Potential Vorticity Budget Research Articles

A Simple Model for Sheddies: Ocean Eddies Formed from Shed Vorticity

AbstractRecent studies show that vertical eddy diffusivity is sufficient on its own to introduce intense horizontal shear layers at sloping ocean margins (Molemaker et al.; Gula et al.; Dewar et al.). These layers influence mesoscale energy and potential vorticity budgets but cannot be fully represented in models without sloping boundaries, no-slip boundary conditions, and sufficiently high resolution. This paper investigates the detachment of these shear layers and their subsequent rolling up into concentrated eddies. These shed eddies, or “sheddies,” may have significant oceanographic impacts. Their growth is considered using a simple point vortex model that adapts the Brown–Michael model of vortex shedding to quasigeostrophic flow and allows detailed consideration of the vorticity fluxes. The model shows good qualitative agreement with observations and experimental and numerical results. It is applied to a number of examples of well-known cases of sheddy formation, including the Agulhas cyclones, California Undercurrent, and Canary Eddy Corridor, and also is used to investigate the effects of shed vorticity in the growth of the Cook Strait eddy and the interaction of the North Brazil Current rings with the islands of the Lesser Antilles.

On the Role of the African Topography in the South Asian Monsoon

Abstract The Somali jet, a strong low-level cross-equatorial flow concentrated in a narrow longitudinal band near the coast of Somalia, is a key feature of the South Asian monsoon (SAM) circulation. Previous work has emphasized the role of the East African highlands in strengthening and concentrating the jet. However, the fundamental dynamics of the jet remains debated, as does its relation to the SAM precipitation. In this study, numerical experiments with modified topography over Africa are conducted with the GFDL atmospheric model, version 2.1 (AM2.1), general circulation model (GCM) to examine the influence of topography on the Somali jet and the SAM precipitation. It is found that when the African topography is removed, the SAM precipitation moderately increases in spite of a weakening of the cross-equatorial Somali jet. The counterintuitive precipitation increase is related to lower-level cyclonic wind anomalies, and associated meridional moisture convergence, which develop over the Arabian Sea in the absence of the African topography. Potential vorticity (PV) budget analyses along particle trajectories show that this cyclonic anomaly primarily arises because, in the absence of the blocking effect by the African topography and with weaker cross-equatorial flow, air particles originate from higher latitudes with larger background planetary vorticity and thus larger PV.

North Pacific Subtropical Mode Water Volume Decrease in 2006–09 Estimated from Argo Observations: Influence of Surface Formation and Basin-Scale Oceanic Variability

Abstract Analysis of Argo temperature and salinity profiles (gridded at 0.5° × 0.5° resolution for 2005–12) shows a strong North Pacific Subtropical Mode Water (NPSTMW) volume and density decrease during 2006–09. In this time period, upper-ocean temperature, stratification, and potential vorticity (PV) all increased within the region in and around the NPSTMW low-PV pool, contributing to the NPSTMW volume decrease in two ways: (i) the volume of water satisfying the low-PV constraint that is part of the “mode water” definition decreased, and (ii) some water that was initially in the NPSTMW density range σθ = 25.0–25.5 kg m−3 was transformed into lighter water. Both changes in density and in PV in the NPSTMW region were a manifestation of basinwide changes. A positive PV anomaly started to propagate westward from the central Pacific in 2005, followed by a negative density anomaly in 2007, which caused a dramatic NPSTMW volume and density decrease. A Walin estimate of surface formation in the NPSTMW density range accounted better (although not entirely) for the interannual variability of the volume of water in the NPSTMW density range without imposing the PV < 2 × 10−10 m−1 s−1 constraint than did the same estimate with the PV constraint imposed. This underlines the importance of the PV constraint in identifying the mode water. The mode water evolution cannot be fully described from a density budget alone; rather, the PV budget must be considered simultaneously.

