On the Geostrophic Adjustment of an Isolated Lens: Dependence on Burger Number and Initial Geometry*

Stuart, Grant A.; Sundermeyer, Miles A.; Hebert, Dave

doi:10.1175/2010jpo4476.1

Cited by 10 publications

(8 citation statements)

References 63 publications

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“…This vortex is well studied and has been widely used to model isolated vortices, especially in the oceans (e.g. Gent & McWilliams 1986;Morel & McWilliams 1997;Stuart, Sundermeyer & Hebert 2011).…”

Section: Gaussian Solution To the Dissipationless Boussinesq Equationsmentioning

confidence: 99%

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The universal aspect ratio of vortices in rotating stratified flows: theory and simulation

2012

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We derive a relationship for the vortex aspect ratio α (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Väisälä frequencies within the vortex N c and in the background fluid outside the vortexN, the Coriolis parameter f and the Rossby number Ro of the vortex: α 2 = Ro(1 + Ro)f 2 /(N 2 c −N 2 ). This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for α has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have N 2 c >N 2 ; weak anticyclones (with |Ro| < 1) must have N 2 c N 2 . We verify our relation for α with numerical simulations of the threedimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localized region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically computed vortices validate our relationship for α, and generally they differ significantly from the values obtained from the much-cited conjecture that α = f /N in quasi-geostrophic vortices.

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Section: Gaussian Solution To the Dissipationless Boussinesq Equationsmentioning

confidence: 99%

“…generated from diapycnal mixing (see e.g. McWilliams 1988;Stuart et al 2011). Our flow is initialized with v = 0 andρ = 0.…”

Section: Case A: Run-down Experimentsmentioning

confidence: 99%

The universal aspect ratio of vortices in rotating stratified flows: theory and simulation

2012

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“…Various formation mechanisms were proposed, including baroclinic instability of undercurrents (Jungclaus, 1999), lateral frictional processes near capes or promontories (D'Asaro, 1988b;Molemaker et al, 2015), diapycnal mixing whether by bottom friction (McWilliams, 1985) or locally intensified internal wave breaking (Lelong & Sundermeyer, 2005;Stuart et al, 2011), winter convection (Testor & Gascard, 2003), or subduction along frontal zones (Ou & Gordon, 2002;Thomas, 2008). They are associated with low values of Ertel potential vorticity (PV) and Brunt-Väisälä frequency, and fairly high Rossby numbers.…”

Section: Introductionmentioning

confidence: 99%

Intrathermocline Eddies Embedded Within an Anticyclonic Vortex Ring

Meunier

Tenreiro

Pallàs‐Sanz

et al. 2018

Geophysical Research Letters

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High‐resolution hydrographic measurements reveal the presence of three intrathermocline eddies (ITEs) embedded within a loop current eddy. ITEs are lenticular bodies of nearly homogeneous water, which contrasts with the well‐stratified surrounding water. Their radii and thickness ranged between 19–32 km and 150–250 m. Negative relative vorticity within their cores (down to −0.85 times the Coriolis frequency), along with a large negative stratification anomaly, results in low Ertel potential vorticity and intense negative Ertel potential vorticity anomalies. Vortex stretching and relative vorticity have comparable contributions to potential vorticity anomaly, resulting in Burger numbers of order unity. The similarity of thermohaline properties within the ITE's cores and the surrounding loop current eddy water suggests that these ITEs likely form by intense mixing events followed by Rossby adjustment.

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“…The present study builds on previous work of monopolar shielded vortices by focusing on an S vortex originating from a density mixed patch. Such vortices have been studied numerically by Lelong and Sundermeyer (2005) and in the laboratory by Stuart et al (2011). However, in those studies, vortex stability was not considered.…”

Section: Introductionmentioning

confidence: 99%

Vortex Stability in a Large-Scale Internal Wave Shear

Brunner-Suzuki

Sundermeyer

Lelong

2012

Journal of Physical Oceanography

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The effect of a large-scale internal wave on a multipolar compound vortex was simulated numerically using a 3D Boussinesq pseudospectral model. A suite of simulations tested the effect of a background internal wave of various strengths, including a simulation with only a vortex. Without the background wave, the vortex remained apparently stable for many hundreds of inertial periods but then split into two dipoles. With increasing background wave amplitude, and hence shear, dipole splitting occurred earlier and was less symmetric in space. Theoretical considerations suggest that the vortex alone undergoes a self-induced mixed barotropic–baroclinic instability. For a vortex plus background wave, kinetic energy spectra showed that the internal wave supplied energy for the dipole splitting. In this case, it was found that the presence of the wave hastened the time to instability by increasing the initial perturbation to the vortex. Results suggest that the stability and fate of submesoscale vortices in the ocean may be significantly modified by the presence of large-scale internal waves. This could in turn have a significant effect on the exchange of energy between the submesoscale and both larger and smaller scales.

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On the Geostrophic Adjustment of an Isolated Lens: Dependence on Burger Number and Initial Geometry*

Cited by 10 publications

References 63 publications

The universal aspect ratio of vortices in rotating stratified flows: theory and simulation

The universal aspect ratio of vortices in rotating stratified flows: theory and simulation

Intrathermocline Eddies Embedded Within an Anticyclonic Vortex Ring

Vortex Stability in a Large-Scale Internal Wave Shear

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