Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-19T21:55:57.575Z Has data issue: false hasContentIssue false

Turbulent mixing in stratified fluids: layer formation and energetics

Published online by Cambridge University Press:  26 April 2006

Young-Gyu Park
Affiliation:
MIT-WHOI Joint Program in OceanographyWoods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
J. A. Whitehead
Affiliation:
Department of Physical Oceanography Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Anand Gnanadeskian
Affiliation:
MIT-WHOI Joint Program in OceanographyWoods Hole Oceanographic Institution, Woods Hole, MA 02543, USA

Abstract

Water with constant initial salt stratification was mixed with a horizontally moving vertical rod. The initially linear density profile turned into a series of steps when mixing was weak, in agreement with instability theory by Phillips (1972) and Posmentier (1977). For stronger mixing no steps formed. However, in all cases mixed layers formed next to the top and bottom boundaries and expanded into the interior due to the no-flux condition at the horizontal boundaries. The critical Richardson number Rie, dividing experiments with steps and ones without, increases with Reynolds number Re as Rie ≈ exp(Re/900). Steps evolved over time, with small ones forming first and larger ones appearing later. The interior seemed to reach an equilibrium state with a collection of stationary steps. The boundary mixed layers continued to penetrate into the interior. They finally formed two mixed layers separated by a step, and ultimately acquired the same densities so the fluid became homogeneous. The length scale of the equilibrium steps, ls, is a linear function of U/Ni, where U is the speed of the stirring rod and Ni is the buoyancy frequency of the initial stratification. The mixing efficiency Rf also evolved in relation to the evolution of the density structure. During the initiation of the steps, Rf showed two completely different modes of evolution depending on the overall Richardson number of the initial state, Rio. For Rio [Gt ] Rie, Rf increased initially. However for Rio near Rie, Rf decreased. Then the steps reached an equilibrium state where Rf was constant at a value that depended on the initial stratification. The density flux was measured to be uniform in the layered interior irrespective of the interior density gradient during the equilibrium state. Thus, the density (salt) was transported from the bottom boundary mixed layer through the layered interior to the top boundary mixed layer without changing the interior density structure. The relationship between Ril and Rf was found for Ril > 1, where Ril is the Richardson number based on the thickness of the interface between the mixed layers. Rf decreases as Ril increases, consistent with the most crucial assumption of the instability theory of Phillips/Posmentier.

Type
Research Article
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Gibson, C. H. 1980 Fossil temperature, salinity and vorticity turbulence in the ocean. In Marine Turbulence (ed. J. C. Nihoul), pp. 221257. Elsevier.
Gibson, C. H. 1982 Alternative interpretations for microstructure patches in the thermocline. J. Phys. Oceanogr. 12, 374383.Google Scholar
Gibson, C. H. 1986 Internal waves, fossil turbulence, and composite ocean microstructure spectra. J. Fluid Mech. 168, 89117.Google Scholar
Gibson, C. H. 1987a Oceanic turbulence: big bangs and continuous creation. J. Physiochem. Hydrodyn. 8, 122.Google Scholar
Gibson, C. H. 1987b Fossil turbulence and intermittency in sampling oceanic mixing processes. J. Geophys. Res. 92, 53835404.Google Scholar
Gregg, M. C. 1989 Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94, 96869698.Google Scholar
Gregg, M. C. 1991 A study of mixing in the ocean: a brief history. Oceanography 4, 3945.Google Scholar
Hogg, N. G., Biscaye, P., Gardner, W. & Schmitz, W. J. Jr 1982 On the transport and modification of the Antarctic Bottom Water in the Vema Channel. J. Mar. Res. 40 (Suppl.), 231263.Google Scholar
Ivey, G. N. & Corcos, G. M 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 126.Google Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature turbulence in a stratified fluid. Part I: The energetics of mixing. J. Phys. Oceanogr. 21, 650658.Google Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 323.Google Scholar
Linden, P. F. 1980 Mixing across a density interface produced by grid turbulence. J. Fluid Mech. 100, 691703.Google Scholar
Munk, W. H. 1966 Abyssal Recipes. Deep-Sea kes. 13, 707730.Google Scholar
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321345.Google Scholar
Phillips, O. M. 1972 Turbulence in a strongly stratified fluid - Is it unstable? Deep-Sea Res. 19, 7981.Google Scholar
Posmentier, E. S. 1977 The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr. 7, 292300.Google Scholar
Ruddick, B. R., McDougall, T. J. & Turner, J. S. 1989 The formation of layers in a uniformly stirred density gradient. Deep-Sea Res. 36, 597609.Google Scholar
Schmitt, R. W., Toole, J. M., Koehler, R. L., Mellinger, E. C. & Doherty, K. W. 1988 The development of a fine- and microstructure profiler. J. Atmos. Ocean. Tech. 5, 484500.Google Scholar
Thorpe, S. A. 1982 On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid. J. Fluid Mech. 124, 391409.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639656.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Whitehead, J. A. Jr & Worthington, L. V. 1982 The flux and mixing rates of Antarctic Bottom Water within the North Atlantic. J. Geophys. Res. 87, 79037924.Google Scholar