FIG 26 - uploaded by Alvaro Viudez
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Three-dimensional sketch of the ageostrophic motion in the baroclinic dipole. The circled cross and circled dot indicate upwelling and downwelling, respectively.
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The three-dimensional motion of mesoscale baroclinic dipoles is simulated using a nonhydrostatic Boussinesq numerical model. The initial conditions are two ellipsoidal vortices of positive and negative potential vorticity anomalies. The flow is moderately ageostrophic with a maximum absolute Rossby number equal to 0.71. The trajectory of the dipole...
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The processes involved in the vertical splitting of vortices in geophysical dipoles, rotating and stably stratified, are investigated using a three-dimensional numerical model under the f-plane and Boussinesq approximations. Vertical splitting in asymmetric dipoles is possible when the vortices have a similar amount of potential vorticity but signi...
Citations
... Results are given in figure 19 for all non-destructive interactions. It should be noted that Pallàs-Sanz & Viúdez (2007) quantified the asymmetry between the two vortices by measuring the curvature of the trajectory. ...
We investigate the nonlinear evolution of pairs of three-dimensional, equal-sized and opposite-signed vortices at finite Froude and Rossby numbers. The two vortices may be offset in the vertical direction. The initial conditions stem from relative equilibria obtained numerically in the quasi-geostrophic regime, for vanishing Froude and Rossby numbers. We first address the linear stability of the quasi-geostrophic opposite-signed pairs of vortices, and show that for all vertical offsets, the vortices are sensitive to an instability when close enough together. In the nonlinear regime, the instability may lead to the partial destruction of the vortices. We then address the nonlinear interaction of the vortices for various values of the Rossby number. We show that as the Rossby number increases, destructive interactions, where the vortices break into pieces, may occur for a larger separation between the vortices, compared to the quasi-geostrophic case. We also show that for well-separated vortices, the interaction is non-destructive, and ageostrophic effects lead to the deviation of the trajectory of the pair of vortices, as the anticyclonic vortex dominates the interaction. Finally, we show that the flow remains remarkably close to a balanced state, emitting only waves containing negligible energy, even when the interaction leads to the destruction of the vortices.
... The process of interaction between cyclonic and anticyclonic eddies, in the form of the creation of a counter-rotating eddy dipole structure, is particularly interesting, since these interactions can change eddy properties and shape (Cresswell & Legeckis, 1986;Pallàs-Sanz & Viúdez, 2007). This change in shape could be important for the transport of heat, salt, and biological material in light of the effect which eddy eccentricity has on the retention or leakage of water within these eddies (Pilo et al., 2018). ...
In western boundary current systems, sharp velocity gradients between the poleward flowing jet and coastal waters generally act to inhibit cross‐shelf exchange. Downstream of jet separation, dynamic mesoscale eddies dominate the flow. In the East Australian Current System, counter‐rotating eddy dipoles are often present which, in the appropriate configuration, have potential to drive cross‐shelf transport. However, this eddy dipole mode is poorly understood in the framework of cross‐shelf exchange and the effect of these structures on shelf waters is uncertain. Using 25 years of satellite altimetry, as well as in situ sampling of a typical dipole event, we investigate the characteristics of eddy‐driven cross‐shelf exchange. We show that the maximum onshore velocity is driven by an eddy dipole structure and occurs in a defined latitudinal band between 33°S and 34°S more than 50% of the time. We sample a typical eddy dipole and find a strong onshore jet, 37 km wide, with velocities up to 1.78 m s and a transport of at least 16 Sv. Hydrographic data from an autonomous underwater glider show that this jet manifests on the shelf as a subsurface intrusion of warm salty water extending from offshore up onto the midshelf. In the light of climatic changes in western boundary current transport and the increase in their eddy kinetic energy, understanding eddy‐driven cross‐shelf exchange is important to predict future changes to the shelf water mass.
... At the ocean surface, the dominant (i.e., leading-order) geostrophic velocity can be treated as non-divergent and purely solenoidal. The corresponding ageostrophic velocity corrections to the leading-order fields are 3D, weakly 2D-divergent at the surface, and characterized by small vertical velocities [17][18][19][20][21][22]. At the surface, this flow correction can be treated as divergent (potential) component of the combined 2D velocity field responsible for advection and clustering of material tracers. ...
