Eddy Potential Vorticity Flux Research Articles

Instability and Mesoscale Eddy Fluxes in an Idealized 3‐Layer Beaufort Gyre

AbstractWe study the impacts of a continental slope on instability and mesoscale eddy fluxes in idealized 3‐layer numerical model simulations. The simulations are inspired by and mimic the situation in the Arctic Ocean's Beaufort Gyre, where anti‐cyclonic winds drive anti‐cyclonic currents that are guided by the continental slope. The forcing and currents are retrograde with respect to topographic Rossby waves. The focus of the analysis is on eddy potential vorticity (PV) fluxes and eddy‐mean flow interactions under the Transformed Eulerian Mean framework. Eddy lateral vorticity fluxes dominate over the continental slope where eddy form stress, that is, vertical momentum flux, is suppressed due to the topographic PV gradient. The diagnosis also shows that while eddy momentum fluxes are up‐gradient over parts of the slope, the total quasi‐geostrophic PV flux is down‐gradient everywhere. We then calculate the linearly unstable modes of the time‐mean state and find that the most unstable mode contains several key features of the observed finite‐amplitude fluxes over the slope, including down‐gradient PV fluxes. When accounting for additional unstable modes, more qualitative features of the observed eddy fluxes in the numerical model are reproduced.

Changes in the tropical upper-tropospheric zonal momentum balance due to global warming

Abstract. We study the zonal momentum budget of the deep upper tropics in the context of present and future climates. In the zonal mean, as is known, a robust balance exists between the acceleration by the horizontal eddy momentum flux convergence and the deceleration by the mean meridional momentum advection. During summer, climatological stationary Rossby waves over the Asian monsoon longitudes converge westerly momentum into the tropics and are the primary contributors to the eddy term. During winter, anomalous westerly winds over the tropical east Pacific allow extratropical waves to propagate into the deep tropics, where they tend to break and decelerate the flow. When integrated over all longitudes, we find that eddies from these two regions sum constructively in summer and destructively in winter, always yielding a net positive momentum forcing that balances the mean flow term. The state-of-the-art CMIP6 suite qualitatively captures these features in the historical run and shows that the momentum fluxes change due to global warming. In summer, stationary eddy circulations in the Asian monsoon zone weaken in the upper troposphere (UT) but strengthen in the lower stratosphere (LS). Greater upward mass flux from the troposphere forces a stronger divergence and a more intense circulation in the LS following a Sverdrup vorticity balance. We observe this strengthening of summertime tropical and subtropical stationary waves in the LS over all longitudes and verify it in an idealized aquaplanet general circulation model experiment. In winter, we find that eddy westerlies over the east Pacific longitudes decrease in strength due to the expected weakening of the subtropical stationary waves with warming. This causes a significant decrease in the propagation of extratropical waves into this region, along with a drop in eddy potential vorticity fluxes associated with these waves. Thus, apart from the mean meridional flux, which weakens due to the projected weakening of the Hadley cells, our analysis of warming simulations clearly suggests significant and robust changes in the eddy momentum fluxes in the deep tropics. Potential implications of these changes in the context of the zonal mean flow and regional circulations are discussed.

Middepth Zonal Velocity in the Southern Tropical Indian Ocean: Striation-Like Structures and Their Dynamics

Abstract In this study, the upper-ocean absolute geostrophic currents in the southern Indian Ocean are constructed using Argo temperature and salinity data from the middepth (1000 m) zonal velocity derived from the Argo float trajectory. The results reveal alternating quasi-zonal striation-like structures of middepth zonal velocity in the equatorial and southern tropical Indian Ocean. Specifically, the eastward time-mean flows are located at the equator and 2°, 5°, 8°, 13°, 16°, 18°–19°, and 21°–22°S, with a meridional scale of ∼300 km. The generation mechanisms of the striation-like zonal velocity structure differ between the near-equatorial and off-equatorial regions. The triad of baroclinic Rossby wave instability plays a significant role in near-equatorial striations. In the south, the high potential vorticity (PV) of Antarctic intermediate water and low PV of southern Indian Ocean Subantarctic Mode Water lead to strong baroclinic instability, which increases the eddy kinetic energy in the middepth layer, thus contributing to a turbulent PV gradient. The convergence/divergence of the eddy PV flux generates the quasi-zonal striations. The meridional scale of the striations is controlled by the most unstable wavelength of baroclinic instability, which explains the observations. Significance Statement The middepth zonal velocity resembles a system of eastward/westward jets with a considerably smaller width than the larger-scale ocean surface circulation. Such a phenomenon always occurs in a turbulent ocean that presents eddy or eddy–mean flow interactions. This study used float observations to reveal a robust middepth zonal velocity in the southern tropical Indian Ocean, where the width of the eastward time-mean flows is approximately 300 km. Smaller eddies drive the zonal currents with a smaller width, and the energy of the eddies is released from the unstable vertical structure at middepths. This study provides new insights into the generation mechanism of small-width zonal current structures in the deep ocean.

