Planetary Vorticity Gradient Research Articles

Distinct Impacts of Topographic versus Planetary PV Gradients on Baroclinic Turbulence

Abstract The impacts of topographic versus planetary potential vorticity (PV) gradients on fully developed geostrophic turbulence are often treated as dynamically equivalent in theoretical understanding and parameterizations of ocean mesoscale turbulence. Using a suite of homogeneous, two-layer quasigeostrophic (QG) turbulence simulations, we identify similarities and distinctions of topographic versus planetary PV gradients in modulating turbulent eddy energy and fluxes. We show that, while an elevated background PV gradient can suppress geostrophic turbulence, a positive (negative) bottom slope with respect to the orientation of isopycnal slope barotropizes (debarotropizes) the turbulent energy at large scales, which contrasts with a dynamically inert planetary PV gradient in the modewise energy transfer. Then, in the presence of weak bottom drag, a positive slope energizes large-scale along-slope jets and limits small-scale barotropic eddies, both of which yield stronger eddy suppression effects than from a planetary PV gradient; by contrast, a negative slope hinders along-slope jet formation by enhancing the dual-energy cascade cycling, which alleviates the topographic suppression on eddies. In the presence of strong bottom drag, a positive slope elevates barotropic eddy energy, which further enhances the eddy-driven fluxes; by contrast, a negative slope confines turbulent energy to the baroclinic mode, which is strongly damped, causing further weakened turbulent energy and eddy fluxes. A flow regime captured by linear QG theories also emerges as the turbulent energy cascade is jointly suppressed by negative slopes and strong bottom drag. This study provides insights into parameterizing mesoscale eddy effects across sloping bathymetry in predictive ocean models.

The structural compactness of a tropical cyclone seed affects its persistence

Abstract Tropical cyclones (TC) are often generated from pre-existing “seed” vortices. Seeds with higher persistence might have a higher chance to undergo TC genesis. What controls seed persistence remains unclear. This study proposes that planetary Rossby wave drag is a key factor that affects seed persistence. Using recently developed theory for the response of a vortex to the planetary vorticity gradient, a new parameter given by the ratio of the maximum wind speed (Vmax) to the Rhines speed at the radius of maximum wind (Rmax), here termed “vortex compactness” (Cv), is introduced to characterize the vortex weakening by planetary Rossby wave drag. The relationship between vortex compactness and weakening rate is tested via barotropic β-plane experiments. The vortex’s initial Cv is varied by systematically varying their initial Vmax and Rmax in idealized wind profile models. Experiments are also conducted with real-world seed vortices from reanalysis data, which possess natural compactness variability. The weakening rate depends strongly on the vortex’s initial Cv across both idealized and real-world experiments, and the initial axis-asymmetry introduces minor differences. Experiments doubling the size of seed vortices cause them to weaken more rapidly, in line with other experiment sets. The dependence of the weakening rate on initial compactness can be predicted from a simple theory, which is more robust for more compact vortices. Our results suggest that a seed’s structure strongly modulates how long it can persist in the presence of a planetary vorticity gradient. Connections to real seeds on Earth are discussed.

Inferring Tracer Diffusivity From Coherent Mesoscale Eddies

AbstractMixing along isopycnals plays an important role in the transport and uptake of oceanic tracers. Isopycnal mixing is commonly quantified by a tracer diffusivity. Previous studies have estimated the tracer diffusivity using the rate of dispersion of surface drifters, subsurface floats, or numerical particles advected by satellite‐derived velocity fields. This study shows that the diffusivity can be more efficiently estimated from the dispersion of coherent mesoscale eddies. Coherent eddies are identified and tracked as the persistent sea surface height extrema in both a two‐layer quasigeostrophic (QG) model and an idealized primitive equation (PE) model. The Lagrangian diffusivity is estimated using the tracks of these coherent eddies and compared to the diagnosed Eulerian diffusivity. It is found that the meridional coherent eddy diffusivity approaches a stable value within about 20–40 days in both models. In the QG model, the coherent eddy diffusivity is a good approximation to the upper‐layer tracer diffusivity in a broad range of flow regimes, except for small values of bottom friction or planetary vorticity gradient, where the motions of same‐sign eddies are correlated over long distances. In the PE model, the tracer diffusivity has a complicated vertical structure and the coherent eddy diffusivity is correlated with the tracer diffusivity at the e‐folding depth of the energy‐containing eddies where the intrinsic speed of the coherent eddies matches the rms eddy velocity. These results suggest that the oceanic tracer diffusivity at depth can be estimated from the movements of coherent mesoscale eddies, which are routinely tracked from satellite observations.