The Poleward Motion of Extratropical Cyclones from a Potential Vorticity Tendency Analysis

Abstract The poleward propagation of midlatitude storms is studied using a potential vorticity (PV) tendency analysis of cyclone-tracking composites, in an idealized zonally symmetric moist GCM. A detailed PV budget reveals the important role of the upper-level PV and diabatic heating associated with latent heat release. During the growth stage, the classic picture of baroclinic instability emerges, with an upper-level PV to the west of a low-level PV associated with the cyclone. This configuration not only promotes intensification, but also a poleward tendency that results from the nonlinear advection of the low-level anomaly by the upper-level PV. The separate contributions of the upper- and lower-level PV as well as the surface temperature anomaly are analyzed using a piecewise PV inversion, which shows the importance of the upper-level PV anomaly in advecting the cyclone poleward. The PV analysis also emphasizes the crucial role played by latent heat release in the poleward motion of the cyclone. The latent heat release tends to maximize on the northeastern side of cyclones, where the warm and moist air ascends. A positive PV tendency results at lower levels, propagating the anomaly eastward and poleward. It is also shown here that stronger cyclones have stronger latent heat release and poleward advection, hence, larger poleward propagation. Time development of the cyclone composites shows that the poleward propagation increases during the growth stage of the cyclone, as both processes intensify. However, during the decay stage, the vertical alignment of the upper and lower PV anomalies implies that these processes no longer contribute to a poleward tendency.

The non‐conservation of potential vorticity by a dynamical core compared with the effects of parametrized physical processes

Numerical models of the atmosphere combine a dynamical core, which approximates solutions to the adiabatic, frictionless governing equations for fluid dynamics, with tendencies arising from the parametrization of other physical processes. Since potential vorticity (PV) is conserved following fluid flow in adiabatic, frictionless circumstances, it is possible to isolate the effects of non‐conservative processes by accumulating PV changes in an air‐mass‐relative framework. This ‘PV tracer technique’ is used to accumulate separately the effects on PV of each of the different non‐conservative processes represented in a numerical model of the atmosphere. Dynamical cores are not exactly conservative because they introduce, explicitly or implicitly, some level of dissipation and adjustment of prognostic model variables which acts to modify PV. Here, the PV tracers technique is extended to diagnose the cumulative effect of the non‐conservation of PV by a dynamical core and its characteristics relative to the PV modification by parametrized physical processes.Quantification using the Met Office Unified Model reveals that the magnitude of the non‐conservation of PV by the dynamical core is comparable to those from physical processes. Moreover, the residual of the PV budget, when tracing the effects of the dynamical core and physical processes, is at least an order of magnitude smaller than the PV tracers associated with the most active physical processes. The implication of this work is that the non‐conservation of PV by a dynamical core can be assessed in case‐studies with a full suite of physics parametrizations and directly compared with the PV modification by parametrized physical processes. The non‐conservation of PV by the dynamical core is shown to move the position of the extratropical tropopause while the parametrized physical processes have a lesser effect at the tropopause level.

The Role of Convective Heating in Tropical Cyclone Eyewall Ring Evolution

Abstract The purpose of this study is to analyze the role of diabatic heating in tropical cyclone ring structure evolution. A full-physics three-dimensional modeling framework is used to compare the results with two-dimensional modeling approaches and to point to limitations of the barotropic instability theory in predicting the storm vorticity structure configuration. A potential vorticity budget analysis reveals that diabatic heating is a leading-order term and that it is largely offset by potential vorticity advection. Sawyer–Eliassen integrations are used to diagnose the secondary circulation (and corresponding vorticity tendency) forced by prescribed heating. These integrations suggest that diabatic heating forces a secondary circulation (and associated vorticity tendency) that helps maintain the original ring structure in a feedback process. Sensitivity experiments of the Sawyer–Eliassen model reveal that the magnitude of the vorticity tendency is proportional to that of the prescribed heating, indicating that diabatic heating plays a critical role in adjusting and maintaining the eyewall ring.

