Figure - available from: Journal of Geophysical Research: Oceans

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# (a) The eddy diffusivity of density (or equivalently, the nondimensional flux of potential vorticity in the upper layer) for the quasi‐geostrophic simulations with varying zonal slope in the same style as Figure 2. (b) The eddy diffusivity of potential vorticity in the lower layer. The upper layer is omitted because it is identical to (a) with an additional factor of 1/1+β.

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This study attempts to identify the equilibration mechanisms of baroclinic instability and investigate the effects of the orientation of the background flow and topography on eddy‐induced transport. The analysis is based on growth rate balance theory, which assumes that nonlinear equilibration occurs when the growth rate of the primary baroclinic i...

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Recently introduced in oceanography to interpret the near surface circulation, Transition Path Theory ( TPT ) is a methodology that rigorously characterizes ensembles of trajectory pieces flowing out from a source last and into a target next, i.e., those that most productively contribute to transport. Here we use TPT to frame, in a statistically mo...

## Citations

... Such an endeavor would require the development of an analytical framework representing the leakage of the vortex thickness anomaly into the far field}an interesting challenge in its own right. The largely unexplored dynamics of vortices in nonzonal background flows (e.g., Brown et al. 2019), motivate the corresponding generalization of the vortex propagation and adjustment theory. These extensions should incorporate strong horizontal shears often found in western boundary currents. ...

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.

... Arbic et al. 2019;Klymak et al. 2021) and the topographic control of the flow stability (e.g. Chen, Kamenkovich & Berloff 2015;Brown, Gulliver & Radko 2019). A distinct group of studies explored configurations where bathymetry affects transient eddies that, in turn, modulate time-mean flows (e.g. ...

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.

... In fact, some of the longest-lived coherent structures are situated over prominent topographic features (Dewar, 1998;de Miranda et al., 1999), which can be attributed to the mechanisms originally advocated by Bretherton and Haidvogel (1976) and Verron and Le Provost (1985). Topographic influences on baroclinic instability have been explored by Hart (1975), Benilov (2005), Rabinovich et al. (2018), and Brown et al. (2019). Promising attempts have also been made to parameterize the effects of topography using statistical circulation models (Alvarez et al., 1994;Chavanis & Sommeria, 2002;Frederiksen & O'Kane, 2005;Merryfield & Holloway, 2002;Okane & Frederiksen, 2004;Polyakov, 2001). ...

Plain Language Summary
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 currents, such as the Gulf Stream, Agulhas, and Kuroshio. However, scientists are not entirely sure what allows rings to maintain their strength and persist for long periods. In particular, early theoretical models suggest that such large‐scale vortices are unstable and therefore should quickly disintegrate. In this study, we suggest that the resolution of the vortex longevity conundrum could lie in an unexpected direction—topography. The seafloor contains numerous underwater mountains, ridges, and valleys which, surprisingly, can dramatically affect rings that spin several kilometers above the bottom. Using numerical simulations with flat and realistically varying bottom, we demonstrate that eddies above rough topography persist much longer than their counterparts with identical parameters above a flat seafloor. We also show that there is a critical height of the bottom roughness which allows the surface‐intensified rings to remain stable and maintain their structure for years.

... The terms "meridional" and "zonal" here describe spectral components with relatively low wavenumbers in the north-south (l ≈ 0) and east-west (k ≈ 0) directions, respectively. The dynamics conceptualized by the growth rate balance theory (Radko et al. 2014;Brown et al. 2019) are also at play in the present model. ...

... These structures are interpreted as secondary instabilities of primary, rapidly growing meridional modes. The balance between the linear amplification of primary modes and the disruptive action of their secondary instabilities is the cornerstone of the "growth rate balance" theory of nonlinear equilibration (Radko et al. 2014;Brown et al. 2019). It is of interest to determine whether the ideas behind the growth rate balance theory are relevant for the weakly nonlinear limit captured by the reduced-dynamics model. ...

... 0. These harmonics act to reinforce the linear amplification of unstable modes, although this tendency is much weaker than the adverse action of zonally elongated harmonics. The analysis in Fig. 11a also supports the growth balance theory (Radko et al. 2014;Brown et al. 2019), which attributes the equilibration of primary (predominantly meridional) unstable modes to the adverse action of their secondary (predominantly zonal) instabilities. The localized pattern of stabilizing modes in the spectral space suggests that the equilibration of baroclinic instability could be described by low-dimensional truncated models (e.g., Pedlosky 2019). ...

We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasi-geostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

... While the effects of topography on baroclinic instability and on ensuing eddies have already been addressed in a number of studies, this research area has been disproportionately dominated by models in which scales of topography are commensurate with or exceed those of mesoscale variability (e.g. Chen & Kamenkovich 2013;Radko & Kamenkovich 2017;Brown, Gulliver & Radko 2019). The impact of submesoscale topography -defined here as structures with a lateral extent of 1-10 km -has been much less investigated. ...

This study explores the control of mesoscale variability by topographic features with lateral scales that are less than the scale of the eddies generated by baroclinic instability. These dynamics are described using a combination of numerical simulations and an asymptotic multiscale model. The multiscale method makes it possible to express the system dynamics by a closed set of equations written entirely in terms of mesoscale variables, thereby providing a physical basis for the development of submesoscale parameterization schemes. The submesoscale topography is shown to influence such fundamental properties of mesoscale variability as the meridional eddy-induced transport and eddy kinetic energy. It is argued that the adverse influence of submesoscale topography on baroclinic instability is ultimately caused by the homogenization tendency of potential vorticity in the bottom density layer. The multiscale model formally assumes a substantial separation between the scales of interacting flow components. However, the comparison of asymptotic solutions with their submesoscale-resolving numerical counterparts indicates that the multiscale method is remarkably accurate even when scale separation is virtually non-existent.

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.