A Simple Eddy Potential Vorticity Flux Closure

AbstractIt is shown that within the limits of quasi‐geostrophic scaling, biharmonic mixing of potential vorticity is equivalent to biharmonic lateral friction together with biharmonic isopycnal thickness mixing in primitive equations, all with the same viscosity. The problem of unbalanced zonal forces related to the planetary vorticity gradient disappears using a biharmonic instead of a harmonic closure. The former is appropriate for eddy‐permitting ocean models which are replacing now more and more the non‐eddy‐resolving model versions in coupled state‐of‐the‐art climate models. Numerical experiments demonstrate that including biharmonic thickness mixing has some benefits regarding stronger eddy production in marginally eddying ocean models, in particular when the grid size is larger than the baroclinic Rossby radius. Going to finer grids where relative vorticity dominates, however, using only biharmonic friction becomes similar to biharmonic mixing of potential vorticity, justifying the long‐standing use of biharmonic friction in reasonably well resolved eddy‐permitting ocean models.

Annular self-organization of the two-dimensional vorticity condensate

Self-organization of the vorticity condensate of forced two-dimensional turbulence is examined in analogy with the mixing of a background planetary vorticity gradient in geophysical flows. Starting from the theoretical vorticity profile of the condensate, different scenarios are illustrated by the construction of idealized angular momentum conserving rearrangements of vorticity into a staircase profile similar to the potential vorticity staircase of $\beta$ -plane turbulence. Two sets of numerical experiments are then presented that illustrate a similar self-organization of the background vorticity gradient in fully turbulent flows. In the first set of experiments, the flow is initialized with a laminar vortex dipole corresponding to the theoretical condensate vorticity profile. A fluctuation vorticity field is then induced by a stochastic forcing at smaller scales, which induces an azimuthally symmetric self-organization of the laminar flow into distinct annular bands. In the second set of experiments, the flow is initialized from rest with stochastic forcing generating a turbulent inverse energy cascade, out of which emerges the condensate in a self-consistent evolution as the turbulent energy accumulates at the domain scale. A self-organization of the condensate is again observed, giving a distinct annular structure on top of the theoretically predicted condensate profile. A major difference from the potential vorticity staircase of geophysical flows is the emergence in many cases of significantly non-monotonic radial vorticity profiles.

Tropical Cyclone Size Is Strongly Limited by the Rhines Scale: Experiments with a Barotropic Model

Abstract Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone. Significance Statement Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

Three-Dimensional Baroclinic Eddies in the Ocean: Evolution, Propagation, Overall Structures, and Angular Models