On the Crossover of Boundary Currents in an Idealized Model of the Red Sea

AbstractThe west-to-east crossover of boundary currents has been seen in mean circulation schemes from several past models of the Red Sea. This study investigates the mechanisms that produce and control the crossover in an idealized, eddy-resolving numerical model of the Red Sea. The authors also review the observational evidence and derive an analytical estimate for the crossover latitude. The surface buoyancy loss increases northward in the idealized model, and the resultant mean circulation consists of an anticyclonic gyre in the south and a cyclonic gyre in the north. In the midbasin, the northward surface flow crosses from the western boundary to the eastern boundary. Numerical experiments with different parameters indicate that the crossover latitude of the boundary currents changes with f0, β, and the meridional gradient of surface buoyancy forcing. In the analytical estimate, which is based on quasigeostrophic, β-plane dynamics, the crossover is predicted to lie at the latitude where the net potential vorticity advection (including an eddy component) is zero. Various terms in the potential vorticity budget can be estimated using a buoyancy budget, a thermal wind balance, and a parameterization of baroclinic instability.

Coastal circulation driven by short-period upwelling-favorable winds in the northern Baja California region

Coastal upwelling in the California Current System depends on the synoptic variability of wind stress fields. In this system, the effects of short-period (days) wind stress fluctuations on coastal ocean circulation are particularly important south of Point Conception. Upwelling and relaxation events in northern Baja California’s coastal waters are examined using shipboard measurements of water properties and currents during October 2009. Satellite-derived variables are also included in the analysis. An upwelling event and a relaxation event, both with short periods (4–3 days), are reported here. The quasigeostrophic theory is used to elucidate differences in upwelling and relaxation ocean behavior. There are noticeable differences in the potential vorticity budget on two typical isopycnals from the study area, namely, the 24.1σθ and the 26.0σθ. Planetary vorticity is the leading term (10−9) on the two isopycnals not only during upwelling but also during relaxation. However, in the upper isopycnal, relative vorticity is larger during upwelling than during relaxation, while the stretching term is of the same order in both events; conversely, in the lower isopycnal, relative vorticity is of the same order in both events, while the stretching term is larger during upwelling than during relaxation. As a consequence of the conservation of potential vorticity, two ageostrophic circulation cells are established during upwelling, one in the upper isopycnal and the other in the lower isopycnal. The upwelling front dynamics generates the upper ageostrophic circulation cell, and the symmetric instability generates the lower ageostrophic circulation cell. The ageostrophic circulation cells are missing during relaxation.

Effect of the atmospheric heat source on the development and eastward movement of the Tibetan Plateau vortices

Based on the final analyses data (FNL) of the Global Forecasting System of the National Centers for Environment Prediction (NCEP) and the radiosonde data over the Tibetan Plateau, evolutions of two types of the Tibetan Plateau vortices, moving-off the plateau (Type A) and dying-out on the plateau (Type B), are investigated respectively. Compared to Type B vortices, the large-scale circulations associated with Type A vortices show stronger ridge to the north of the plateau and deeper trough near the Bay of Bengal at 500 hPa, and the southwesterly flow from the trough and the northwesterly flow from the ridge converge more intensively to the east of Type A vortices. Meanwhile, at 200 hPa the divergence on the right-hand side of the upper westerly jet is just over the vortices. The convergence at 500 hPa and divergence at 200 hPa provide favourable conditions for the development and eastward motion of the vortices. The diagnoses of the potential vorticity (PV) budgets reveal that in the developing stages of the two types of vortices, the vertical distribution of the atmospheric heat source determines both their intensity and the moving direction. In the decaying stage, the maintenance and eastward movement for Type A vortices mainly depend on the convergence of the strong northwesterly and southwesterly to the east of the vortices. For Type B vortices, the vertical PV flux divergence caused by the ascending motion around the vortices reduces the intensity of the vortices and is unfavourable for their eastward motion.

Roles of an upper-level cold vortex and low-level baroclinicity in the development of polar lows over the Sea of Japan

The relationship between a synoptic-scale, upper-level cold vortex and a meso-α scale polar low (PL) over the Sea of Japan, and the role played by low-level baroclinicity in the development of the PL were investigated. We examined three PLs from the perspective of potential vorticity (PV) and energy budgets, using mesoscale analysis data with a horizontal resolution of ~11 km. During the development stage of each PLs, a meso-α scale upper-level PV (UPV) anomaly, which intrudes to around the 700–600 hPa level and which is just a part of a synoptic-scale PV anomaly accompanying the cold vortex, moved to the west side of a low-level PL. The PL was located in a wide region of low static stability in the lower troposphere. These conditions suggested that the synoptic-scale cold vortex, accompanied by a cold dome and the different scales of UPV anomalies, played a role in creating a favourable environment for the PL development. One of the common characteristics of the PL cases studied here was that, in contrast to the low-level PL, the upper-level disturbance associated with the meso-α scale UPV anomaly showed no development at all. This is likely because of the mobile UPV anomaly cut off from its source. Low-level baroclinicity, which varied with time, was an important factor in differentiating the PL shape and the energy sources necessary for PL development. Furthermore, the strength of baroclinicity, through its enhancement of mesoscale fronts and convection, affected diabatic processes, as well as baroclinic development.