Deterministic Model of the Eddy Dynamics for a Midlatitude Ocean Model

AbstractMesoscale eddies, although being on scales ofO(20–100) km, have a disproportionate role in shaping the mean stratification, which varies on the scale ofO(1000) km. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to gridscale numerical viscosity, mesoscale-permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasigeostrophic model at mesoscale-resolving resolution in a double gyre configuration and formulate a deterministic closure for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. Our closure successfully reproduces the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the mesoscale-resolving model. One novel point about our approach is that we account for nonlocal eddy feedbacks onto the mean flow by solving the “subgrid” eddy PV equation prognostically in addition to the mean PV.

Updraft Maintenance and Axisymmetrization during Secondary Eyewall Formation in a Model Simulation of Hurricane Matthew (2016)

Abstract As a follow-on to a previous study on secondary eyewall formation (SEF) in a simulation of Hurricane Matthew (2016), this study investigates the emergence and maintenance of an asymmetric rainband updraft region that leads to an SEF event. Under moderate deep-layer environmental wind shear, the storm develops a quasi-stationary rainband complex with intense, persistent updrafts in its left-of-shear, downwind end. Using a budget of equivalent potential temperature θE, it is demonstrated that the maintenance of the left-of-shear updraft is aided by a mesoscale cold pool induced by rainband stratiform cooling which interacts with the storm’s moist envelope of high-θE air. An extended period of destabilization occurs through differential horizontal advection of θE in the boundary layer, which continuously replenishes the moist instability that would otherwise be depleted by the updrafts. The initial lifting of the updraft is found to be the result of buoyancy advection resulting from the density contrast between the surface cold pool and the inner-core high-θE air. A potential vorticity (PV) budget analysis shows that these left-of-shear updrafts generate low- to midlevel PV through diabatic heating and boundary layer processes, which shapes the local PV enhancement and propagates cyclonically downwind. Meanwhile, in the mid- to upper levels, eddy PV flux convergence and PV generation continue to occur in the stratiform precipitation extending downwind into the upshear quadrants, which substantially increases the azimuthal mean PV at the radius of the developing secondary eyewall and marks the occurrence of the axisymmetrization process.

Diffusion-rotational parameterization of eddy fluxes of potential vorticity: barotropic flow in the zonal channel

The problem of parametrization of the eddy fluxes of a potential vorticity is discussed. Traditional diffusion parameterization is complemented by the inclusion of a rotational component. For the analysis of the new scheme, a quasi-geostrophic model of the dynamics of the barotropic flow in a zonal channel with a non-uniform bottom is used. An analytical solution of the problem is found and the influence of topography on the flow disturbances is discussed. It is shown that the equation for the eddy potential enstrophy allows to relate diffusion and «rotational» coefficients.

Diffusion-Rotational Parameterization of Eddy Fluxes of Potential Vorticity: Barotropic Flow in the Zonal Channel

The problem of parametrization of the eddy fluxes of a potential vorticity is discussed. Traditional diffusion parameterization is complemented by the inclusion of a rotational component. For the analysis of the new scheme, a quasi-geostrophic model of the dynamics of the barotropic flow in a zonal channel with a non-uniform bottom is used. An analytical solution of the problem is found and the influence of topography on the flow disturbances is discussed. It is shown that the equation for the eddy potential enstrophy allows to relate diffusion and «rotational» coefficients.

Potential vorticity redistribution by localised transient forcing in the shallow-water model

This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of $\unicode[STIX]{x1D6FD}$-plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.

Is the Coefficient of Eddy Potential Vorticity Diffusion Positive? Part I: Barotropic Zonal Channel

AbstractThe question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

The Finite-Amplitude Evolution of Mixed Kelvin–Rossby Wave Instability and Equatorial Superrotation in a Shallow-Water Model and an Idealized GCM

Abstract An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.

