The motion of a vortex near a gap in a wall

Johnson, E. R.; McDonald, N. Robb

doi:10.1063/1.1637603

Cited by 32 publications

(42 citation statements)

References 12 publications

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“…8 Idealised models which assume two-dimensional flow of an inviscid fluid have been used to construct the Hamiltonian, or Kirchhoff-Routh path function, 9 for a single point vortex near a gap, in an infinitely long and infinitesimally thin straight barrier in the rigid lid case (i.e., infinite Rossby radius). 10 The main result is that vortices that start far upstream of the gap at greater than half the gap width from the barrier leap across the gap. Vortices far upstream starting closer to the barrier pass through the gap.…”

Section: Introductionmentioning

confidence: 99%

“…It is an iterative method based on perturbing about the exact solution for the infinite Rossby radius case. 10 …”

Section: Appendix: Alternative Form Of the Integral Equation And Its mentioning

confidence: 99%

“…In this Appendix, an alternative numerical method is described to solve (8)- (10). It is an iterative method based on perturbing about the exact solution for the infinite Rossby radius case.…”

Section: Appendix: Alternative Form Of the Integral Equation And Its mentioning

confidence: 99%

“…Quasi-geostrophic dynamics in a single layer with reduced gravity is used to derive an integral equation whose solution gives the velocity field at the vortex, enabling its trajectory to be computed. For finite a the integral equation must be solved numerically, unlike the rigid lid case (a → ∞), 10 where complex variable methods give exact point vortex trajectories.…”

Section: Introductionmentioning

confidence: 99%

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Finite Rossby radius effects on vortex motion near a gap

2012

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The continuous spectrum of time-harmonic shear layers Phys. Fluids 24, 034101 (2012) The interaction of a vortex ring with a sloped sediment layer: Critical criteria for incipient grain motion Phys. Fluids 24, 026604 (2012) Numerical study of flow characteristics behind a stationary circular cylinder with a flapping plate Phys. This work investigates the effect of the Rossby radius of deformation on the motion of a vortex near a gap in an infinitely long barrier. A key parameter determining the behaviour of the vortex is a, the ratio of the Rossby radius of deformation to the width of the gap. Assuming quasi-geostrophic dynamics for a single-layer, reducedgravity fluid, an integral equation is derived whose solution gives the velocity at any point in the fluid. The integral equation is solved numerically and the velocity field is integrated to give the trajectories of point vortices. Combined with the method of contour dynamics, the method can be used to compute the evolution of finite area patches of constant vorticity. The trajectories of point vortices and vortex patches are compared. The patches are initially circular and the centroids of those vortex patches that remain close to circular follow the trajectory and speed of their equivalent point vortices when appropriately normalised. The critical point vortex trajectory (the separatrix) which divides vortices that leap across the gap and those that pass through, is computed for various a. Decreasing the Rossby radius of deformation increases the tendency of vortices to pass through the gap. The effect of various background flows on both point vortex and vortex patch motion is also described.

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Section: Introductionmentioning

confidence: 99%

“…It is an iterative method based on perturbing about the exact solution for the infinite Rossby radius case. 10 …”

Section: Appendix: Alternative Form Of the Integral Equation And Its mentioning

confidence: 99%

Section: Appendix: Alternative Form Of the Integral Equation And Its mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Rossby radius effects on vortex motion near a gap

2012

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“…This formulation has been used by Johnson & McDonald 4,5 who modelled vortex patches as point vortices in order to investigate the paths of ocean vortex patches in the vicinity of boundaries such as islands or coastal gaps. However, with the exception of a few contour dynamics calculations (e.g.…”

Section: Introductionmentioning

confidence: 99%

Deformation of vortex patches by boundaries

2013

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The deformation of two-dimensional vortex patches in the vicinity of fluid boundaries is investigated. The presence of a boundary causes an initially circular patch of uniform vorticity to deform. Sufficiently far away from the boundary, the deformed shape is well approximated by an ellipse. This leading order elliptical deformation is investigated via the elliptic moment model of Melander, Zabusky & Styczek [M. V. Melander, N. J. Zabusky & A. S. Styczek, J. Fluid. Mech., 167, 95 (1986)]. When the boundary is straight, the centre of the elliptic patch remains at a constant distance from the boundary, and the motion is integrable. Furthermore, since the straining flow acting on the patch is constant in time, the problem is that of an elliptic vortex patch in constant strain, which was analysed by Kida [S. Kida, J. Phys. Soc. Japan, 50, 3517 (1981)]. For more complicated boundary shapes, such as a square corner, the motion is no longer integrable. Instead, there is an adiabatic invariant for the motion. This adiabatic invariant arises due to the separation in times scales between the relatively rapid time scale associated with the rotation of the patch and the slower time scale associated with the self-advection of the patch along the boundary. The interaction of a vortex patch with a circular island is also considered. Without a background flow, conservation of angular impulse implies that the motion is again integrable. The addition of an irrotational flow past the island can drive the patch towards the boundary, leading to the possibility of large deformations and breakup.Comment: 19 pages, 16 figure

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Vortex motion on a sphere: barrier with two gaps

Nelson¹,

McDonald²

2009

Iutam Bookseries

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The motion of a vortex near a gap in a wall

Cited by 32 publications

References 12 publications

Finite Rossby radius effects on vortex motion near a gap

Finite Rossby radius effects on vortex motion near a gap

Deformation of vortex patches by boundaries

Vortex motion on a sphere: barrier with two gaps

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