AbstractThe evolution and dynamics of an initially Gaussian baroclinic vortex embedded in a resting stratification environment are investigated with a three-dimensional primitive equation model. The vortex evolution process strongly depends on multiple parameters. Particularly, the effects of the gradient of planetary vorticity, nonlinearity, and friction have been studied to evaluate their roles. Comparisons with previous results from a simplified model are made. We particularly focus on interactions between vortices at different levels to understand their evolution. Additionally, a set of numerical simulations has been performed to examine the role of parameter space (Froude–Rossby number) on the evolution of eddies. The evolution and propagation of the vortex is affected by the planetary vorticity gradient; nonlinearity accelerates the transfer of energy from low to high angular mode and speeds up the propagation of eddies. A new finding is that a “double dipole” structure is observed with the development of a vortex, which is located in the core and edge regions, respectively. Only eddies in a finite depth range can maintain synchronous motion, and the dispersive translation paths in all levels imply that initially aligned eddies finally develop into misaligned structures and lead the tilted axis. In contrast to the results in a previous study, eddies have a southward drift irrespective of the vortex polarity. The eddies in the upper level maintain strong stability; in the middle depths, eddies decay rapidly where they form mixed barotropic and baroclinic instabilities. The energy budget analysis demonstrates the complex energy conversion between eddy and angular modes. The Burger number is the most important factor affecting the pattern of eddy evolution.

Strongest MJO on Record Triggers Extreme Atacama Rainfall and Warmth in Antarctica

AbstractTropical perturbations have been shown theoretically and observationally to excite long‐range atmospheric responses in the form of Rossby wave teleconnections that result from the equator to pole gradient of planetary vorticity. An extreme teleconnection event occurred during March 2015 in the Southeastern Pacific. As a result, extreme high temperatures were observed in Southwestern South America and the Antarctic Peninsula simultaneously with an extreme rainfall and flood event in the hyperarid Atacama desert. We show that the origin of these seemingly disconnected extreme events can be traced to a Rossby wave response to the strongest Madden‐Julian Oscillation (MJO) on record in the tropical central Pacific. A barotropic wave number 3 to 4 perturbation with group velocity between 15 and 30 m/s is consistent with the trajectory and timing followed by the upper‐level anomalies radiating away from the tropics after the MJO episode.

Topographic Influence on Baroclinic Instability and the Mesoscale Eddy Field in the Northern North Atlantic Ocean and the Nordic Seas

AbstractA weak planetary vorticity gradient and weak density stratification in the northern North Atlantic and Nordic seas lead to time-mean currents that are strongly guided by bottom topography. The topographic steering sets up distinct boundary currents with strong property fronts that are prone to both baroclinic and barotropic instability. These instability processes generate a macroturbulent eddy field that spreads buoyancy and other tracers out from the boundary currents and into the deep basins. In this paper we investigate the particular role played by baroclinic instability in generating the observed eddy field, comparing predictions from linear stability calculations with diagnostics from a nonlinear eddy-permitting ocean model hindcast. We also look into how the bottom topography impacts instability itself. The calculations suggest that baroclinic instability is a consistent source of the eddy field but that topographic potential vorticity gradients impact unstable growth significantly. We also observe systematic topographic effects on finite-amplitude eddy characteristics, including a general suppression of length scales over the continental slopes. Investigation of the vertical structure of unstable modes reveal that Eady theory, even when modified to account for a bottom slope, is unfit as a lowest-order model for the dynamics taking place in these ocean regions.

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models. Part I: From cyclostrophic super‐rotation to geostrophic turbulence

The regimes of possible global atmospheric circulation patterns in an Earth‐like atmosphere are explored using a simplified Global Circulation Model (GCM) based on the University of Hamburg's Portable University Model for the Atmosphere (PUMA)—with simplified (linear) boundary‐layer friction, a Newtonian cooling scheme, and dry convective adjustment (designated here as PUMA‐S). A series of controlled experiments is conducted by varying planetary rotation rate and imposed equator‐to‐pole temperature difference. These defining parameters are combined further with each other into dimensionless forms to establish a parameter space in which the occurrences of different circulation regimes are mapped and classified. Clear, coherent trends are found when varying planetary rotation rate (thermal Rossby number) and frictional and thermal relaxation time‐scales. The sequence of circulation regimes as a function of parameters, such as the planetary rotation rate, strongly resembles that obtained in laboratory experiments on rotating, stratified flows, especially if a topographic β‐effect is included in those experiments to emulate the planetary vorticity gradients in an atmosphere induced by the spherical curvature of the planet. A regular baroclinic wave regime is also obtained at intermediate values of thermal Rossby number and its characteristics and dominant zonal wavenumber depend strongly on the strength of radiative and frictional damping. These regular waves exhibit some strong similarities to baroclinic storms observed on Mars under some conditions. Multiple jets are found at the highest rotation rates, when the Rossby deformation radius and other eddy‐related length‐scales are much smaller than the radius of the planet. These exhibit some similarity to the multiple zonal jets observed on gas giant planets. Jets form on a scale comparable to the most energetic eddies and the Rhines scale poleward of the supercritical latitude. The balance of heat transport varies strongly with Ω∗ between eddies and zonally symmetric flows, becoming weak with fast rotation.