Summer circulation structure and formation mechanism in the Beibu Gulf

Due to limited in situ data and diagnostic numerical models, the summer circulation structure and formation mechanism in the Beibu Gulf have always been in controversy in the past 50 years. Therefore, a new three-dimensional hindcast model was built within the northwestern South China Sea (SCS), forced with the daily averaged wind, heat flux, lateral flux, as well as tidal harmonic and eight major rivers discharges. And the east boundary was set up far away off the Qiongzhou Strait (QS). Lastly, the model results were consistent with not only the synchronous observation data from the project 908 but also the historical observed data. As a result, the summer circulation structure was revealed that the southern Gulf was occupied by an anticyclonic eddy whereas the northern Gulf was dominated by a cyclonic gyre. Although the circulation major structure was stable, its area and strength had yearly and monthly oscillation. The other three sensitive experiments indicated that the circulations in the southern and northern Gulf were driven by the SCS circulation and monsoon wind, respectively. After the theoretical analysis of the potential vorticity budget, it was further revealed the circulation in the northern Gulf was driven by the positive wind stress curl in summer. Besides, the river discharge was also significant as the vertical circulation had two layer structures outside the mouth of the Red River. Generally, this work calls for the further research on other subjects, such as ocean biogeochemical or marine fisheries.

Potential Vorticity Budgets in the North Atlantic Ocean

Abstract This paper focuses on potential vorticity (PV) budgets in the North Atlantic with an emphasis on the wind-driven subtropical gyre. Since PV is the key dynamical variable of the wind-driven circulation, these budgets are important to understand. PV is a conservative quantity on isopycnals and can only enter or exit through the boundaries, like the lateral topography or the surface. The latter fluxes are diagnosed and tested against the evolution of the PV content in an isopycnal layer. The former are computed using the Bernoulli function. The essential result is found for all the tested isopycnals, and the dominant feature of PV is recirculation, with very little added at the surface or the boundaries. Density coordinates are well suited to understanding PV circulation. A novel technique for computing the Bernoulli function is proposed. The Bernoulli function is governed by a simple elliptic equation and the solutions demonstrate the dominant contribution of PV advection.

Volume and Potential Vorticity Budgets of Eighteen Degree Water

Abstract Mode waters are a distinctive baroclinic feature of the World Ocean characterized by relatively weak vertical stratification. They correspond dynamically to low potential vorticity (PV). In the North Atlantic subtropical gyre, the mode waters have become known as Eighteen Degree Water. Their dynamics involves air–sea interaction, diapycnal and isopycnal mixing, and subduction. Understanding mode water dynamics is therefore both challenging and important since it connects several aspects of the ocean circulation. Mass and PV budget of the mode water's core, evaluated in a realistic primitive equation North Atlantic model, are used to characterize mode water maintenance. It is shown that the surface PV flux has very little impact on mode water; the surface buoyancy flux in combination with eddy mass flux is the most important control on mode water structure. A mean PV formalism is used to show that the PV and water-mass formation budgets are intrinsically linked. A decomposition of the budget demonstrates the role of the mean PV field in permitting the eddy mass flux to discharge the net formation to the surrounding fluid.

