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On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid

Published online by Cambridge University Press:  20 April 2006

S. A. Thorpe
Affiliation:
Institute of Oceanographic Sciences, Wormley, Godalming, Surrey, U.K.

Abstract

Experiments have been made to examine the fluid motion and density perturbations caused by oscillating a grid of vertical bars horizontally in a uniformly stratified fluid at frequency ω greatly exceeding the buoyancy frequency N. A highly turbulent region is produced near the grid. Beyond this lies a region of intrusive layers as described by Ivey & Corcos (1982), while further from the grid the motion is dominated by internal waves. The boundary between the turbulent region and the intrusive region is clearly defined, and the width of the former region appears to be proportional to $y = a^{\frac{3}{4}}M^{\frac{1}{4}}(\omega/N)^{\frac{1}{2}}$, where a is the amplitude and M the mesh length of the grid. The vertical scale of the layers, which sometimes form to give a regular sequence of high and low density gradients, is also proportional to y. This scaling is shown to be consistent with that found by Hopfinger & Toly (1976) in their study of motion produced by grids oscillating in homogeneous fluids, while the abrupt change in character of the motion at the edge of the turbulent region is in accord with measurements made by Dickey & Mellor (1980) in the wake of a grid drawn steadily through a stratified fluid. The scaling is also in accord with Ivey & Corcos’ observations of the width of the turbulent region, the thickness of the layers, and the vertical flux of density.

The observation of the layers is considered in the light of conjectures about the instability of turbulent motion in stratified fluids. The character and conditions of generation of the layers are consistent with their being a manifestation of the instability, but the identification is not conclusive.

Type
Research Article
Copyright
© 1982 Cambridge University Press

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References

Amen, R. & Maxworthy, T. 1980 The gravitational collapse of a mixed region into a linearly stratified fluid. J. Fluid Mech. 96, 6580.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177192.Google Scholar
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 1332.Google Scholar
Hopfinger, E. J. & Toly, J.-A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155176.Google Scholar
Ivey, G. N. & Corcos, G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 126.Google Scholar
Kranenburg, C. 1982 Stability conditions for gradient-transport models of transient densitystratified shear flow. Geophys. Astrophys. Fluid Dyn. 19, 93104.Google Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 323.Google Scholar
Mcewan, A. D. 1976 Angular momentum diffusion and the initiation of cyclones. Nature 260, 126128.Google Scholar
Mendenhall, C. E. & Mason, M. 1923 The stratified subsidence of fine particles. Proc. Natn. Acad. Sci. 9, 199202.Google Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435443.Google Scholar
Phillips, O. M. 1972 Turbulence in a stratified fluid: is it stable? Deep-Sea Res. 19, 7981.Google Scholar
Posmentier, E. S. 1977 The generation of salinity fine structure by vertical diffusion. J. Phys. Oceanogr. 7, 298301.Google Scholar
Scorer, R. S. 1966 Origin of cyclones. Sci. J. 2, 4652.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375400.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Wu, J. 1969 Mixed region collapse with internal wave generation in the density-stratified medium. J. Fluid Mech. 35, 531544.Google Scholar
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293301.Google Scholar