Hamiltonian Structure and a Variational Principle for Grounded Abyssal Flow on a Sloping Bottom in a Mid‐Latitude β‐Plane

AbstractObservations, numerical simulations, and theoretical scaling arguments suggest that in mid‐latitudes, away from the high‐latitude source regions and the equator, the meridional transport of abyssal water masses along a continental slope correspond to geostrophic flows that are gravity or density driven and topographically steered. These dynamics are examined using a nonlinear reduced‐gravity geostrophic model that describes grounded abyssal meridional flow over sloping topography that crosses the planetary vorticity gradient. It is shown that this model possesses a noncanonical Hamiltonian formulation. General nonlinear steady solutions to the model can be obtained for arbitrary bottom topography. These solutions correspond to nonparallel shear flows that flow across the planetary vorticity gradient. If the in‐flow current along the poleward boundary is strictly equatorward, then no shock can form in the solution in the mid‐latitude domain. It is also shown that the steady solutions satisfy the first‐order necessary conditions for an extremal to a suitably constrained potential energy functional. Sufficient conditions for the definiteness of the second variation of the constrained energy functional are examined. The theory is illustrated with a nonlinear steady solution corresponding to an abyssal flow with upslope and down slope groundings in the height field.

Meridional dynamics of grounded abyssal water masses on a sloping bottom in a mid-latitude -plane

Observations, numerical simulations and theoretical scaling arguments suggest that in mid-latitudes, away from the source regions and the equator, the meridional transport of abyssal water masses along a continental slope corresponds to planetary geostrophic flows that are gravity- or density-driven and topographically steered. We investigate these dynamics using a nonlinear reduced-gravity model that can describe grounded abyssal meridional flow over sloping topography that crosses the planetary vorticity gradient. Exact nonlinear steady and time-dependent solutions are obtained. The general steady theory is illustrated for a non-parallel equatorward flow that possesses a single along-slope grounding along the upslope flank of the current (complementing previous work). Four specific nonlinear time-dependent solutions are described. Two initial-value problems are solved exactly. The first initial configuration corresponds to an equatorward abyssal flow that has no cross-slope shear in the along-slope velocity and possesses a single grounding along the upslope flank of the current. The nonlinear time-dependent evolution of this initial current into a non-parallel shear flow is described. The second initial condition corresponds to an isolated radially symmetric grounded abyssal pool or dome. The nonlinear time-dependent evolution of this abyssal dome, which propagates equatorward with unsteady along- and cross-slope velocities while deforming into an elliptically shaped abyssal dome with $\unicode[STIX]{x1D6FD}$-induced diminishing height, is described. Finally, the nonlinear time-dependent boundary-value problem can be solved exactly in which the in-flow boundary condition on the poleward boundary of the mid-latitude domain corresponds to a time-dependent abyssal current with both an upslope and downslope grounding. Two specific time-dependent boundary conditions are examined. The first corresponds to a time-limited surge in the equatorward volume transport in the abyssal current along the poleward boundary. The second configuration corresponds to the nonlinear evolution of a finite-amplitude downslope plume or loop that forms in the abyssal current that is reminiscent of those seen in baroclinic instability simulations.

