Advection of a vortex pair atmosphere in a velocity field of point vortices*

Meleshko, V. V.; Konstantinov, M. Yu.; Gurzhi, A. A.; Konovaljuk, T. P.

doi:10.1063/1.858335

Cited by 43 publications

(20 citation statements)

References 32 publications

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“…Note also that the simple structure of the solution enables an approximation for the mass transport due to the pseudoimage. See Meleshko et al (1992) for details concerning the calculation of the size of a dipole atmosphere. Note in particular that the mass transport is related to the distance of the vortex from the escarpment.…”

Section: Short-time Vortex Trajectorymentioning

confidence: 99%

The motion of a singular vortex near an escarpment

2001

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McDonald (1998) has studied the motion of an intense, quasi-geostrophic, equivalentbarotropic, singular vortex near an infinitely long escarpment. The present work considers the remaining cases of the motion of weak and moderate intensity singular vortices near an escarpment. First, the limit that the vortex is weak is studied using linear theory. For times which are short compared to the advective time scale associated with the vortex it is found that topographic waves propagate rapidly away from the vortex and have no leading-order influence on the vortex drift velocity. The vortex propagates parallel to the escarpment in the sense of its image in the escarpment. The mechanism for this motion is identified and is named the pseudoimage of the vortex. Large-time asymptotic results predict that vortices which move in the same direction as the topographic waves radiate non-decaying waves and drift slowly towards the escarpment in response to wave radiation. Vortices which move in the opposite direction to the topographic waves reach a steadily propagating state. Contour dynamics results reinforce the linear theory in the limit that the vortex is weak, and show that the linear theory is less robust for vortices which move counter to the topographic waves. Second, contour dynamics results for a moderate intensity vortex are given. It is shown that dipole formation is a generic feature of the motion of moderate intensity vortices and induces enhanced motion in the direction perpendicular to the escarpment.

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Section: Short-time Vortex Trajectorymentioning

confidence: 99%

The motion of a singular vortex near an escarpment

2001

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“…From their relative strengths we derived a criterion (34) for leapfrogging to occur. The gallery of pictures in section 4 and the qualitative sketch (figure 7) lead to a set of criteria that we observe when we are given strengths, widths, and separation, i.e., K 1 , K 2 , y 1 , y 2 , d. Then, with x r0 , y r0 given by (25) with the choice K 2 ≤ K 1 we may distinguish some cases of the motion of two vortex pairs and briefly describe each of them:…”

Section: Discussionmentioning

confidence: 99%

“…with x r0 and y r0 as defined in (25). In this situation, vortex pair 1 passes through vortex pair 2 and x r → −∞.…”

Section: Discussionmentioning

confidence: 99%

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Collinear interaction of vortex pairs with different strengths—Criteria for leapfrogging

Mavroyiakoumou

Berkshire

2020

Physics of Fluids

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We formulate a system of equations that describes the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves along the same axis in the same sense. In much of the literature, the vortex pairs have equal strength. The vortex pairs can either escape to infinite separation or undergo a periodic leapfrogging motion. We determine an explicit criterion in terms of the initial horizontal separation of the vortex pairs given as a function of the ratio of their strengths, to describe a periodic leapfrogging motion when interacting along the line of symmetry. In an appendix we also contrast a special case of interaction of a vortex pair with a single vortex of the same strength in which a vortex exchange occurs.

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“…Vortex dipoles can transport water and its content for many kilometers. It is therefore both important and interesting to analyse the regular and chaotic dynamics they exhibit [12][13][14][15][16][17][18][19][20][21][22][23][24] . The evolution of a pair of uniform vorticity patches has been the topic of many previous works [25][26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

2018

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We investigate the evolution of a pair of two-dimensional, opposite-signed, finitesize vortices interacting with a fixed point vortex. The present paper builds on the accompanying study [Koshel, K. V., Reinaud, J. N., Riccardi, G. and Ryzhov, E. A. Phys. Fluids (2018)] focusing on the motion of a pair of point vortices impinging on a fixed point vortex. Here, in contrast, the pair of opposite-signed finite-size vortices, or vortex dipole for simplicity, can deform. This deformation has an impact on the dynamics. We show that, as expected, finite size vortices behave like point vortices if they are distant enough from each other. This allows one to recover the rich and diverse set of possible trajectories for the dipole. This includes the regimes of intricate bounded motion when the finite-size vortices remain stable near the fixed vortex for a long time. On the other hand, we show that large finite-size vortices can deform significantly and deviate from the trajectories of equivalent point vortices. When the shear that the vortices induce on each other is large enough, the finite size vortices may break into smaller structures or may even be completely strained out.

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Advection of a vortex pair atmosphere in a velocity field of point vortices*

Cited by 43 publications

References 32 publications

The motion of a singular vortex near an escarpment

The motion of a singular vortex near an escarpment

Collinear interaction of vortex pairs with different strengths—Criteria for leapfrogging

Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

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