Eddy Lifetime, Number, and Diffusivity and the Suppression of Eddy Kinetic Energy in Midwinter

Abstract The wintertime evolution of the North Pacific storm track appears to challenge classical theories of baroclinic instability, which predict deeper extratropical cyclones when baroclinicity is highest. Although the surface baroclinicity peaks during midwinter, and the jet is strongest, eddy kinetic energy (EKE) and baroclinic conversion rates have a midwinter minimum over the North Pacific. This study investigates how the reduction in EKE translates into a reduction in eddy potential vorticity (PV) and heat fluxes via changes in eddy diffusivity. Additionally, it augments previous observations of the midwinter storm-track evolution in both hemispheres using climatologies of tracked surface cyclones. In the North Pacific, the number of surface cyclones is highest during midwinter, while the mean EKE per cyclone and the eddy lifetime are reduced. The midwinter reduction in upper-level eddy activity hence is not associated with a reduction in surface cyclone numbers. North Pacific eddy diffusivities exhibit a midwinter reduction at upper levels, where the Lagrangian decorrelation time is shortest (consistent with reduced eddy lifetimes) and the meridional parcel velocity variance is reduced (consistent with reduced EKE). The resulting midwinter reduction in North Pacific eddy diffusivities translates into an eddy PV flux suppression. In contrast, in the North Atlantic, a milder reduction in the decorrelation time is offset by a maximum in velocity variance, preventing a midwinter diffusivity minimum. The results suggest that a focus on causes of the wintertime evolution of Lagrangian decorrelation times and parcel velocity variance will be fruitful for understanding causes of seasonal storm-track variations.

The Interaction of Recirculation Gyres and a Deep Boundary Current

AbstractMotivated by the proximity of the Northern Recirculation Gyre and the deep western boundary current in the North Atlantic, an idealized model is used to investigate how recirculation gyres and a deep flow along a topographic slope interact. In this two-layer quasigeostrophic model, an unstable jet imposed in the upper layer generates barotropic recirculation gyres. These are maintained by an eddy-mean balance of potential vorticity (PV) in steady state. The authors show that the topographic slope can constrain the northern recirculation gyre meridionally and that the gyre’s adjustment to the slope leads to increased eddy PV fluxes at the base of the slope. When a deep current is present along the topographic slope in the lower layer, these eddy PV fluxes stir the deep current and recirculation gyre waters. Increased proximity to the slope dampens the eddy growth rate within the unstable jet, altering the geometry of recirculation gyre forcing and leading to a decrease in overall eddy PV fluxes. These mechanisms may shape the circulation in the western North Atlantic, with potential feedbacks on the climate system.

Emergent eddy saturation from an energy constrained eddy parameterisation

The large-scale features of the global ocean circulation and the sensitivity of these features with respect to forcing changes are critically dependent upon the influence of the mesoscale eddy field. One such feature, observed in numerical simulations whereby the mesoscale eddy field is at least partially resolved, is the phenomenon of eddy saturation, where the time-mean circumpolar transport of the Antarctic Circumpolar Current displays relative insensitivity to wind forcing changes. Coarse-resolution models employing the Gent–McWilliams parameterisation with a constant Gent–McWilliams eddy transfer coefficient seem unable to reproduce this phenomenon. In this article, an idealised model for a wind-forced, zonally symmetric flow in a channel is used to investigate the sensitivity of the circumpolar transport to changes in wind forcing under different eddy closures. It is shown that, when coupled to a simple parameterised eddy energy budget, the Gent–McWilliams eddy transfer coefficient of the form described in Marshall et al. (2012) [A framework for parameterizing eddy potential vorticity fluxes, J. Phys. Oceanogr., vol. 42, 539–557], which includes a linear eddy energy dependence, produces eddy saturation as an emergent property.

The Role of Eddy Diffusivity on a Poleward Jet Shift

Abstract The authors use a quasigeostrophic (QG) two-layer model to examine how eddies modify the meridional asymmetry of a zonal jet. The initial asymmetry is introduced in the model’s “radiative equilibrium state” and is intended to mimic a radiatively forced poleward jet shift simulated by climate models. The calculations show that the initial “poleward” jet shift in the two-layer model is amplified by eddy potential vorticity fluxes. This eddy-accentuation effect is greater as the baroclinicity of the equilibrium state is reduced, suggesting that seasonal variations in baroclinicity may help explain observed and modeled jet-shift sensitivity to season. The eddy-accentuated jet shift from the corresponding radiative equilibrium state is more clearly visible in the slowly varying, eddy-free reference state of Nakamura and Zhu. This reference state formally responds only to nonadvective, nonconservative processes, but ultimately arises from the advective eddy fluxes. The implication is that fast eddies are capable of driving a slowly varying jet shift, which may be balanced by nonconservative processes such as radiative heating/cooling.

