Travelling vortices over mountains and the long-term structure of the residual flow

Sansón, L. Zavala; Gonzalez, Jeasson F.

doi:10.1017/jfm.2021.567

Cited by 5 publications

(9 citation statements)

References 52 publications

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“…Though there is a very small vorticity exchange between the poles and a small vorticity leakage to the background field, the vortex interaction may be considered, from a practical point of view, as an elastic interaction. This description of an elastic interaction contributes to several previous studies involving eddy-pair interactions, including interactions of dipoles with solid boundaries (de Ruijter et al, 2004; Kloosterziel et al, 1993;Tenreiro et al, 2006;Verzicco et al, 1995;Voropayev & Afanasyev, 1992;Zavala Sansón & Gonzalez, 2021), interactions of dipoles with inertia-gravity waves (Claret & Viúdez, 2010;Huang et al, 2017), and dipole-dipole interactions (Dubosq & Viúdez, 2007;McWilliams & Zabusky, 1982;Meleshko & van Heijst, 1994;Velasco Fuentes & van Heijst, 1995;Voropayev & Afanasyev, 1992). In the cases of dipole-dipole and dipole-vortex interactions both elastic and inelastic processes are possible depending on the initial vorticity distribution, which includes the location, orientation and vorticity distributions of the eddies (Aref, 1979;Meleshko & van Heijst, 1994).…”

Section: Discussionmentioning

confidence: 59%

“…The eddy‐pair or dipole possesses a propagation speed, and may be considered as the simplest self‐induced translating vortex structure (Afanasyev, 2003; Carton, 2001). For this reason it can interact with, for example, a submarine mountain (Zavala Sansón & Gonzalez, 2021), a coastline (de Ruijter et al., 2004), a solid cylinder (Verzicco et al., 1995), different topography (Kloosterziel et al., 1993; Tenreiro et al., 2006; van Heijst & Clercx, 2009; Zavala Sansón, 2007), inertia–gravity waves (Claret & Viúdez, 2010; Huang et al., 2017), other dipoles (Afanasyev, 2003; Dubosq & Viúdez, 2007; McWilliams & Zabusky, 1982; Velasco Fuentes & van Heijst, 1995; Voropayev & Afanasyev, 1992) or other multipolar vortices (Besse et al., 2014; Viúdez, 2021; Voropayev & Afanasyev, 1992). Most of these interactions seem to be inelastic, in the sense that the vorticity of the eddy‐pair suffers irreversible changes during the interaction, for example, during vortex merging or partial or complete straining out processes (Dritschel, 1995; Dritschel & Waugh, 1992; Dubosq & Viúdez, 2007; McWilliams & Zabusky, 1982; Voropayev & Afanasyev, 1992).…”

Section: Introductionmentioning

confidence: 99%

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Elastic Interaction Between a Mesoscale Eddy‐Pair and an Axisymmetrical Eddy

Zoeller

Viúdez

2023

JGR Oceans

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We investigate numerically the elastic interaction between an eddy‐pair and an axisymmetrical eddy in inviscid isochoric two‐dimensional (2D) flows, as well as in three‐dimensional (3D) flows under the quasi‐geostrophic (QG) approximation. The eddy‐pair is a straight moving Lamb‐Chaplygin dipole where the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical eddy. The results for the 2D and 3D cases show that interactions with almost no vorticity exchange, or vorticity loss to the background field between ocean eddies, but causing changes in their displacement velocity, are possible. When the eddy‐pair approaches the axisymmetrical eddy, their respective potential flows interact, the eddy‐pair's trajectory acquires curvature and their vorticity poles separate. In the QG dynamics, the eddies suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the anticyclonic eddy of the pair elongates, simultaneously the cyclonic eddy of the pair evolves toward spherical geometry, and the axisymmetrical eddy acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the eddy‐pair moves away from the axisymmetrical eddy, its poles close, returning to their original geometry, and the anticyclonic and cyclonic eddies continue as an eddy‐pair with a straight trajectory but along a new direction. The interaction is sensitive to the initial conditions and, depending on the initial position of the eddy‐pair, as well as on small changes in the vorticity distribution of the axisymmetrical eddy, inelastic interactions may instead occur.

