Vorticity Gradient Research Articles

Linear and Nonlinear Dynamics of North Atlantic Oscillations: A New Thinking of Symmetry Breaking

Abstract Observations reveal that the North Atlantic Oscillation (NAO) exhibits a strong asymmetry: large amplitude, long persistence, and westward movement in its negative phase (NAO−) and conversely in its positive phase (NAO+). Further calculations show that blocking days occur frequently over the North Atlantic (Eurasia) after the NAO− (NAO+) peaks, thus indicating that North Atlantic blocking occurs because of the retrogression of the NAO−, whereas blocking occurs over Eurasia because of enhanced downstream energy dispersion of the NAO+. Motivated by a unified nonlinear multiscale interaction (UNMI) model, the authors define dispersion, nonlinearity, and movement indices to describe the basic characteristics of the NAO. On this basis, the physical cause of the strong asymmetry or symmetry breaking of the NAO is examined. It is revealed that the strong asymmetry between the NAO+ and NAO− may be associated with the large difference of the North Atlantic jet in intensity and latitude between both phases. When the NAO+ grows, the North Atlantic jet is intensified and shifts northward and corresponds to reduced nonlinearity and enhanced energy dispersion because of an increased difference between its group velocity and phase speed related to enhanced meridional potential vorticity gradient. Thus, the NAO+ has smaller amplitude, eastward movement, and less persistence. Opposite behavior is seen for the NAO− because of the opposite variation of the North Atlantic jet during its life cycle. Thus, the above results suggest that the NAO+ (NAO−) tends to be a linear (nonlinear) process as a natural consequence of the NAO evolution because of different changes in the North Atlantic jet between both phases.

Submesoscale Turbulence over a Topographic Slope

Regions of the ocean near continental slopes are linked to significant vertical velocities caused by advection over a sloping bottom, frictional processes and diffusion. Oceanic motions at submesoscales are also characterized by enhanced vertical velocities, as compared to mesoscale motions, due to greater contributions from ageostrophic flows. These enhanced vertical velocities can make an important contribution to turbulent fluxes. Sloping topography may also induce large-scale potential vorticity gradients by modifying the slope of interior isopycnal surfaces. Potential vorticity gradients, in turn, may feed back on mesoscale stirring and the generation of submesoscale features. In this study, we explore the impact of sloping topography on the characteristics of submesoscale motions. We conduct high-resolution (1 km × 1 km) simulations of a wind-driven frontal current over an idealized continental shelf and slope. We explore changes in the magnitude, skewness and spectra of surface vorticity and vertical velocity across different configurations of the topographic slope and wind-forcing orientations. All of these properties are strongly modulated by the background topography. Furthermore, submesoscale characteristics exhibit spatial variability across the continental shelf and slope. We find that changes in the statistical properties of submesoscale motions are linked to mesoscale stirring responding to differences in the interior potential vorticity distributions, which are set by frictional processes at the ocean surface and over the sloping bottom. Improved parameterizations of submesoscale motions over topography may be needed to simulate the spatial variability of these features in coarser-resolution models, and are likely to be important to represent vertical nutrient fluxes in coastal waters.

Decadal Relationship between the Stratospheric Arctic Vortex and Pacific Decadal Oscillation

Abstract Using reanalysis datasets and numerical simulations, the relationship between the stratospheric Arctic vortex (SAV) and the Pacific decadal oscillation (PDO) on decadal time scales was investigated. A significant in-phase relationship between the PDO and SAV on decadal time scales during 1950–2014 is found, that is, the North Pacific sea surface temperature (SST) cooling (warming) associated with the positive (negative) PDO phases is closely related to the strengthening (weakening) of the SAV. This decadal relationship between the North Pacific SST and SAV is different from their relationship on subdecadal time scales. Observational and modeling results both demonstrate that the decadal variation in the SAV is strongly affected by the North Pacific SSTs related to the PDO via modifying the upward propagation of planetary wavenumber-1 waves from the troposphere to the stratosphere. The decreased SSTs over the North Pacific tend to result in a deepened Aleutian low along with a strengthened jet stream over the North Pacific, which excites a weakened western Pacific pattern and a strengthened Pacific–North American pattern. These tropospheric circulation anomalies are in accordance with the decreased refractive index (RI) at middle and high latitudes in the northern stratosphere during the positive PDO phase. The increased RI at high latitudes in the upper troposphere impedes the planetary wavenumber-1 wave from propagating into the stratosphere, and in turn strengthens the SAV. The responses of the RI to the PDO are mainly contributions of the changes in the meridional gradient of the zonal-mean potential vorticity via alteration of the baroclinic term .

