Figure - available from: Geophysical Research Letters
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Linear analysis of the two‐layer quasi‐geostrophic model. Panel (a) shows the natural log of the net perturbation energy for values of Hrms from 0 to 400 m. Panel (b) presents the growth rate (λ) as a function of roughness (Hrms), illustrating the systematic weakening of vortex instability with increasing variance of sea‐floor topography.
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Swirls of circular currents tens to hundreds of kilometers in diameter known as ocean rings are critically important for transporting heat and nutrients throughout the ocean. Such structures usually reside in the upper ocean (top 1,000 m) and can last from months to several years. Ocean rings are often emitted by strong curre...
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Citations
... In some cases, the topography may produce a secondary circulation that reinforces mean flow (Holloway, 1987;1992) or create energy cascades that ultimately produce relatively narrow zonal currents (Vallis and Maltrud, 1993). Rough bathymetry can also dramatically alter the stability characteristics of large-scale currents, which was demonstrated for parallel flows (LaCasce et al., 2019;Radko, 2020) and axisymmetric oceanic vortices known as rings (Gulliver and Radko, 2022a;2022b). The latter study argued that the suppression of baroclinic instability by rough seafloor could add years to ocean rings' lifespan. ...
... Following Gulliver and Radko (2022a;2022b), we construct bottom topography as a sum of Fourier modes with random phases and spectral amplitudes conforming to (2). However, in the present simulations, the nominal RMS height of topography ðg 0 Þ and its nominal wavenumbers ðk 0 ; l 0 Þ are scaled down to match the dimensions of the rotating tank. ...
This study presents numerical analogs of laboratory experiments designed to explore the interaction of broad geophysical flows with irregular small-scale bathymetry. The previously reported "sandpaper" theory offered a succinct description of the cumulative effect of small-scale topographic features on large-scale flow patterns. However, initial investigations have been conducted using numerical models with simplified quasi-geostrophic equations that may inadequately represent the dynamics realized in the world's oceans. This investigation advances previous efforts by using a fully nonlinear Navier-Stokes model configured for rotating tank experiments to (i) validate theory and (ii) offer guidance for future physical experiments that will ground-truth theoretical ideas.
... The present study can be advanced in numerous directions by systematically increasing the complexity and realism of the model configuration, including, for instance, the atmospheric forcing, continental boundaries, bottom topography, or higher vertical modes. Furthermore, the bottom drag in the present version is described by linear friction, which may not represent the essential effects of rough topography (Gulliver and Radko, 2022b). Nevertheless, even the analysis of the most basic system suggests that the vortex dynamics and eddy-induced transport could be profoundly different in EB and WB flows and should be explored further. ...
We identify and explore the fundamental differences in the dynamics of mesoscale vortices in eastward background (EB) parts in mid-latitude ocean gyres and in westward background (WB) return flows. In contrast to eddy behavior in EB flow, a systematic meridional drift of eddies in WB flow results in poleward expulsion of cold-core cyclones and equatorward expulsion of warm-core anticyclones from the unstable zone with a negative potential vorticity gradient (PVG). Consequently, heat can be transferred further by upper ocean vortices intrinsically coupled with deep opposite sign partners. Such structures can drift through the stable zone with positive PVG in both layers. This mechanism of lateral transfer is not captured by local models of homogeneous turbulence. The crossflow drift is related to the coupling of the upper vortices with opposite sign deep eddies shifted eastward. The abyssal vortices can be viewed as lee Rossby waves induced by their upper-layer partners and described analytically in the vicinity of the latitude of marginal stability. Here, we show how such self-amplifying hetons, emerging in homogeneous turbulence, saturate when they approach locally stable regions of inhomogeneous currents. The presented results indicate that subtropical regions with return WB flows in the upper layer favor long-distance heat transport by spatially coherent eddies in accordance with observations and motivate the development of non-local parameterizations of eddy fluxes.
... In contrast, the vortex above irregular topography remains coherent and nearly steady throughout the entire simulation. This topographic stabilization is consistent with our earlier findings (Gulliver & Radko 2022) and calls for a more systematic analysis. ...
... Another robust tendency revealed by this analysis is the topographic stabilization of axisymmetric vortices. While this effect has already been observed in topography-resolving simulations of Gulliver and Radko (2022), the more efficient parametric model permits its systematic exploration over a wide range of governing parameters. We argue that the conditions for topographic stabilization are unrestrictive and commonly met in nature, which could explain the abundance of long-lived mesoscale eddies in all ocean basins (e.g. ...