This work deals with buoyant tracers floating at the ocean surface, where the geostrophic velocity component is two dimensional and rotational (nondivergent) and the ageostrophic component can contain rotational and potential (divergent) contributions that are comparable in size. We consider a random kinematic flow model and study the process of clustering, that is, aggregation of the floating tracer in localized spatial patches. In the long-time limit and in the cases of strongly and weakly divergent flows, the existing analytical theory predicts the process of exponential clustering, which is the emergence of spatial singularities containing all the available tracer. Here we confirm this analytical prediction, in numerical model solutions spanning different combinations of rotational and potential surface velocity components, and report that exponential clustering persists even in weakly divergent flows, however at significantly slower rates. For a wide range of parameters, we analyze not only the exponential clustering but also the other type of tracer aggregation, referred to as fragmentation clustering, as well as the coarse-graining effects on clustering. For the presented analysis we consider ensembles of Lagrangian particles and introduce and apply the statistical topography methodology.
... The presence of several Agulhas rings and cyclonic eddies can induce the generation of dipole structures comparable to the Heton model of Hogg and Stommel (1985). These oceanic dipoles have been observed using satellite imagery thanks to their surface signature, described as a mushroomlike pattern in various regions, and have been characterized with numerical simulations and analytical theories (Ahlnäs et al., 1987;Hooker and Brown, 1994;Hooker et al., 1995;Millot and Taupier-Letage, 2005;Pallàs-Sanz and Viúdez, 2007;Baker-Yeboah et al., 2010a). These counterrotating eddies enhance horizontal transport of heat along isopycnals, particularly across frontal structures (Spall, 1995) and vertical diapycnal mixing. ...
The eastern side of the South Atlantic Meridional overturning circulation
Basin-wide Array (SAMBA) along 34.5° S is used to assess the
nonlinear, mesoscale dynamics of the Cape Basin. This array presently
consists of current meter moorings and bottom mounted Current and Pressure recording Inverted Echo
Sounders (CPIES)
deployed across the continental slope. These data, available from September
2014 to December 2015, combined with satellite altimetry allow us to
investigate the characteristics and the impact of mesoscale dynamics on local
water mass distribution and cross-validate the different data sets. We
demonstrate that the moorings are affected by the complex dynamics of the
Cape Basin involving Agulhas rings, cyclonic eddies and anticyclonic eddies
from the Agulhas Bank and the South Benguela upwelling front and filaments.
Our analyses show that exchange of water masses happens through the advection
of water by mesoscale eddies but also via wide water mass intrusions
engendered by the existence of intense dipoles. These complex dynamics induce
strong intra-seasonal upper-ocean velocity variations and water mass
exchanges between the shelf and the open ocean but also across the
subantarctic and subtropical waters. This work presents the first independent
observations comparison between full-depth moorings and CPIES data sets
within the eastern South Atlantic region that gives some evidence of eastern
boundary buoyancy anomalies associated with migrating eddies. It also
highlights the need to continuously sample the full water depth as
inter-basin exchanges occur intermittently and affect the whole water column.
... These diagnostics, however, require observations with high spatial and temporal resolutionboth hard to achieve when observing mesoscale eddies (Allen et al., 2001;Martin & Richards, 2001). Another way to study the vertical circulation in the ocean is by analyzing the output of numerical models (e.g., Flierl & Mied, 1985;Pallas-Sanz & Viudez, 2007;Viudez & Dritschel, 2003). Modeled vertical velocity, however, cannot be easily validated against observations, and results from idealized simulations are not always applicable to real ocean eddies. ...
Vertical motions within eddies play an important role in the exchange of properties and energy between the upper ocean and the ocean interior. Here, we analyse alternating upward and downward cells in anticyclonic eddies in the East Australian Current region using a global eddy resolving model. The cells explain over 50% of the variance of vertical velocity within these eddies. We show that the upward and downward cells relate to eddy distortion, defined as the change in eddy shape over time. In anticyclonic eddies in the Southern Hemisphere, an inward distortion is associated with upward motion and an outward distortion is associated with downward motion. We discuss two mechanisms that link eddy distortion to vertical velocity. One mechanism relates to changes in stratification and relative vorticity in the eddy interior. The other mechanism, relates to divergence of the horizontal flow in different quadrants of the eddy. We show that mesoscale changes in sea level anomaly can be used to infer the vertical motion within eddies.