Drag reduction and thrust generation by tangential surface motion in flow past a cylinder

Sensitivity of drag to tangential surface motion is calculated in flow past a circular cylinder in both two- and three-dimensional conditions at Reynolds number \(\textit{Re} \le 1000\). The magnitude of the sensitivity maximises in the region slightly upstream of the separation points where the contour lines of spanwise vorticity are normal to the cylinder surface. A control to reduce drag can be obtained by (negatively) scaling the sensitivity. The high correlation of sensitivities of controlled and uncontrolled flow indicates that the scaled sensitivity is a good approximation of the nonlinear optimal control. It is validated through direct numerical simulations that the linear range of the steady control is much higher than the unsteady control, which synchronises the vortex shedding and induces lock-in effects. The steady control injects angular momentum into the separating boundary layer, stabilises the flow and increases the base pressure significantly. At \(\textit{Re}=100\), when the maximum tangential motion reaches 50% of the free-stream velocity, the vortex shedding, boundary-layer separation and recirculation bubbles are eliminated and 32% of the drag is reduced. When the maximum tangential motion reaches 2.5 times of the free-stream velocity, thrust is generated and the power savings ratio, defined as the ratio of the reduced drag power to the control input power, reaches 19.6. The mechanism of drag reduction is attributed to the change of the radial gradient of spanwise vorticity (\(\partial _{r} \hat{\zeta }\)) and the subsequent accelerated pressure recovery from the uncontrolled separation points to the rear stagnation point.

Effect of the slip length on the flow over a hydrophobic circular cylinder

The laminar flow (Reynolds number ranging from 60 to 180) past a hydrophobic circular cylinder is conducted by the time-dependent simulation with focus on the effect of dimensionless slip length, LS (ranging from 0.01 to 0.25), on total, viscous and pressure drag coefficients. It is found that the viscous drag plays a major role in drag reduction, for low Reynolds (Re < 100) and small slip length (LS < 0.02). When the Reynolds number and slip length are large enough, the decrease of total drag mainly depends on the pressure drag. The pressure drag coefficient increases with the Reynolds number when LS ranges from 0 to 0.02. For LS of 0.05, however, it has a different trend. Due to small proportion of viscous drag to total drag coefficient, the effect of viscous drag on the total drag is less important. The adverse pressure gradient appears on the circular cylinder and increases with the slip length. The pressure distribution is mainly affected by the vorticity gradient, fluid convection and the stability. Meanwhile, as Reynolds number equals to 100, the separation point moves downstream. This results in the increase of vortex shedding frequency and the decrease of vortex intensity at LS ranging from 0 to 0.11. As slip length increases to 0.25, the flow is stable. These results can provide useful information on the drag reduction control of the cylinder surface.

Can Large Oceanic Vortices Be Stable?

AbstractObservations show that radii of oceanic eddies often exceed the Rossby radius of deformation, whereas theoretical studies suggest that such vortices should be unstable. The present paper resolves this paradox by presenting a wide class of large geostrophic vortices with a sign‐definite gradient of potential vorticity (which makes them stable), in an ocean where the density gradient is mostly confined to a thin near‐surface layer (which is indeed the case in the real ocean). The condition of a thin “active” layer is what makes the present work different from the previous theoretical studies and is of utmost importance. It turns out that without it, the joint requirement that a vortex be large and have a sign‐definite potential vorticity gradient trivializes the problem by eliminating all vortices except nearly barotropic ones.

Effect of boreal spring precipitation anomaly pattern change in the late 1990s over tropical Pacific on the atmospheric teleconnection

Observational evidence showed that the leading mode of precipitation variability over the tropical Pacific during boreal spring experienced a pronounced interdecadal change around the late 1990s, characterized by a precipitation pattern shift from an eastern Pacific (EP) type to a central Pacific (CP) type. The distinct impacts of such a precipitation pattern shift on the extratropical atmospheric teleconnection were examined. An apparent poleward teleconnection extending from the tropics to the North Atlantic region was observed after 1998, while, there was no significant teleconnection before 1998. To understand why only the CP–type precipitation mode is associated with a striking atmospheric teleconnection after 1998, diagnostic analyses with the Eliassen–Palm flux and Rossby wave source (RWS) based on the barotropic vorticity equation were performed. The results show that for the EP–type precipitation mode, no significant RWS anomalies appeared over the subtropical Pacific due to the opposite effect of the vortex stretching and absolute vorticity advection processes. For the CP–type precipitation mode, however, there are both significant vorticity forcing source over the subtropical CP and clear poleward–propagation of Rossby wave. The spatial distribution of the CP–type precipitation pattern tends to excite a conspicuous anomalous southerly and a well–organized negative vorticity center over the subtropical CP where both the mean absolute vorticity gradient and mean divergence flow are large, hence, the interaction between the heating–induced anomalous circulation and the basic state made the generation of Rossby waves conceivable and effective. Such corresponding teleconnection responses to the prescribed heating were also examined by using a Linear Baroclinic Model (LBM). It turned out that significant poleward teleconnection pattern is only caused by the CP–type precipitation mode, rather than by the EP–type precipitation mode. Further sensitive experiments demonstrated that the change in spring basic state before and after 1998 played a relatively minor role in exciting such a teleconnection pattern, when compared with the tropical precipitation anomaly pattern change.