This study explores the impact of small-scale variability in the bottom relief on the dynamics and evolution of broad baroclinic flows in the ocean. The analytical model presented here generalizes the previously reported barotropic 'sandpaper' theory of flow-topography interaction to density-stratified systems. The multiscale asymptotic analysis leads to an explicit representation of the large-scale effects of irregular bottom roughness. The utility of the multiscale model is demonstrated by applying it to the problem of topography-induced spin-down of an axisymmetric vortex. We find that bathymetry affects vortices by suppressing circulation in their deep regions. As a result, vortices located above rough topography tend to be more stable than their flat-bottom counterparts. The multiscale theory is validated by comparing corresponding topography-resolving and parametric simulations.
... LaCasce et al. 2019; Radko 2020) of the significance of bathymetry is the dramatic impact of sea-floor roughness on the intensity of mesoscale variability, traditionally defined as flow components with a lateral extent of 10-100 km. Particularly relevant to the present investigation are the findings of Gulliver & Radko (2022), who analysed the effects of irregular topography on the stability and longevity of ocean rings. This study explored the parameter regime in which the lateral extent of primary flows greatly exceeded that of individual topographic features -the configuration aptly dubbed the 'sandpaper model'. ...
... The name was chosen to invoke the associations with fine abrasive particles of sandpaper that may be individually insignificant but have a tangible cumulative effect in grinding down much larger objects. A series of simulations in Gulliver & Radko (2022) revealed dramatic dissimilarities in the evolution of coherent vortices in flat-bottom basins and in the presence of realistic topographic patterns. The set-up of these experiments is illustrated by the schematic diagram in figure 1. ...
This study examines the impact of small-scale irregular topographic features on the dynamics and evolution of large-scale barotropic flows in the ocean. A multiscale theory is developed, which makes it possible to represent large-scale effects of the bottom roughness without explicitly resolving small-scale variability. The analytical model reveals that the key mechanism of topographic control involves the generation of a small-scale eddy field associated with considerable Reynolds stresses. These eddy stresses are inversely proportional to the large-scale velocity and adversely affect mean circulation patterns. The multiscale model is applied to the problem of topography-induced spin-down of a large circularly symmetric vortex and is validated by corresponding topography-resolving simulations. The small-scale bathymetry chosen for this configuration conforms to the Goff-Jordan statistical spectrum. While the multiscale model formally assumes a substantial separation between the scales of interacting flow components, it is remarkably accurate even when scale separation is virtually non-existent.
Recently, Jánosi et al. (2019) introduced the concept of a “vortex proxy” based on an observation of strong correlations between integrated kinetic energy and integrated enstrophy over a large enough surface area. When mesoscale vortices are assumed to exhibit a Gaussian shape, the two spatial integrals have particularly simple functional forms, and a ratio of them defines an effective radius of a “proxy vortex”. In the original work, the idea was tested over a restricted area in the Californian Current System. Here we extend the analysis to global scale by means of 25 years of AVISO altimetry data covering the (ice-free) global ocean. The results are compared with a global vortex database containing over 64 million mesoscale eddies. We demonstrate that the proxy vortex representation of surface flow fields also works globally and provides a quick and reliable way to obtain coarse-grained vortex statistics. Estimated mean eddy sizes (effective radii) are extracted in very good agreement with the data from the vortex census. Recorded eddy amplitudes are directly used to infer the kinetic energy transported by the mesoscale vortices. The ratio of total and eddy kinetic energies is somewhat higher than found in previous studies. The characteristic westward drift velocities are evaluated by a time-lagged cross-correlation analysis of the kinetic energy fields. While zonal mean drift speeds are in good agreement with vortex trajectory evaluation in the latitude bands 30–5∘ S and 5–30∘ N, discrepancies are exhibited mostly at higher latitudes on both hemispheres. A plausible reason for somewhat different drift velocities obtained by eddy tracking and cross-correlation analysis is the fact that the drift of mesoscale eddies is only one component of the surface flow fields. Rossby wave activities, coherent currents, and other propagating features on the ocean surface apparently contribute to the zonal transport of kinetic energy.
This study explores the dynamics of intense coherent vortices in large-scale vertically sheared flows. We develop an analytical theory for vortex propagation and validate it by a series of numerical simulations. Simulations are conducted using both stable and baroclinically unstable zonal background flows. We find that vortices in stable westward currents tend to adjust to an equilibrium state characterized by quasi-uniform zonal propagation. These vortices persist for long periods, during which they propagate thousands of kilometers from their points of origin. The adjustment tendency is realized to a much lesser extent in eastward background flows. These findings may help to explain the longevity of the observed oceanic vortices embedded in predominantly westward flows. Finally, we examine the influence of background mesoscale variability induced by baroclinic instability of large-scale flows on the propagation and persistence of isolated vortices.