Bottom Boundary Potential Vorticity Injection from an Oscillating Flow: A PV Pump

AbstractOceanic boundary currents over the continental slope exhibit variability with a range of time scales. Numerical studies of steady, along-slope currents over a sloping bathymetry have shown that cross-slope Ekman transport can advect buoyancy surfaces in a bottom boundary layer (BBL) so as to produce vertically sheared geostrophic flows that bring the total flow to rest: a process known as buoyancy shutdown of Ekman transport or Ekman arrest. This study considers the generation and evolution of near-bottom flows due to a barotropic, oscillating, and laterally sheared flow over a slope. The sensitivity of the boundary circulation to changes in oscillation frequency ω, background flow amplitude, bottom slope, and background stratification is explored. When ω/f ≪ 1, where f is the Coriolis frequency, oscillations allow the system to escape from the steady buoyancy shutdown scenario. The BBL is responsible for generating a secondary overturning circulation that produces vertical velocities that, combined with the potential vorticity (PV) anomalies of the imposed barotropic flow, give rise to a time-mean, rectified, vertical eddy PV flux into the ocean interior: a “PV pump.” In these idealized simulations, the PV anomalies in the BBL make a secondary contribution to the time-averaged PV flux. Numerical results show the domain-averaged eddy PV flux increases nonlinearly with ω with a peak near the inertial frequency, followed by a sharp decay for ω/f > 1. Different physical mechanisms are discussed that could give rise to the temporal variability of boundary currents.

Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses

This work continues development of the framework for dynamically consistent parameterization of mesoscale eddy effects in non-eddy-resolving ocean circulation models. Here, we refine and extend the previous results obtained for the double gyres and aim to account for the eddy backscatter mechanism that maintains eastward jet extension of the western boundary currents. We start by overcoming the local homogeneity assumption and by taking into account full large-scale circulation. We achieve this by considering linearized-dynamic responses to finite-time transient impulses. Feedback from these impulses on the large-scale circulation are referred to as footprints. We find that the local homogeneity assumption yields only quantitative errors in most of the gyres but breaks down in the eastward jet region, which is characterized by the most significant eddy effects. The approach taken provides new insights into the eddy/mean interactions and framework for parameterization of unresolved eddy effects. Footprints provide us with maps of potential vorticity anomalies expected to be induced by transient eddy forcing. This information is used to calculate the equivalent eddy potential vorticity fluxes and their divergences that partition the double-gyre circulation into distinct geographical regions with specific eddy effects. In particular, this allows approximation of the real eddy effects that maintain the eastward jet extension of the western boundary currents and its adjacent recirculation zones. Next, from footprints and their equivalent eddy fluxes and from underlying large-scale flow gradients, we calculate spatially inhomogeneous and anisotropic eddy diffusivity tensor. Its properties suggest that imposing parameterized source terms, that is, equivalent eddy flux divergences, is a better parameterization strategy than implementation of the eddy diffusion.

Dynamical Response to the QBO in the Northern Winter Stratosphere: Signatures in Wave Forcing and Eddy Fluxes of Potential Vorticity

Abstract Wave–mean flow interactions associated with the Holton–Tan effect (HTE), whereby the tropical quasi-biennial oscillation (QBO) modulates the Northern Hemisphere wintertime stratospheric polar vortex, are studied using the ERA-Interim dataset. Significant evidence of the HTE in isentropic coordinates is found, with a weaker and warmer polar vortex present when the lower-stratospheric QBO is in its easterly phase (QBOe). For the first time, the authors quantify the QBO modulation of wave propagation, wave–mean flow interaction, and wave decay/growth via a calculation of potential vorticity (PV)-based measures, the zonal-mean momentum budget, and up-/downgradient eddy PV fluxes. The effect of the tropospheric subtropical jet on QBO modulation of the wave activity is also investigated. In the subtropical-to-midlatitude lower stratosphere, QBOe is associated with an enhanced upward flux of wave activity, and corresponding wave convergence and wave growth, which leads to a stronger poleward zonal-mean meridional circulation and consequently a warmer polar region. In the middle stratosphere, QBOe is associated with increased poleward wave propagation, leading to enhanced wave convergence and in situ wave growth at high latitudes and contributing to the weaker polar vortex. In agreement with recent studies, the results suggest that the critical-line effect cannot fully account for these wave anomalies associated with the HTE. Instead, it is suggestive of a new, additional mechanism that hinges on the QBO-induced meridional circulation effect on the latitudinal positioning of the subtropical jet. Under QBOe, the QBO-induced meridional circulation causes a poleward shift of the subtropical jet, encouraging more waves to propagate into the stratosphere at midlatitudes.