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 Emergence of Shallow Easterly Jets within QBO Westerlies

A configuration of an idealized general circulation model has been obtained in which a deep, stratospheric, equatorial, westerly jet is established that is spontaneously and quasi-periodically disrupted by shallow easterly jets. Similar to the disruption of the quasi-biennial oscillation (QBO) observed in early 2016, meridional fluxes of wave activity are found to play a central role. The possible relevance of two feedback mechanisms to these disruptions is considered. The first involves the secondary circulation produced in the shear zones on the upper and lower flanks of the easterly jet. This is found to play a role in maintaining the aspect ratio of the emerging easterly jet. The second involves the organization of the eddy fluxes by the mean flow: the presence of a weak easterly anomaly within a tall, tropical, westerly jet is demonstrated to produce enhanced and highly focused wave activity fluxes that reinforce and strengthen the easterly anomalies. The eddies appear to be organized by the formation of strong potential vorticity gradients on the subtropical flanks of the easterly anomaly. Similar wave activity and potential vorticity structures are found in the ERA-Interim for the observed QBO disruption, indicating this second feedback was active then.

Frontal dynamics at the edge of the Columbia River plume

In the tidal ebb-cycle at the Mouth of the Columbia River, strong density and velocity fronts sometimes form perpendicular to the coast at the edges of the freshwater plume. They are distinct from previously analyzed fronts at the offshore western edge of the plume that evolve as a gravity-wave bore. We present simulation results to demonstrate their occurrence and investigate the mechanisms behind their frontogenesis and evolution. Tidal velocities on average ranged between 1.5 m s−1 in flood and 2.5 m s−1 in ebb during the brief hindcast period. The tidal fronts exhibit strong horizontal velocity and buoyancy gradients on a scale ∼ 100 m in width with normalized relative vorticity (ζz/f) values reaching up to 50. We specifically focus on the front on the northern edge of the plume and examine the evolution in plume characteristics such as its water mass gradients, horizontal and vertical velocity structure, vertical velocity, turbulent vertical mixing, horizontal propagation, cross-front momentum balance, and Lagrangian frontogenetic tendencies in both buoyancy and velocity gradients. Advective frontogenesis leads to a very sharp front where lateral mixing near the grid-resolution limit arrests its further contraction. The negative vorticity within the front is initiated by the positive bottom drag curl on the north side of the Columbia estuary and against the north jetty. Because of the large negative vorticity and horizontal vorticity gradient, centrifugal and lateral shear instability begins to develop along the front, but frontal fragmentation and decay set in only after the turn of the tide because of the briefness of the ebb interval.

Atmospheric Dynamic and Thermodynamic Processes Driving the Western North Pacific Anomalous Anticyclone during El Niño. Part II: Formation Processes

In Part I, the authors showed that northerly anomalies associated with the Rossby wave response to El Niño heating anomalies in the equatorial central Pacific lead to the southward advection of low moist enthalpy air forming the western North Pacific anomalous anticyclone (WNPAC). Why does such a remote forcing not cause the formation of the anomalous anticyclone in El Niño–developing summer? The physical mechanism responsible for the timing of the WNPAC formation is investigated in Part II. Through both an observational analysis and idealized numerical model experiments, the authors find that the onset timing of the WNPAC relies on the following three factors. The first is a sign change (from positive to negative) of the meridional gradient of background low-level specific humidity over the key tropical western North Pacific (WNP) region in November. The second is a sign change (from positive to negative) of the meridional gradient of background relative vorticity, which efficiently reduces the westward stretch of the Rossby wave gyre anomalies west of the equatorial heating through equivalent beta effect. As a result, the northern branch of the twin cyclonic anomalies induced by El Niño heating withdraws eastward, leaving space for the onset of the WNPAC. The third factor is attributed to local sea surface temperature anomaly (SSTA) forcing. Pacemaker experiments with a coupled global model indicate that cold SSTAs in the tropical WNP play an important role in starting the anomalous anticyclone over the WNP in late fall. In the absence of the local cold SSTA forcing, the formation of the WNPAC would be delayed to El Niño mature winter.