Adiabatic Eastern Boundary Currents

AbstractThe dynamics of the eastern boundary current of a high-resolution, idealized model of oceanic circulation are analyzed and interpreted in terms of residual mean theory. In this framework, it is clear that the eastern boundary current is adiabatic and inviscid. Nevertheless, the time-averaged potential vorticity is not conserved along averaged streamlines because of the divergence of Eliassen–Palm fluxes, associated with buoyancy and momentum eddy fluxes. In particular, eddy fluxes of buoyancy completely cancel the mean downwelling or upwelling, so that there is no net diapycnal residual transport. The eddy momentum flux acts like a drag on the mean velocity, opposing the acceleration from the eddy buoyancy flux: in the potential vorticity budget this results in a balance between the divergences of eddy relative vorticity and buoyancy fluxes, which leads to a baroclinic eastern boundary current whose horizontal scale is the Rossby deformation radius and whose vertical extent depends on the eddy buoyancy transport, the Coriolis parameter, and the mean surface buoyancy distribution.

Energy Dispersion in African Easterly Waves

Abstract The existence of an upstream (eastward) group velocity for African easterly waves (AEWs) is shown based on single-point lag regressions using gridded reanalysis data from 1990 to 2010. The eastward energy dispersion is consistent with the direction of ageostrophic geopotential flux vectors. A local eddy kinetic energy (EKE) budget reveals that, early in the life cycle of AEWs, growth rate due to geopotential flux convergence exceeds baroclinic and barotropic growth rates. Later in the life cycle, EKE decay due to geopotential flux divergence cancels or exceeds baroclinic and barotropic growth. A potential vorticity (PV) budget is used to diagnose tendencies related to group propagation. Although both upstream and downstream group speeds are possible because of the reversal in the mean meridional PV gradient, upstream propagation associated with the positive poleward PV gradient dominates wave packet evolution. Analogous to the concept of downstream development of midlatitude baroclinic waves, new AEWs develop preferentially upstream of the older ones, thus providing a mechanism for seeding new waves. It is suggested that these results are also relevant to AEW intermittency and storm-track structure.

First-Order Scaling Law for Potential Vorticity Extraction due to Wind

AbstractSurface sources and sinks of potential vorticity (PV) have been examined recently in various publications. These are normally identified as the mechanical and buoyant PV fluxes with the former scaled according to wind stress and the latter from buoyancy flux. The authors here examine a PV source that is often overlooked: namely, the diabatically forced source due to wind-driven deepening.Based on an idealized model of the mixed layer, the rate of deepening of the mixed layer due to wind is translated into PV extraction. The authors propose the first-order scaling law as an estimate of the net PV flux due to diabatic wind effects in the absence of other buoyancy effects. This law is verified and calibrated in several numerical experiments. Then, the authors compare the magnitude of the PV extraction due to wind to the other factors responsible for PV input/output: namely, air–sea heat flux, freshwater flux, and Ekman wind-driven currents. Finally, to illustrate the impact of the mixing induced by wind, the authors conclude with a global air–sea PV budget in the North Atlantic basin. The wind-driven diabatic PV flux is found to be comparable to all other sources in all cases and is distinguished by acting only to extract PV.

Diagnostic analysis of the evolution mechanism for a vortex over the Tibetan Plateau in June 2008

Based on the final analyses data (FNL) of the Global Forecasting System of the NCEP and the observational radiosonde data, the evolution mechanism of an eastward-moving low-level vortex over the Tibetan Plateau in June 2008 was analyzed. The results show that the formation of the vortex was related to the convergence between the northwesterly over the central Tibetan Plateau from the westerly zone and the southerly from the Bay of Bengal at 500 hPa, and also to the divergence associated with the entrance region of the upper westerly jet at 200 hPa. Their dynamic effects were favorable for ascending motion and forming the vortex over the Tibetan Plateau. Furthermore, the effect of the atmospheric heat source (Q1) is discussed based on a transformed potential vorticity (PV) tendency equation. By calculating the PV budgets, we showed that Q1 had a great influence on the intensity and moving direction of the vortex. In the developing stage of the vortex, the heating of the vertically integrated Q1 was centered to the east of the vortex center at 500 hPa, increasing PV tendency to the east of the vortex. As a result, the vortex strengthened and moved eastward through the vertically uneven distribution of Q1. In the decaying stage, the horizontally uneven heating of Q1 at 500 hPa weakened the vortex through causing the vortex tubes around the vortex to slant and redistributing the vertical vorticity field.

