Particle transport by a vortex soliton

Kimura, Yoshi; Koikari, Souji

doi:10.1017/s0022112004009383

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…Now, just as in § 2, we can superpose two solutions. We place a second vortex with circulation −Γ , centreline on the plane y = −Y(t) and directed along e = (−sin β, 0, cos β), and with the same Burgers-type cross-sectional structure; this is in effect the 'chopsticks model' of Kimura & Koikari (2004). For the second vortex, the vorticity field is…”

Section: Skewed Burgers Vorticesmentioning

confidence: 99%

Reconnection of skewed vortices

Kimura

Moffatt

2014

J. Fluid Mech.

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Based on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity ν in the limit ν → 0. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.

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Section: Skewed Burgers Vorticesmentioning

confidence: 99%

Reconnection of skewed vortices

Kimura

Moffatt

2014

J. Fluid Mech.

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“…In this paper, we extend the linearised reconnection model numerically to include vortexvortex interaction. We extend the skewed Burgers-type vortices, described as 'chopsticks' (Kimura and Koikari 2004), by adding two ring parts at the ends of vortices to form a closed figure-of-eight vortex (figure 1), and we calculate the velocity vectors of the segments of the single vortex filament by using the Biot-Savart law. To regularise the singular kernel of the Biot-Savart integral, a cut-off method which simply removes the singular interactions from the integration is employed.…”

Section: Introductionmentioning

confidence: 99%

Scaling properties towards vortex reconnection under Biot–Savart evolution

Kimura¹,

Moffatt²

2017

Fluid Dyn. Res.

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Submitted for the DFD17 Meeting of The American Physical SocietyScaling properties towards vortex reconnection under Biot-Savart evolution YOSHIFUMI KIMURA, Nagoya University, KEITH MOFFATT, University of Cambridge -Reconnection of two vortex filaments under the Biot-Savart law is investigated numerically using vortex filaments in the configuration of tilted hyperbolae initially. For the numerical method, the vortices are divided into piecewise linear segments with an initial coordinate stretching by the double exponential formula, and the Biot-Savart integral is approximated by a summation over the segments with a cut-off method to deal with the singular terms. It is demonstrated that the centre parts of the hyperbolae tend to approach and accelerate to form a singularity. Even though the minimum separation of the hyperbolae, the maximum velocity and the maximum axial strain rate show clear scaling exponents close to the singularity of Leray type, the latter two exponents are slightly more singular to cause a production of inflection points and eventually cusp structures at the tips [1] . As a validation of the model, λ 2 , the second eigenvalue of the rate of strain tensor, is investigated around the vortices. It is shown that λ 2 takes negative values near the tip of the vortices for almost all the time. [1] Y. Kimura & K. Moffatt, Scaling properties towards vortex reconnection under Biot-Savart evolution. (2017), Fluid Dyn. Res. in press.

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“…This analysis can be viewed as one of the particle dynamics considered in many situations in earlier studies [25,26].…”

Section: Resultsmentioning

confidence: 99%

“…As Gerstner's wave has been a unique example of explicitly written trajectories, our explicit formula for particle trajectory of Crapper's waves may be worthy of notice. This analysis can be viewed as one of the particle dynamics considered in many situations in earlier studies [25,26].…”

Section: Discussionmentioning

confidence: 99%