The Rhines effect on the geographical characteristics of altimeter-observed eddies

The Rhines effect may be regarded as an interaction between Rossby waves and turbulence, in which the Rossby waves may radiate away eddy energy when their frequencies are equal or larger than those of the turbulence, thereby deforming and eventually destroying the existing eddies. Through comparing eddy-scale velocity and long Rossby wave phase speed in the oceans, a generalized form of the Rhines effect is examined on the geographical characteristics of altimeter-observed eddies. The results show that the generalized Rhines effect has a much greater influence on eddy characteristics than its classical form, which only considers the simple beta effect due to the meridional gradient of planetary vorticity. The largest amount of eddies are detected in regions where eddy-scale velocity is larger than the critical Rossby-wave phase speed considering a generalized beta effect. The eddies in those regions can grow via an inverse kinetic energy cascade and have much larger amplitudes and sizes. The “eddy desert” regions outside of the tropical oceans, which have far fewer detected eddies and much weaker eddy amplitudes, lie in areas where the eddy-scale velocity is less than the critical Rossby-wave phase speed. In those regions, the generalized Rhines effect may be a possible mechanism of suppressing eddy growth.

Beta-plane turbulence above monoscale topography

Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow $U(t)$ and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow $U$ is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of $U$ on parameters such as the planetary potential vorticity (PV) gradient $\unicode[STIX]{x1D6FD}$ and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow $U$ in the limiting cases of weak and strong forcing. If $\unicode[STIX]{x1D6FD}$ is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow $U$ is an unoccupied mean. If $\unicode[STIX]{x1D6FD}$ is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an ‘eddy saturation’ regime in which $U$ is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

The role of intraseasonal variability at mid‐high latitudes in regulating Pacific blockings during boreal winter

ABSTRACTBy using daily National Centers for Environmental Prediction‐Department of Energy reanalysis data from 1979 to 2015, we investigated the connection between Pacific blockings and mid‐high latitude atmospheric intraseasonal oscillation (ISO) at 500 hPa in boreal winter. The ISO perturbation over a key area of 150°E–155°W, 60°–75°N is most co‐variated with Pacific blockings. The averaged geopotential height over this key area exhibits a statistically significant 10–35‐day periodicity. The ISO perturbation associated with the Pacific blocking activity shows pronounced westward propagation. The perturbation initiates at about 120°W, triggered by intraseasonal wave energy accumulation. A geopotential tendency diagnosis reveals that the time change rate of the geopotential height over the key area is primarily attributed to the advection of planetary vorticity by the ISO meridional flow. A mechanism is put forward in which the westward‐propagating ISO perturbations induce a blocking over the Pacific sector. When a strong northward ISO flow arrives in the key area, it acts against the gradient of planetary vorticity, leading to a negative vorticity advection. This negative advection tends to strengthen local anticyclonic vorticity and geopotential height anomalies. Thus, the westward‐propagating ISO meridional flow plays an active role in inducing the low‐frequency blocking activity over the Pacific sector.

A Geometric Interpretation of Eddy Reynolds Stresses in Barotropic Ocean Jets

AbstractBarotropic eddy fluxes are analyzed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analyzed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal-mode solution. This allows a straightforward interpretation of the eddy–mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies that are tilted “against the shear” and extract energy from the mean flow; once the jet stabilizes, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray-tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.

Midlatitude–Equatorial Dynamics of a Grounded Deep Western Boundary Current. Part II: Cross-Equatorial Dynamics

