Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T06:05:51.122Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional vortex-dipole interactions in a stratified fluid

Published online by Cambridge University Press:  26 April 2006

S. I. Voropayev  and
Ya. D. Afanasyev
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
Get access Rights & Permissions [Opens in a new window]

Abstract

Planar motion produced when a viscous fluid is forced from an initial state of rest is studied. We consider a vortex dipole produced by the action of a point force (Cantwell 1986), and a vortex quadrupole produced by the action of two equal forces of opposite direction. We also present results from an experimental investigation into the dynamics of the interactions between vortex dipoles as well as between vortex dipoles and a vertical wall in a stratified fluid. Theoretical consideration reveals that the dynamics of two-dimensional vortex-dipole interactions are determined by two main governing parameters: the dipolar intensity of the vorticity distribution (momentum) and the quadrupolar intensity of the vorticity distribution of the flow. We document details of different basic types of interactions and present a physical interpretation of the results obtained in terms of vortex multipoles: dipoles, quadrupoles and their combinations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 665 - 689
Copyright
© 1992 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

Afanasyev, Ya. D. & Voropayev, S. I. 1989a A model of the mushroom-like currents in a stratified fluid at the source of momentum acting impulsively. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana. 25, 843–851.Google Scholar
Afanasyev, Ya. D. & Voropayev, S. I. 1989b 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. 1989 A model of the mushroom-like currents in a stratified fluid when a source of momentum acts continuously. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana. 25, 741–750.Google Scholar
Barenblatt, G. I., Voropayev, S. I. & Filippov, I. A. 1989 Model of Fedorovian coherent structures in the upper ocean. Dokl. Akad. Nauk SSSR 307, 720–724.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Gantwell, 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
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, 124–132.Google Scholar
Federov, K. N. & Ginzburg, A. I. 1989 Surface Layer of the Ocean. Leningrad: Gidrometeoizdat.
Griffiths, R. W. & Hopfinger, E. J. 1984 The structure of mesoscale turbulence and horizontal spreading at ocean fronts. Deep-Sea Res. 31, 245–269.Google Scholar
Heijst, G. J. F. van & Flor, J. B. 1989a Laboratory experiments on dipole structures in a stratified fluid. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 608–608.
Heijst, G. J. F. van & Flor, J. B. 1989b Dipole formation and collisions in a stratified fluid. Nature 340, 212–215.Google Scholar
Kamke, E. von 1959 Differentialgleichungen. Losungsmethoden und losungen. Leipzig.
Manakov, S. V. & Schur, L. N. 1983 Stochasticity in two-particles dispersion. Pis' V Zh. Tek. Fiz. 37, 45–48.Google Scholar
Nguen Duc, J.-M. & Sommeria, J. 1988 Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175–192.Google Scholar
Orlandi, P. 1990 Vortex dipole rebound from the wall. Phys. Fluids A 2, 1429–1436.Google Scholar
Stern, M. E. & Voropayev, S. I. 1984 Formation of vorticity fronts in shear flow. Phys. Fluids 27, 848–855.Google Scholar
Voropayev, S. I. 1983 Free jet and frontogenesis experiments in shear flow. Tech. Rep. Woods Hole Oceanograph. Inst. WHOI-83–41, pp. 159–159.Google Scholar
Voropayev, S. I. 1987 Modeling of vortex structures in the flow with velocity shear using a jet of variable impulse. Morskoy Hydrofys. Zh. 2 (3–4), 33–39.Google Scholar
Voropayev, S. I., Afanasyev, Ya. D. & Filippov, I. A. 1991 Horizontal jets and vortex dipoles in a stratified fluid. J. Fluid Mech. 227, 543–566.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. & Neelov, I. A. 1991 Laboratory and numerical modelling of vortex dipoles (mushroom-like currents) in a stratified fluid. Okeanologiya 31, 68–75.Google Scholar