The Stability of Vortex Arrays on Double Concentric Circles

概要

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The stability of double circular arrays of vortices is inv<:stigated where eacharray consists of N point vortices of equal strength. The permanent configurationsof the arrays are found to need the vortices of different strength on a differentarray depending on the distance between the arrays. The linear stability of theconfigurations is investigated for several values of V, and it is found that theconfiguration is stable for V= 2 and 3 and there exist almost stable arrangementsfor N :: 4, 5 and 6. The nonlinear stability of the vortex configurations is numeri-cally studied, and it is found that linearly stable configurations are stable againstfinite amplitude disturbances and the almost linearly stable configurations are alsostable for small amplitude disturbances.
1984-10-15