The motion of a singular vortex near an escarpment

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

doi:10.1017/s0022112001006115

Cited by 20 publications

(17 citation statements)

References 29 publications

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“…These theoretical results were confirmed by contour dynamics model simulations. Dunn et al (2001) extended the previous work to weak and medium intensity vortices. They showed that vortices moving against topographic waves radiate energy and move towards the shelf while vortices moving with the topographic waves can reach a steady state.…”

Section: Introductionmentioning

confidence: 56%

Vortex merger near a topographic slope in a homogeneous rotating fluid

et al. 2017

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The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass 1 into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.

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Section: Introductionmentioning

confidence: 56%

Vortex merger near a topographic slope in a homogeneous rotating fluid

et al. 2017

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“…Therefore, Figs 14 and 15 simulate qualitatively the generation of vortices by non‐linear waves. This ill‐understand phenomenon has only lately begun to be studied (Bühler & Jacobson 2001; Dunn et al 2001; Galiev & Galiev 2001; Galiev 2002).…”

Section: Topographic‐resonant Amplification Of Weakly Nonlinear Seimentioning

confidence: 99%

The theory of non-linear transresonant wave phenomena and an examination of Charles Darwin's earthquake reports

Galiev¹

2003

Geophysical Journal International

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SUMMARY A non‐linear theory of transresonant wave phenomena based on consideration of perturbed wave equations is presented. In particular, the waves in a surface layer of a porous compressible viscoelastoplastic material are considered. For such layers the 3‐D equations of deformable media are reduced to 1‐D or 2‐D perturbed wave equations. A set of approximate, closed‐form, general solutions of these equations are presented, which take into account non‐linear, dissipative, dispersive, topographic and boundary effects. Then resonant, site and liquefaction effects are analysed. Resonance is considered as a global parameter. Transresonant evolution of the equations is studied. Within the resonant band, utt≈a20∇2u and the perturbed wave equations transform into non‐linear diffusion equations, either to a basic highly non‐linear ordinary differential equation or to the basic algebraic equation for travelling waves. Resonances can destroy predictability and wave reversibility. Surface topography (valleys, islands, etc.) is considered as a series of earthquake‐induced resonators. A non‐linear transresonant evolution of smooth seismic waves into shock‐, jet‐ and mushroom‐like waves and vortices is studied. The amplitude of the resonant waves may be of the order of the square or cube root of the exciting amplitude. Therefore, seismic waves with a moderate amplitude can be amplified very strongly in natural resonators, whereas strong seismic waves can be attenuated. Reports of the 1835 February 20 Chilean earthquake given by Charles Darwin are qualitatively examined using the non‐linear theory. The theory qualitatively describes the ‘shivering’ of islands and ridges, volcano spouts and generation of tsunami‐like waves and supports Darwin's opinion that these events were part of a single phenomenon. Same‐day earthquake/eruption events and catastrophic amplification of seismic waves near the edge of sediment layers are discussed. At the same time the theory can account for recent counterintuitive results of experiments with water, liquified matter and granular materials.

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“…Further development of the theory of point vortices is reflected in monographs and reviews [6][7][8][9][10][11][12][13][14][15][16]. The classical concept of point vortices was used in problems of meteorology [17][18][19][20][21][22][23] and oceanography in [24][25][26][27][28][29][30]. Gryanik first generalized the theory of two-dimensional vortices to the case of a two-layer [31] and then to an N-layer rotating fluid [32].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach

2020

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The theory of point vortices is used to explain the interaction of a surface vortex with subsurface vortices in the framework of a three-layer quasigeostrophic model. Theory and numerical experiments are used to calculate the interaction between one surface and one subsurface vortex. Then, the configuration with one surface vortex and two subsurface vortices of equal and opposite vorticities (a subsurface vortex dipole) is considered. Numerical experiments show that the self-propelling dipole can either be captured by the surface vortex, move in its vicinity, or finally be completely ejected on an unbounded trajectory. Asymmetric dipoles make loop-like motions and remain in the vicinity of the surface vortex. This model can help interpret the motions of Lagrangian floats at various depths in the ocean.

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The motion of a singular vortex near an escarpment

Cited by 20 publications

References 29 publications

Vortex merger near a topographic slope in a homogeneous rotating fluid

Vortex merger near a topographic slope in a homogeneous rotating fluid

The theory of non-linear transresonant wave phenomena and an examination of Charles Darwin's earthquake reports

Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach

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