Dynamics of a nonlinear dipole vortex

Hesthaven, Jan S.; Lynov, Jens-Peter; Nielsen, A. H.; Rasmussen, Jens Juul; Schmidt, Marcus; Shapiro, E. G.; Turitsyn, Sergei K.

doi:10.1063/1.868470

Cited by 32 publications

(23 citation statements)

References 33 publications

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“…The former consists of an anticyclonic core with two cyclonic satellites, while the latter is a dipole with a reduced global Rossby number, because of larger distance between the two vorticity cores, and essentially nonlinear scatter plot of B versus PV (cf. Hesthaven et al 1995). Recently, we have presented similar results for shock-modons with Ro = 0.4 (transonic one-layer AGM with a hydraulic jump) whose collisions lead to formation of a shock-tripole (Lahaye & Zeitlin 2012).…”

Section: Preliminary Discussion Of the Adjustment Experimentssupporting

confidence: 56%

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Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

Lahaye¹,

Zeitlin²

2012

J. Fluid Mech.

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We study formation and properties of new coherent structures: ageostrophic modons in the two-layer rotating shallow water model. The ageostrophic modons are obtained by 'ageostrophic adjustment' of the exact modon solutions of the twolayer quasi-geostrophic equations with the free surface, which are used to initialize the full two-layer shallow water model. Numerical simulations are performed using a well-balanced high-resolution finite volume numerical scheme. For large enough Rossby numbers, the initial configurations undergo ageostrophic adjustment towards asymmetric ageostrophic quasi-stationary coherent dipoles. This process is accompanied by substantial emission of inertia-gravity waves. The resulting dipole is shown to be robust and survives frontal collisions. It contains captured inertia-gravity waves and, for higher Rossby numbers and weak stratification, carries a (baroclinic) hydraulic jump at its axis. For stronger stratifications and high enough Rossby numbers, 'rider' coherent structures appear as a result of adjustment, with a monopole in one layer and a dipole in another. Other ageostrophic coherent structures, such as two-layer tripoles and two-layer modons with nonlinear scatter plot, result from the collisions of ageostrophic modons. They are shown to be long-living and robust, and to capture waves.

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Section: Preliminary Discussion Of the Adjustment Experimentssupporting

confidence: 56%

“…This structure is coherent, as is clear from the scatter plot. As for its known bidimensional counterpart, it has a strongly nonlinear shape, which is the origin of the name (Hesthaven et al 1995;Kizner & Khvoles 2004b). …”

Section: Agm → Agm + Nagm Collisionmentioning

confidence: 96%

Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

Lahaye¹,

Zeitlin²

2012

J. Fluid Mech.

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“…This solution was suggested about a century ago and has been widely used in various studies. Dipolar vortices in geophysical flows, however, are often slightly compressed in the direction of translation which has been confirmed by laboratory experiments [3,4] and numerical simulations [5,6]. For that reason, in more recent theoretical studies [7,8], the concept of Lamb and Chaplygin was generalized for barotropic f -and β-plane dipoles with elliptical separatrices.…”

Section: Introductionmentioning

confidence: 85%

Barotropic elliptical dipoles in a rotating fluid

Trieling

Santbergen

Heijst

et al. 2009

Theor. Comput. Fluid Dyn.

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Barotropic f -plane dipolar vortices were generated in a rotating fluid and a comparison was made with the so-called supersmooth f -plane solution which-in contrast to the classical Lamb-Chaplygin solution-is marked by an elliptical separatrix and a doubly continuously differentiable vorticity field. Dyevisualization and high-resolution particle-tracking techniques revealed that the observed dipole characteristics (separatrix aspect ratio, cross-sectional vorticity distribution and vorticity versus streamfunction relationship) are in close agreement with those of the supersmooth f -plane solution for the entire lifespan of the dipolar vortex.

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“…Both are known in the context of 2D Euler equations 6,7 and, by extension, are expected in the QG equation. Yet, we observe them in full "compressible" RSW simulations, starting from definitely ageostrophic initial conditions.…”

Section: Agm Fi T Collisionsmentioning

confidence: 96%

Collisions of ageostrophic modons and formation of new types of coherent structures in rotating shallow water model

Lahaye

Zeitlin

2011

Physics of Fluids

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International audienceWe study collisions of recently discovered ageostrophic modons in rotating shallow water model at different values of impact parameter and find that two new types of coherent vortex structures may be formed during this process: "nonlinear" modons, i.e., coherent dipoles with essentially nonlinear scatter plot and coherent tripoles. Both are known for incompressible 2D Euler equations, but were not reported in the "compressible" shallow water model. Inelastic scattering with strong filamentation and shearing is also possible. Surprisingly, the strongly nonlinear process of coherent structure formation leads to almost no emission of inertia-gravity waves. © 2011 American Institute of Physics

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Dynamics of a nonlinear dipole vortex

Cited by 32 publications

References 33 publications

Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

Barotropic elliptical dipoles in a rotating fluid

Collisions of ageostrophic modons and formation of new types of coherent structures in rotating shallow water model

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