... treated as nondivergent (hence purely rotational). The small ageostrophic first-order corrections are three-dimensional (3D) motions; hence they are 2D divergent at the surface [20][21][22][23][24][25] and can be treated as a combination of divergent (potential) and rotational (nondivergent) components. The latter is largely responsible for the clustering process [11,[26][27][28][29][30][31][32][33][34][35][36][37]. ...
... where s hom (t;ρ) and m hom (t;ρ) are, respectively, the specific cluster area and specific cluster mass, defined by the threshold ρ [36,48]. Since ρ(R, t ) is a positive-definite field, the clustering happens with probability one, and the corresponding limits lim t→∞ s hom (t;ρ) → 0, lim t→∞ m hom (t;ρ) → 1 ρ 0 ρ(t ) (21) assert that the cluster area shrinks to zero, while the cluster mass incorporates all the available tracer. From (11) and (20) one can derive the specific functions for the purely divergent velocity field ...
Buoyant material clustering in a stochastic flow, which is homogeneous and isotropic in space and
stationary in time is addressed. The dynamics of buoyant material in three-dimensional hydrodynamic
flows can be considered as the motion of passive tracers in a compressible two-dimensional
velocity field. The latter is of interest in the present study. It is well known that the clustering
of the density of passive tracers occurs in this case. We evaluate the impact of diffusion on the
clustering process by using a numerical model. In general, the effect of diffusion is negligible in
the very beginning of the evolution of initially uniformly distributed passive tracers. Therefore, the
clustering of the density of passive tracers can emerge in accordance with the general theory. We
analyze a long time clustering affected by diffusion and show that the emerged cluster structure
persists in time in spite of the diffusion effect. However, the clusters split in time.
... A horizontal quadrupolar pattern of vertical velocity has previously been associated with the 'classic' dipole structure in model studies of ocean features (Pall as- Sanz and Viú dez, 2007). As indicated in Section 3.2.2, ...
This paper quantitatively assesses the mesoscale spatial variability in vertical velocity associated with an open ocean eddy dipole. High-resolution, in situ data were collected during a research cruise aboard the NERC research ship RRS Discovery to the Iceland Basin in July/August 2007. A quasi-synoptic SeaSoar spatial survey revealed a southeastward flowing jet with counter-rotating eddies on either side. The anti-cyclonic component was identified as a mode water eddy, characterised by a homogenous core (∼35.5 psu and 12 °C) centred at a depth of ∼600 m. Vertical velocities were calculated by inverting the quasi-geostrophic (QG) Omega equation at each point in a three-dimensional grid encompassing the dipole. The strongest vertical velocities (up to 5 m day−1) were found primarily in the central jet between the eddies, as fast flowing water was forced over raised isopycnals associated with the large potential vorticity anomaly of the mode water eddy. Weaker upward (downward) vertical velocity was diagnosed ahead of the cyclonic (mode water) eddy in the direction of propagation, reaching 0.5 m day−1 (2.5 m day−1) at the depth of maximum potential vorticity (PV) anomaly. The results demonstrate that the mesoscale velocity field cannot be accurately reconstructed from analysis of individual isolated eddy features and that detailed three-dimensional maps of potential vorticity are required to quantify the cumulative effects of their interactions. An examination of potential sources of error associated with the vertical velocity diagnosis is presented, including sampling strategy, quasi-synopticity, sensitivity to interpolation length scale and the unquantified effect of lower boundary conditions. The first three of these errors are quantified as potentially reaching 50%, ∼20% and ∼25% of the calculated vertical velocity, respectively, indicating a potential margin of error in the vertical velocity diagnosis of order one.
... The horizontal velocity, which is slightly larger in the anticyclone than in the cyclone, reaches maxima |u h | max = 0.78 at the dipole center (Figure 14b). The vertical velocity (Figure 14c) is three orders of magnitude smaller than |u h |, and has the typical quadrupolar pattern of mesoscale QG dipoles [Pallàs-Sanz and Viúdez, 2007]. ...