Multi-layer quasi-geostrophic ocean dynamics in Eddy-resolving regimes

The multi-layer quasi-geostrophic model of the wind-driven ocean gyres is numerically investigated using a combination of long-time runs (200 years) needed for accurate statistics, spatial resolutions (grid interval of less than one kilometer) needed for accurate representation of mesoscale eddies, and large Reynolds number (Re > 104) needed for more realistic flow regimes. We gradually increased the Reynolds number by lowering the eddy viscosity and analysed the corresponding changes of the large-scale circulation, energetics and eddy fluxes, with the goal to understand how the nonlinear eddy dynamics affects the large-scale ocean circulation, as more and more degrees of freedom become dynamically available. Three- and six-layer configurations of the model are considered in order to understand effects of higher baroclinic modes. A parameter sensitivity study is also carried out to show that the explored flow regime is robust.As Re increases, most properties of the flow show no signs of approaching an asymptote, and the following tendencies are found. The time-mean flow properties tend to an asymptote in the three-layer model but not in the six-layer one, suggesting that higher baroclinic modes are dynamically more active at larger Re. The eddy kinetic and potential energies grow faster in the six-layer case. The intensity of the eddy forcing (eddy flux divergence) increases with Re. The inter-gyre eddy potential vorticity flux is predominantly northward and up-gradient for all Re studied. A comparison of the three- and six-layer model solutions revealed an inhibitory influence of high baroclinic modes on the penetration length of the eastward jet extension of the western boundary currents and on the strength of the adjacent recirculation zones. In large-Re regimes, the population of eddies is mostly sustained by the eddy generation at the eastern end of the eastward jet rather than in its central section. Finally, by studying the numerical convergence of the solutions, we found the empirical dependency between the eddy viscosity and the required grid resolution: halving the viscosity requires halving the grid spacing.

On the dynamical influence of ocean eddy potential vorticity fluxes

The impact of eddy potential vorticity fluxes on the dynamical evolution of the flow is obscured by the presence of large and dynamically-inert rotational fluxes. However, the decomposition of eddy potential vorticity fluxes into rotational and divergent components is non-unique in a bounded domain and requires the imposition of an additional boundary condition. Here it is proposed to invoke a one-to-one correspondence between divergent eddy potential vorticity fluxes and non-divergent eddy momentum tendencies in the quasi-geostrophic residual-mean equations in order to select a unique divergent eddy potential vorticity flux. The divergent eddy potential vorticity flux satisfies a zero tangential component boundary condition. In a simply connected domain, the resulting divergent eddy potential vorticity flux satisfies a powerful optimality condition: it is the horizontally oriented divergent flux with minimum L2 norm. Hence there is a well-defined sense in which this approach removes as much of the dynamically inactive eddy potential vorticity flux as possible, and extracts an underlying dynamically active divergent eddy potential vorticity flux. It is shown that this approach leads to a divergent eddy potential vorticity flux which has an intuitive physical interpretation, via a direct relationship to the resulting forcing of the mean circulation.

Low-Frequency Variability of Monsoon-Driven Circulation with Application to the South China Sea

AbstractThe interannual variability of the upper-ocean circulation forced by seasonally varying monsoonal wind is investigated in a two-layer quasigeostrophic (QG) model, with the aim to understand the low-frequency variability of the South China Sea (SCS) circulation. It is demonstrated that the seasonally varying monsoonal wind can force the upper-ocean circulation with significant internal variability, which is mainly associated with the intrinsic nonlinear dynamics of the summer double-gyre system. This arises from the fact that the intrinsic variability, characterized by the Rossby wave adjustment in the winter single-gyre system, is much weaker than that in the summer double-gyre system driven by the intergyre eddy potential vorticity flux through barotropic instability.