On the interaction between two oppositely signed, shielded, monopolar vortices

M.R. Schmidt, M. Beckers, A.H. Nielsen, J.J. Rasmussen, G.J.F. Heijst, van

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Abstract

The formation two-dimensional dipolar vortices by the interaction between two shielded monopolar vortices with opposite vorticity, as shown in a numerical study by Couder and Basdevant, is investigated in detail, both experimentally, in a nonrotating stratified fluid and numerically by direct solutions of the two-dimensional Navier–Stokes equations. A comparative study between the laboratory experiments and numerical simulations is performed. The vorticity distribution measured in the early stage of the evolution in the laboratory is used as initial data for the simulations, and an additional damping term in the Navier–Stokes equations, that accounts for the vertical diffusion in the laboratory experiments, is used. The results show that, depending on the initial separation between the vortices, the shields of the monopoles are peeled off and indeed a compact dipole with a linear (¿,¿)-relationship is formed, or when the monopoles are further apart the shields of the monopoles are perturbed and two tripoles are formed. The characteristics of the emerged dipole are analyzed and a dye visualization of the dipole formation is performed. A second, more general numerical study yields a relationship between the formation time of the dipole and the initial separation distance between the monopoles and it shows that the deshielding process can be explained by the domination of strain over vorticity.
Original languageEnglish
Pages (from-to)3099-3110
Number of pages12
JournalPhysics of Fluids
Volume10
Issue number12
DOIs
Publication statusPublished - 1998

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