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arXiv · 1806.08173

Three-dimensional stability of leapfrogging quantum vortex rings

Victor P. Ruban
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Abstract

It is shown by numerical simulations within a regularized Biot-Savart law that dynamical systems of two or three leapfrogging coaxial quantum vortex rings having a core width $ξ$ and initially placed near a torus of radii $R_0$ and $r_0$, can be three-dimensionally (quasi-)stable in some regions of parameters $Λ=\ln(R_0/ξ)$ and $W=r_0/R_0$. At fixed $Λ$, stable bands on $W$ are intervals between non-overlapping main parametric resonances for different (integer) azimuthal wave numbers $m$. The stable intervals are most wide ($ΔW\sim$ 0.01--0.05) between $m$-pairs $(1,2)$ and $(2,3)$ at $Λ\approx$ 4--12 thus corresponding to micro/mesoscopic sizes of vortex rings in the case of superfluid $^4$He. With four and more rings, at least for $W>0.1$, resonances overlap for all $Λ$ and no stable domains exist.

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Victor P. Ruban. 2018-08-24. Three-dimensional stability of leapfrogging quantum vortex rings. https://doi.org/10.1063/1.5047471

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