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Section: Discussionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Elastic Interaction Between a Mesoscale Eddy‐Pair and an Axisymmetrical Eddy

Zoeller

Viúdez

2023

JGR Oceans

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“…This behaviour resembles the asymmetric dipolar solutions obtained in Gonzalez & Zavala Sansón (2021), which rotate steadily around a seamount or valley. In Zavala Sansón & Gonzalez (2021), we reported that the residual flow over a submarine mountain after the passage of a travelling vortex is a dipolar structure that remains trapped around the tip of the mountain. A similar structure was found in laboratory experiments in a large rotating tank (Zavala Sansón et al.…”

Section: Discussionmentioning

confidence: 94%

“…The obstruction and eventual destruction of vortices encountering topographic obstacles in a rotating system have been studied in laboratory experiments (Zavala Sansón 2002; Zavala Sansón, Barbosa Aguiar & van Heijst 2012) and numerical simulations (e.g. van Geffen & Davies 2000; Zavala Sansón & Gonzalez 2021).…”

Section: Introductionmentioning

confidence: 99%

“…In some cases, vortical structures can be trapped over the topography (Zavala Sansón et al. 2012; Zavala Sansón & Gonzalez 2021), and a natural question concerns the stability of such configurations. Carton & Legras (1994) studied the stability of shielded circular vortices over an axisymmetric parabolic bottom, and found that if the vortex core is cyclonic, then a compact and stable tripolar structure emerges.…”

Section: Introductionmentioning

confidence: 99%

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Linear stability of monopolar vortices over isolated topography

Gonzalez

Sansón

2023

J. Fluid Mech.

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The linear instability of circular vortices over isolated topography in a homogeneous and inviscid fluid is examined for the shallow-water and quasi-geostrophic models in the $f$ -plane. The eigenvalue problem associated with azimuthal disturbances is derived for arbitrary axisymmetric topographies, either submarine mountains or valleys. Amended Rayleigh and Fjørtoft theorems with topographic effects are given for barotropic instability, obtaining necessary criteria for instability when the potential vorticity gradient is zero somewhere in the domain. The onset of centrifugal instability is also discussed by deriving the Rayleigh circulation theorem with topography. The barotropic instability theorems are applied to a wide family of nonlinear, quasi-geostrophic solutions of circular vortices over axisymmetric topographic features. Flow instability depends mainly on the vortex/topography configuration, as well as on the vortex size in comparison with the width of the topography. It is found that anticyclones/mountains and cyclones/valleys may be unstable. In contrast, cyclone/mountain and anticyclone/valley configurations are stable. These statements are validated with two numerical methods. First, the generalised eigenvalue problem is solved to obtain the wavenumber of the fastest-growing perturbations. Second, the evolution of the vortices is simulated numerically to detect the development of linear perturbations. The numerical results show that for unstable vortices over narrow topographies, the fastest growth rate corresponds to mode $1$ , which subsequently forms asymmetric dipolar structures. Over wide topographies, the fastest perturbations are mainly modes $1$ and $2$ , depending on the topographic features.

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Elastic Interaction between a Vortex Dipole and an Axisymmetrical Vortex in Quasi-Geostrophic Ocean Dynamics

Zoeller

Viúdez

2022

Preprint

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We investigate numerically the elastic interaction between a dipole and an axisymmetrical vortex in inviscid isochoric twodimensional (2D), as well as in three-dimensional (3D) flows under the quasi-geostrophic (QG) approximation. The dipole is a straight moving Lamb-Chaplygin (L-C) vortex such that the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical vortex. The results for the 2D and 3D cases show that, when the L-C dipole approaches the vortex, their respective potential flows interact, the dipole's trajectory acquires curvature and the dipole's vorticity poles separate. In the QG dynamics, the vortices suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the negative vorticity pole elongates, simultaneously, the positive vorticity pole evolves towards spherical geometry and the axisymmetrical vortex acquires prolate ellipsoidal geometry in the vertically stretched QG space.Once the L-C dipole moves away from the vortex, its poles close, returning the vortices to their original geometry, and the dipole continues with a straight trajectory but along a direction different from the initial one. The vortices preserve, to a large extent, their amount of vorticity and the resulting interaction may be practically qualified as an elastic interaction. The interaction is sensitive to the initial conditions and, depending on the initial position of the dipole as well as on small changes in the vorticity distribution of the axisymmetrical vortex, inelastic interactions may instead occur.

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Travelling vortices over mountains and the long-term structure of the residual flow

Abstract: Abstract

Cited by 5 publications

References 52 publications

Elastic Interaction Between a Mesoscale Eddy‐Pair and an Axisymmetrical Eddy

Elastic Interaction Between a Mesoscale Eddy‐Pair and an Axisymmetrical Eddy

Linear stability of monopolar vortices over isolated topography

Elastic Interaction between a Vortex Dipole and an Axisymmetrical Vortex in Quasi-Geostrophic Ocean Dynamics

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