Nonlinear behaviour of interacting mid-latitude atmospheric vortices

Cosgrove, Jason Michael; Forbes, Lawrence K.

doi:10.1007/s10665-016-9871-9

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…e interaction between strong cyclonic vortices and the accompanied secondary circulation structures under various flow conditions requires comprehensive exploration through theoretical analysis, numerical simulation, and laboratory experiments. ey may provide invaluable ingredients for understanding the physics of intense oceanic eddies [33,36] or atmospheric vortices [37] with coherent wave trains [38] and they will be reported elsewhere.…”

Section: Discussionmentioning

confidence: 99%

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

Chen¹,

Leu²,

Liu³

et al. 2021

Mathematical Problems in Engineering

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A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.

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Section: Discussionmentioning

confidence: 99%

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

Chen¹,

Leu²,

Liu³

et al. 2021

Mathematical Problems in Engineering

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show abstract

“…The following outlines the derivation of the Dirichlet boundary value problem and the earlier paper by Cosgrove & Forbes (2017) gives a derivation for the corresponding similar Robin boundary value problem. The state variables are given the value one on the boundaries of the δ-plane and the velocity components are zero there.…”

Section: T H E S P E C T R a L S O L U T I O N M E T H O Dmentioning

confidence: 99%

“…It has been shown previously by Cosgrove & Forbes (2017) that the results of simulating interacting atmospheric vortices using the f-plane approximation can be misleading due to false reflections off the artificial boundaries, especially when Dirichlet boundary conditions are involved. To overcome this phenomenon, Cosgrove & Forbes (2017) used Robin boundary conditions to absorb and minimize the influence of such reflections. However, using the δ-plane approximation, the numerical solutions obtained using Dirichlet and Robin boundary conditions are virtually identical, indicating that the δ-plane approximation with its quadratic variation is capable of absorbing false reflections.…”

Section: P R E S E N Tat I O N O F R E S U Lt Smentioning

confidence: 99%

A δ-plane simulation of anticyclones perturbing circumpolar flows to form a transient north polar hexagon

Cosgrove¹,

Forbes²

2017

Monthly Notices of the Royal Astronomical Society

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Saturn's North Polar Hexagon was discovered by Godfrey who pieced together map projections of images captured by the Voyager mission to unveil a hexagonal structure over the north pole of Saturn. This article attempts to answer whether or not a hexagonal structure can be formed through anticyclones impinging on the dominant eastward circumpolar flow and is in part based upon the proposed theory by Allison et al. that the Hexagon may be the result of at least one impinging anticyclone perturbing a circumpolar jet centrally located around the 76 • N latitude. A high-latitude δ-plane approximation is used to simulate the interaction between an initially circular circumpolar jet and at least one perturbing anticyclone. Our simulations with one perturbing anticyclone failed to form a hexagonal structure; yet by including an additional anticyclone it was found that depending on the strength, location and radius of the perturbing anticyclones a hexagonal feature could develop. However, the longevity and drift rate of the actual Hexagon must be attributed to other factors not considered in this paper.

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Compressibility effects on outflows in a two-fluid system. 1. Line source in cylindrical geometry

Krzysik

Forbes

2017

J Eng Math

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Nonlinear behaviour of interacting mid-latitude atmospheric vortices

Cited by 3 publications

References 26 publications

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

A δ-plane simulation of anticyclones perturbing circumpolar flows to form a transient north polar hexagon

Compressibility effects on outflows in a two-fluid system. 1. Line source in cylindrical geometry

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