The interaction between submesoscale baroclinic vortical structures and
large amplitude inertia-gravity waves (IGWs), with emphasis on the
vertical velocity, is numerically investigated using a high-resolution
three-dimensional non-hydrostatic model. A rich variety of vortex-wave
interactions are possible depending on the potential vorticity (PV)
content and length scale of the submesoscale monopoles or dipoles, and
on the amplitude and wave number of the IGWs. On the one hand, large
amplitude IGWs cause horizontal and vertical advection of the vortices,
which conserve their stability though their geometry is largely modified
by the wave motion. On the other hand, the horizontal vortical motion
Doppler shifts the local frequency of IGWs. The vortical angular
velocity and vortex density stratification lead to a wave dispersion
relation involving the effective Coriolis frequency (Coriolis frequency
plus the vortical angular velocity) and the total
Brunt-Väisälä frequency. This inhomogeneous change in the
local wave frequency causes IGWs to depart from their initial plane
geometry. In the particular case of inertial waves, the nonlinear
vortex-wave interaction generates spiral IGWs, having vertical
velocities one order of magnitude larger than the submesoscale vortical
flow in the absence of waves.
... They observe internal gravity wave generation during the evolution of the vortex, a priori related to filamentation. With the same equations, Pallas-Sanz and Viudez [121] investigate the three-dimensional ageostrophic motion in a mesoscale vortex dipole. For a small distance between a cyclone and an anticyclone, the vortices drift as a compact dipole and the vertical velocity pattern is octupolar. ...
Oceanic vortices (also called eddies) come under a large variety of sizes, from a few kilometers up to 300 km in diameter. Vertically, their extent can also range from a few tens of meters up to (nearly) the whole ocean depth. They can be intensified near the surface, near the thermocline, or near the bottom. They can be generated by the instability or by the change of direction of ocean currents, by geostrophic adjustment after convection, or via topographic influences (e.g., lee eddies behind islands).
... Because of their important role in geophysical fluid dynamics, dipoles have been the subject of a large number of theoretical, laboratory, observational, and numerical studies. To mention just a few, some have addressed the dipole formation [van Heijst and Flór, 1989;Mied et al., 1991;Spall and Robinson, 1990;Kloosterziel and van Heijst, 1991;Spall, 1995;Orlandi and Carnevale, 1999;Sansón et al., 2001;Feng et al., 2007], the dipole structure [Norbury, 1973;Fedorov and Ginsburg, 1986;Couder and Basdevant, 1986;Sheres and Kenyon, 1989;Simpson and Lynn, 1990;Carton, 2001], and dipole dynamics [Pierrehumbert, 1980;Rasmussen et al., 1996;Eames and Flór, 1998;Kizner et al., 2003;Pallàs-Sanz and Viúdez, 2007]. Other investigations have focused on their interaction, namely dipole-dipole interaction [McWilliams and Zabusky, 1982;van Heijst and Flór, 1989;Velasco Fuentes and van Heijst, 1995;Dubosq and Viúdez, 2007], dipole-topography interaction [Kloosterziel et al., 1993;Carnevale et al., 1997], and dipole-wave interaction [Godoy-Diana et al., 2006]. ...
Mesoscale oceanic vortex dipoles are stable coherent vortex structures formed by two closely packed regions of opposite sign vertical vorticity. The authors investigate periodic oscillations in the vortices that make barotropic and baroclinic dipoles depart from a complete steady state. These oscillations are a pair of vortex Rossby waves (VRWs) and are numerically simulated using a three-dimensional, Boussinesq, and f-plane model. The evolution of balanced (void of inertia-gravity waves), static, and inertially stable dipoles is examined under different initial conditions. These initial conditions include the vortex potential vorticity (PV) geometry, initial distance between vortices, and PV extrema. The numerical results show that each VRW is an oscillation with azimuthal wave number 2 that amplifies preferentially at two vortex locations and has an angular phase speed of the same sign as the vortex vertical vorticity. The VRWs in the dipole (dipole VRWs) imply an oscillation in the dipole speed of displacement and, in baroclinic dipoles, interchange between kinetic and potential energy as well. In the absence of any external forcing, the amplitude, periodicity, and phase speed of the dipole VRWs depend on the initial conditions, especially on the PV extrema, vortex geometry, and initial distance between vortices. It is found that steady dipoles are possible but their steadiness is not robust in the sense that any small perturbation will cause the development of VRWs.
