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A study of streamwise vortex structure in a stratified shear layer

Published online by Cambridge University Press:  26 April 2006

David G. Schowalter
Affiliation:
Department of Applied Mechanics and Engineering Sciences 0411, University of California, San Diego, La Jolla, CA 92093, USA Current address: Department of Marine, Earth and Atmospheric Science, Box 8208, North Carolina State University, Raleigh, NC 27695, USA.
Charles W. Van Van Atta
Affiliation:
Department of Applied Mechanics and Engineering Sciences 0411, University of California, San Diego, La Jolla, CA 92093, USA
Juan C. Lasheras
Affiliation:
Department of Applied Mechanics and Engineering Sciences 0411, University of California, San Diego, La Jolla, CA 92093, USA

Abstract

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. As the spanwise vorticity layer rolls up and pulls high-density fluid above low-density fluid, a local instability results. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. A simple numerical model is proposed which captures the relevant physics of the flow evolution. It is found that, depending on the location, streamwise vortices resulting from vortex stretching may be weakened or enhanced by the stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the timescale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

Type
Research Article
Copyright
© 1994 Cambridge University Press

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References

Aref, H. & Tryggvason, G. 1989 Model of Rayleigh–Taylor instability. Phys. Rev. Lett. 62, N7, 749.Google Scholar
Barrett, T. K. & Van Atta, C. W. 1991 Experiments on the inhibition of mixing in stably stratified decaying turbulence using laser Doppler anemometry and laser-induced fluorescence. Phys. Fluids A 3, 1321.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1.Google Scholar
Browand, F. K. & Winant, C. D. 1973 Laboratory observations of shear-layer instability in a stratified fluid. Boundary-Layer Met. 5, 67.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Dimotakis, P. E. & Brown, G. L. 1976 The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J. Fluid Mech. 78, 535.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability, chap 1. Cambridge University Press.
Farmer, D. M. & Armi, L. 1988 The flow of Atlantic Water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1.Google Scholar
Gartrell, G. 1979 Studies on the mixing in a density-stratified shear flow. PhD thesis, Division of Engineering and Applied Science, California Institute of Technology.
Hannoun, I. A. 1985 Matching the refractive index in density stratified flows. W.M. Keck Laboratory of Hydraulics and Water Resources Tech. Mem. 85-1. California Institute of Technology.
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319.Google Scholar
Klaassen, G.P. & Peltier, W. R. 1985a The onset of turbulence in finite-amplitude Kelvin-Helmholtz billows. J. Fluid Mech. 155, 1.Google Scholar
Klaassen, G.P. & Peltier, W.R. 1985b The effect of the Prandtl number on the evolution and stability of Kelvin–Helmholtz billows. Geophys. Astrophys. Fluid Dyn. 32, 23.Google Scholar
Klaassen, G.P. & Peltier, W.R. 1991 The influence of stratification on secondary instability in free shear layers. J. Fluid Mech. 227, 71.Google Scholar
Konrad, J. H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion- limited chemical reactions. Project SQUID Tech. Rep. CIT-8-PU.
Koop, C.G. & Browand, F.K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135.Google Scholar
Lamb, H. 1932 Hydrodynamics, chap. 7. Dover.
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53.Google Scholar
Lawrence, G. A., Lasheras, J. C. & Browand, F. K. 1987 Shear instabilities in stratified flow. Third Intl Symp. on Stratified Flows, 2360.
Liepmann, H. W. & Laufer, J. 1947 Investigation of free turbulent mixing. NACA Tech. Note 1257.
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139.Google Scholar
Marmorino, G. O. 1987 Observations of small-scale mixing processes in the seasonal thermocline, part II: wave breaking. J. Phys. Oceanogr. 17, 1348.Google Scholar
McDougall, T. J. 1979 On the elimination of refractive-index variations in turbulent density stratified liquid flows. J. Fluid Mech. 93, 83.Google Scholar
Nakamura, Y., Leonard, A. & Spalart, P. 1982 Vortex simulation of an inviscid shear layer. AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, St. Louis. AIAA-82-0948.
Orlanski, I. & Bryan, K. 1969 Formation of the thermocline step structure by large amplitude internal gravity waves. J. Geophys. Res. 74, 6975.Google Scholar
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin–Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215.Google Scholar
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup. J. Fluid Mech. 243, 183.Google Scholar
Schowalter, D. G. 1993 The effect of stable stratification on three-dimensional structure in shear layers. PhD dissertation, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego.
Staquet, C. 1989 Influence of a shear on a stably-stratified flow. Turbulence and Coherent Structures: Selected papers from “Turbulence 89: Organized Structures and Turbulence in Fluid Mechanics,” Grenoble, 18–21 September 1989.
Staquet, C. & Riley, J. J. 1989 On the velocity field associated with potential vorticity. Dyn. Atmos. Oceans 14, 93.Google Scholar
Thorpe, S. A. 1985 Laboratory observations of secondary structures in Kelvin–Helmholtz billows and consequences for ocean mixing. Geophys. Astrophys. Fluid Dyn. 34, 175.Google Scholar
Thorpe, S. A., Hall, A. J., Taylor, C. & Allen, J. 1977 Billows in Loch Ness. Deep-Sea Res. 24, 371.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237.Google Scholar
Woods, J. D. 1968 Wave-induced shear instability in the summer thermocline. J. Fluid Mech. 32, 791.Google Scholar