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Horizontal jets and vortex dipoles in a stratified fluid

Published online by Cambridge University Press:  26 April 2006

S. I. Voropayev ,
Ya. D. Afanasyev  and
I. A. Filippov
S. I. Voropayev
Affiliation:
Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, Moscow 117218, USSR
Ya. D. Afanasyev
Affiliation:
Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, Moscow 117218, USSR
I. A. Filippov
Affiliation:
Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, Moscow 117218, USSR
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Abstract

When a horizontal force is applied locally to some volume of a viscous densitystratified fluid, flows with high concentration of vertically oriented vorticity (vortex dipoles) are generated. The processes of generation and evolution with time of these unsteady flows in a stratified fluid are studied. A convenient way to produce and study these flows in the laboratory is to use a submerged horizontal jet as a ‘point’ source of momentum. The main governing parameter (the ‘force’) is easily controlled in this case. Two regimes were studied: starting jets with dipolar vortex fronts (the force acts continuously) and impulsive vortex dipoles (the force acts for a short period of time). A conductivity microprobe, aluminium powder, shadowgraph, thymol-blue and other techniques have been used to measure the velocity and density distributions in the flows. It is found that in both regimes the flows are self-similar: the lengthscale of the flows increases with time as t½ for starting jets and as t1/3 for vortex dipoles. Detailed information about the generation mechanism, kinematics and dynamics of the flows is obtained. On the basis of similarity principles a theoretical explanation of the experimental results is given. The theory is in good agreement with the results obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 543 - 566
Copyright
© 1991 Cambridge University Press