Buoyancy and Wind-Driven Convection at Mixed Layer Density Fronts

Abstract In this study, the influence of a geostrophically balanced horizontal density gradient on turbulent convection in the ocean is examined using numerical simulations and a theoretical scaling analysis. Starting with uniform horizontal and vertical buoyancy gradients, convection is driven by imposing a heat loss or a destabilizing wind stress at the upper boundary, and a turbulent layer soon develops. For weak lateral fronts, turbulent convection results in a nearly homogeneous mixed layer (ML) whose depth grows in time. For strong fronts, a turbulent layer develops, but this layer is not an ML in the traditional sense because it is characterized by persistent horizontal and vertical gradients in density. The turbulent layer is, however, nearly homogeneous in potential vorticity (PV), with a value near zero. Using the PV budget, a scaling for the depth of the turbulent low PV layer and its time dependence is derived that compares well with numerical simulations. Two dynamical regimes are identified. In a convective layer near the surface, turbulence is generated by the buoyancy loss at the surface; below this layer, turbulence is generated by a symmetric instability of the lateral density gradient. This work extends classical scalings for the depth of turbulent boundary layers to account for the ubiquitous presence of lateral density gradients in the ocean. The new results indicate that a lateral density gradient, in addition to the surface forcing, can affect the stratification and the rate of growth of the surface boundary layer.

Transport and Mixing in the Extratropical Tropopause Region in a High-Vertical-Resolution GCM. Part I: Potential Vorticity and Heat Budget Analysis

Abstract A high-vertical-resolution general circulation model (GCM) output has been analyzed to clarify transport and mixing processes in the extratropical tropopause region. The high-resolution GCM, with a vertical resolution of about 300 m above the extratropical upper troposphere, allows simulation of fine atmospheric structures near the tropopause, such as the extratropical tropopause transition layer (ExTL) and the tropopause inversion layer (TIL). The high-resolution GCM realistically simulates fine thermal and dynamic structures in the extratropical tropopause region. The thickness and maximum stability of the simulated TIL are consistent with observations. The high-resolution output was analyzed using a zonal mean potential vorticity (PV) equation to identify dominant transport processes in the extratropical tropopause region. In the Northern Hemisphere extratropics during winter, mean downward advection sharpens the PV gradient between the tropopause and 20 K below it, whereas latitudinal variation in isentropic mixing sharpens the vertical PV gradient between the tropopause and 10 K above it. During summer, vertical mixing substantially sharpens the vertical PV gradient at 10–25 K above the tropopause. These sharpening effects may be strongly related to the formation mechanisms of strong concentration gradients of chemical tracers around the ExTL. Mechanisms of evolution of the TIL are also discussed by analyzing a thermodynamic equation. Downward heat advection and radiation processes primarily determine the seasonality of the TIL. The analysis results suggest that the locations of the TIL and the ExTL can be similar because of common dynamic processes and interactions between constituent distributions and thermal structure.

Quasi-stationary striations in basin-scale oceanic circulation: vorticity balance from observations and eddy-resolving model

Recently, prominent jet-like features of the ocean circulation, called striations, with a meridional scale of O(300–500 ;km) and extending for thousands of kilometers in length, have been detected in satellite and in situ observations and in high-resolution numerical models. In this paper, we study quasi-stationary striations, which are best seen in the multi-year time-averaged velocity fields. Using 1993–2002 mean dynamic ocean topography, satellite altimeter observations, and output of the Ocean General Circulation Model for the Earth Simulator, the dynamics of the quasi-stationary striations in the eastern parts of the subtropical North and South Pacific are examined by assessing individual terms in the time-averaged equations of relative and potential vorticity. While non-linear effects are found to be essential in the dynamics of the striations, rejecting some linear hypotheses forwarded in the earlier studies, the relevance of the Rhines mechanism is not confirmed. Eddy flux does not act as a relative vorticity source for the striations. Using the potential vorticity (PV) diagnostics, we show that the time-mean PV is not conserved along the time-mean streamlines, and on the scale of the striations these changes in PV are largely induced by the eddy flux of layer thickness. The fact that eddy fluxes contribute to the striations’ time-mean PV budget suggests that the striations are not a kinematical artifact of time-averaging of westward-propagating eddies.