J. Imberger,et al.  On the nature of turbulence in a stratified fluid , 1991 .

[73]  Benîrt Cushman-Roisin.  Deepening of the wind‐mixed layer: A model of the vertical structure , 1981 .

[74]  E. Hopfinger,et al.  On mixing across an interface in stably stratified fluid , 1986, Journal of Fluid Mechanics.

[75]  O. Phillips.  The dynamics of the upper ocean , 1966 .

[76]  C. Gibson.  Fossil turbulence and intermittency in sampling oceanic mixing processes , 1987 .

[77]  J. Deardorff.  A Multi-Limit Mixed-Layer Entrainment Formulation , 1983 .

[78]  P. Durbin,et al.  The Structure and Dynamics of the Ocean Surface Mixed Layer , 1975 .

[79]  K. Denman,et al.  Upper Layer Modification at Ocean Station Papa: Observations and Simulation , 1973 .

[80]  R. R. Long,et al.  Turbulent mixing with stabilizing surface buoyancy flux , 1980 .

[81]  W. R. Lindberg,et al.  An experimental study of entraining, stress‐driven, stratified flow in an annulus , 1983 .

[82]  T. McDougall.  Measurements of turbulence in a zero-mean-shear mixed layer , 1979, Journal of Fluid Mechanics.

[83]  J. Turner,et al.  Turbulent entrainment in stratified flows , 1959, Journal of Fluid Mechanics.

[84]  D. Carruthers,et al.  Turbulent Flow Near Density Inversion Layers , 1986 .

[85]  R. R. Long,et al.  Entrainment due to turbulent shear flow at the interface of a stably stratified fluid , 1986 .

[86]  E. Hopfinger,et al.  A boundary layer topped by a density interface , 1981, Journal of Fluid Mechanics.

[87]  Imad A. Hannoun,et al.  Turbulent mixing at a shear-free density interface , 1988, Journal of Fluid Mechanics.

[88]  E. Wolanski,et al.  Turbulent entrainment across stable density step structures , 1975 .

[89]  H. Yamazaki.  Stratified Turbulence near a Critical Dissipation Rate , 1990 .

[90]  F. Heidt.  The growth of the mixed layer in a stratified fluid due to penetrative convection , 1977 .

[91]  K. Moran,et al.  The Use of Ground-Based Doppler Radars to Measure Gradients, Fluxes and Structure Parameters in Elevated Layers , 1982 .

[92]  J. Andre,et al.  Mean and Turbulent Structures of the Oceanic Surface layer as Determined from One-Dimensional, Third-Order Simulations , 1985 .

[93]  J. Turner,et al.  Buoyancy Effects in Fluids , 1973 .