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References

Abramovich, S. & Solan, A. 1973 The initial development of a submerged laminar round jet. J. Fluid Mech. 59, 791–801.Google Scholar
Afanasyev, Ya, D. & Voropayev, S. I. 1989 On the spiral structure of the mushroom-like currents in the ocean. Dokl. Akad. Nauk SSSR 308, 179–183.Google Scholar
Afanasyev, Ya, D., Voropayev, S. I. & Filippov, I. A. 1988 Laboratory investigation of flat vortex structures in a stratified fluid. Dokl. Akad. Nauk SSSR 300, 704–707.Google Scholar
Afanasyev, Ya, D., Voropayev, S. I. & Filippov, I. A. 1990 Conductivity microprobe for fine structure measurements in stratified flows. Okeanologiya 30, 502–504.Google Scholar
Ahlnäs, K., Royer, T. C. & George, T. H. 1987 Multiple dipole eddies in the Alaska coastal current. J. Geophys. Res. 92, 41–47.Google Scholar
Baker, D. T. 1966 A technique for the precise measurements of small fluid velocities. J. Fluid Mech. 26, 573–575.Google Scholar
Barenblatt, G. I. 1979 Similarity, Self-Similarity and Intermediate Asymptotics. New York: Consultant Bureau.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Cantwell, B. J. 1986 Viscous starting jets. J. Fluid Mech. 173, 159–189.Google Scholar
Couder, Y. & Basdevant, C. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225–251.Google Scholar
Escudier, M. P. & Maxworthy, T. 1973 On the motion of turbulent thermals. J. Fluid Mech. 61, 541–552.Google Scholar
Flierl, G. R., Stern, M. E. & Whitehead, J. A. 1983 The physical significance of modons: Laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233–263.Google Scholar
Gärtner, V. 1983 Visualization of particle displacement and flow in a stratified salt water. Exps Fluids 1, 55–56.Google Scholar
Ginsburg, A. I. & Fedorov, K. N. 1984 The evolution of a mushroom-formed current in the ocean. Dokl. Akad. Nauk SSSR 274, 481–484.Google Scholar
Heijst, G. J. F. Van 1989 Experiments on coherent structures in two-dimensional turbulence In Proc. 5th European Phys. Soc. Liquid State Conf. on Turbulence, pp. 110–111. Moscow, Inst. for Problems in Mech., USSR Acad. Sci.
Heijst, G. J. F. Van & Flor, J. B. 1989 Laboratory experiments on dipole structures in a stratified fluid. Mesoscale/Synoptic coherent structures in geophysical turbulence In Proc. 20th Intl Liege Colloqu. on Ocean Hydrodynamics. Oceanography Series, vol. 50, pp. 591–608 Elsevier.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. 1944 New exact solution of Navier–Stokes equations. Rep. USSR Acad. Sci. 43, 286–288.Google Scholar
Mcwilliams, J. C. 1983 Interaction of isolated vortices II. Geophys. Astrophys. Fluid Dyn. 24, 1–22.Google Scholar
Mcwilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Mcwilliams, J. C. & Zabusky, J. N. 1982 Interactions of isolated vortices I. Geophys. Astrophys. Fluid Dyn. 19, 207–227.Google Scholar
Nguyen Due, J.-M. & Sommeria, J. 1988 Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175–192.Google Scholar
Papaliou, D. D. 1985 Magneto-fluid mechanic turbulent vortex street In 4th Beer-Sheva Seminar on MHD flows and turbulence. AIAA Progress series, vol. 100, pp. 152–173
Schlichting, H. 1955 Boundary Layer Theory. McGraw-Hill.
Simpson, J. E. 1987 Gravity Currents: In the Environment and the Laboratory. Ellis Horwood.
Slezkin, N. A. 1934 On the case when the equations of motion for viscous fluid can be integrated. Sci. Papers Moscow State Univ. 2, 115–121.Google Scholar
Squire, H. B. 1951 The round laminar jet. Q. J. Mech. Appl. Maths 4, 321–329.Google Scholar
Stern, M. E. & Voropayev, S. I. 1984 Formation of vorticity fronts in shear flow. Phys. Fluids 27, 848–855.Google Scholar
Turner, J. S. 1964a The flow into an expanding spherical vortex. J. Fluid Mech. 18, 195–208.Google Scholar
Turner, J. S. 1964b The dynamics of spheroidal masses of buoyant fluid. J. Fluid Mech. 19, 481–490.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar
Voropayev, S. I. 1983 Free jet and frontogenesis experiments in shear flow. Tech. Rep., Woods Hole Oceanographic Inst., WHOI-83–41, pp. 147–159Google Scholar
Voropayev, S. I. 1985 A theory of self-similar development of a jet in a density homogeneous fluid. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 21, 1290–1294.Google Scholar
Voropayev, S. I. 1987 Modeling of vortex structures in shear flow using a jet of variable impulse. Morskoy Hydrof. Zh. 2, 33–39.Google Scholar
Voropayev, S. I. 1989 Flat vortex structures in a stratified fluid. Mesoscale/Synoptic coherent structures in geophysical turbulence In Proc. 20th Intl Liege Colloqu. on Ocean Hydrodynamics. Oceanography Series, vol. 50, pp. 671–690 Elsevier.
Voropayev, S. I. 1990 Self-similar structures in 2-D turbulence: experimental and theoretical study of vortex multipoles In Proc. 3rd European Turbulence Conference, Stockholm, Sweden (in press).
Voropayev, S. I. & Afanasyev, Ya, D. 1991 Two-dimensional vortex dipole interactions in a stratified fluid. J. Fluid Mech. (submitted).Google Scholar
Voropayev, S. I. & Filippov, I. A. 1985 Development of a horizontal jet in a homogeneous and stratified fluids: Laboratory experiments. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana, 21, 964–972.Google Scholar
Voropayev, S. I., Filippov, I. A. & Afanasyev, Ya, D. 1989 Self-similar coherent structures in 2-D turbulence: vortex dipoles, quadrupoles and other structures In Proc. 5th European Phys. Soc. Liquid State Conf. on Turbulence, Suppl. issue, pp. 22–23 Moscow, Inst. for Problems in Mech., USSR Acad. Sci.
Voropayev, S. I. & Neelov, I. A. 1991 Laboratory and numerical modeling of vortex dipoles (mushroom-like currents) in a stratified fluid. Okeanologiya 31, 68–75.Google Scholar