AbstractThis is Part II of a two-part theoretical study into the midlatitude–cross-equatorial dynamics of a deep western boundary current (DWBC) in an idealized meridionally aligned, differentially rotating ocean basin with zonally varying parabolic bottom topography. Part I determined the midlatitude flow across the planetary vorticity gradient and the dynamics of the DWBC as it begins to enter the equatorial region in the “intermediate equatorial region.” Part II determines the nonlinear dynamics of the DWBC as it flows across the basin along the equator in the “inner equatorial region.” The large-scale structure of the flow within the inner equatorial region corresponds to a zonally aligned nonlinear stationary planetary wave pattern that meanders about the equator in which the flow exits the equatorial region on the eastern side of the basin. In addition to numerically determining the pathlines for the large-scale equatorial flow, an approximate nonlinear model is introduced for which an analytical solution can be obtained for the nonlinear planetary wave along the equator. If the DWBC exits the equatorial region into the opposite hemisphere from its source hemisphere, the characteristic curves associated with the flow must necessarily intersect within the inner equatorial region. It is in the regions of intersecting characteristics that dissipation makes a leading-order contribution to the dynamics and induces the requisite potential vorticity adjustment permitting the cross-equatorial flow of a DWBC that is in planetary geostrophic dynamical balance in midlatitudes.

Synthesis of Vortex Rossby Waves. Part II: Vortex Motion and Waves in the Outer Waveguide

Abstract Beta, the meridional gradient of planetary vorticity, causes tropical cyclones to propagate poleward and westward at approximately 2 m s−1. In a previous shallow-water linear model, the simulated vortex accelerated without limit, ostensibly because beta forced a free linear mode. In the analogous nonlinear model, wave–wave interaction limited the propagation speed. Subsequent work based upon the asymmetric balance (AB) approximation was unable to replicate the linear result. The present barotropic nondivergent model replicates the linear beta gyres as a streamfunction dipole with a uniform southeasterly ventilation flow across the vortex. The simulated storm accelerates to unphysical, but finite, speeds that are limited by vorticity filamentation. In the analogous nonlinear model, nonlinearly forced wavenumber-1 gyres have opposite phase to the linear gyres so that their ventilation flow counteracts advection by the linear gyres to limit the overall vortex speed to approximately 3 m s−1. A bounded mean vortex with zero circulation at large radius must contain an outer annulus of anticyclonic vorticity to satisfy the circulation theorem. The resulting positive mean vorticity gradient constitutes an outer waveguide that supports downstream-propagating, very-low-frequency vortex Rossby waves. It is confined between an inner critical radius where the waves are absorbed and an outer turning point where they are reflected. Vorticity filamentation at the critical radius limits the beta-drift acceleration. The original unlimited linear acceleration stemmed from too-weak dissipation caused by second-order diffusion applied to velocity components instead of vorticity. Fourth-order diffusion and no outer waveguide in the Rankine-like vortex of the AB simulations plausibly explain the different results.

Parameterization of eddy fluxes based on a mesoscale energy budget

It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.

S3T Stability of the Homogeneous State of Barotropic Beta-Plane Turbulence

Abstract Zonal jets and nonzonal large-scale flows are often present in forced–dissipative barotropic turbulence on a beta plane. The dynamics underlying the formation of both zonal and nonzonal coherent structures is investigated in this work within the statistical framework of stochastic structural stability theory (S3T). Previous S3T studies have shown that the homogeneous turbulent state undergoes a bifurcation at a critical parameter and becomes inhomogeneous with the emergence of zonal and/or large-scale nonzonal flows and that these statistical predictions of S3T are reflected in direct numerical simulations. In this paper, the dynamics underlying the S3T statistical instability of the homogeneous state as a function of parameters is studied. It is shown that, for weak planetary vorticity gradient β, both zonal jets and nonzonal large-scale structures form from upgradient momentum fluxes due to shearing of the eddies by the emerging infinitesimal flow. For large β, the dynamics of the S3T instability differs for zonal and nonzonal flows but in both the destabilizing vorticity fluxes decrease with increasing β. Shearing of the eddies by the mean flow continues to be the mechanism for the emergence of zonal jets while nonzonal large-scale flows emerge from resonant and near-resonant triad interactions between the large-scale flow and the stochastically forced eddies. The relation between the formation of large-scale structure through modulational instability and the S3T instability of the homogeneous state is also investigated and it is shown that the modulational instability results are subsumed by the S3T results.