Submesoscale Coherent Structures on the Continental Shelf

AbstractDiscovery and analysis of submesoscale variability O(0.3–30) km on the continental shelf is made possible by a high-resolution (Δx = 75 m) Regional Oceanic Modeling System (ROMS) simulation of the Southern California Bight (SCB). This variability is manifest in ubiquitous yet ephemeral coherent structures: fronts, filaments, and vortices. Similar to their open-ocean counterparts, fronts and filaments on the shelf are identified by their strong vertical velocity, surface convergence, cyclonic vorticity, and horizontal density gradient. Life cycles of these features typically last 3–5 days, with the formation dominated by a horizontal advective tendency that increases density and velocity gradients (i.e., frontogenesis). The shape of the coastline and depth of the water column both influence the abundance and spatial orientation of shallow-water fronts and filaments. Closer to shore, fronts and filaments often align themselves parallel to isobaths, and headlands often act as sites of intense vorticity generation through bottom stress. A quasi-steady, approximate momentum balance among rotation, pressure gradient, and vertical mixing—known as turbulent thermal wind (TTW)—often is valid in the strong secondary circulations local to fronts and filaments. However, front and filament circulations subject to strong diurnal variation in surface heating and vertical mixing are inconsistent with steady-state TTW balance. The secondary circulations can induce ephemeral material trapping and substantial vertical heat fluxes on the shelf.

Simulations of eddy kinetic energy transport in barotropic turbulence

Spatially localized stochastic forcing generates turbulent dynamics in a 2D fluid with a uniform background vorticity gradient, enabling a study of the turbulent transport of kinetic energy.

Equatorward dispersion of a high-latitude volcanic plume and its relation to the Asian summer monsoon: a case study of the Sarychev eruption in 2009

Abstract. Tropical volcanic eruptions have been widely studied for their significant contribution to stratospheric aerosol loading and global climate impacts, but the impact of high-latitude volcanic eruptions on the stratospheric aerosol layer is not clear and the pathway of transporting aerosol from high latitudes to the tropical stratosphere is not well understood. In this work, we focus on the high-latitude volcano Sarychev (48.1° N, 153.2° E), which erupted in June 2009, and the influence of the Asian summer monsoon (ASM) on the equatorward dispersion of the volcanic plume. First, the sulfur dioxide (SO2) emission time series and plume height of the Sarychev eruption are estimated with SO2 observations of the Atmospheric Infrared Sounder (AIRS) and a backward trajectory approach using the Lagrangian particle dispersion model Massive–Parallel Trajectory Calculations (MPTRAC). Then, the transport and dispersion of the plume are simulated using the derived SO2 emission time series. The transport simulations are compared with SO2 observations from AIRS and validated with aerosol observations from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). The MPTRAC simulations show that about 4 % of the sulfur emissions were transported to the tropical stratosphere within 50 days after the beginning of the eruption, and the plume dispersed towards the tropical tropopause layer (TTL) through isentropic transport above the subtropical jet. The MPTRAC simulations and MIPAS aerosol data both show that between the potential temperature levels of 360 and 400 K, the equatorward transport was primarily driven by anticyclonic Rossby wave breaking enhanced by the ASM in boreal summer. The volcanic plume was entrained along the anticyclone flows and reached the TTL as it was transported southwestwards into the deep tropics downstream of the anticyclone. Further, the ASM anticyclone influenced the pathway of aerosols by isolating an aerosol hole inside of the ASM, which was surrounded by aerosol-rich air outside. This transport barrier was best indicated using the potential vorticity gradient approach. Long-term MIPAS aerosol detections show that after entering the TTL, aerosol from the Sarychev eruption remained in the tropical stratosphere for about 10 months and ascended slowly. The ascent speed agreed well with the ascent speed of the water vapor tape recorder. Furthermore, a hypothetical MPTRAC simulation for a wintertime eruption was carried out. It is shown that under winter atmospheric circulations, the equatorward transport of the plume would be suppressed by the strong subtropical jet and weak wave breaking events. In this hypothetical scenario, a high-latitude volcanic eruption would not be able to contribute to the tropical stratospheric aerosol layer.

Lattice Boltzmann model capable of mesoscopic vorticity computation.

It is well known that standard lattice Boltzmann (LB) models allow the strain-rate components to be computed mesoscopically (i.e., through the local particle distributions) and as such possess a second-order accuracy in strain rate. This is one of the appealing features of the lattice Boltzmann method (LBM) which is of only second-order accuracy in hydrodynamic velocity itself. However, no known LB model can provide the same quality for vorticity and pressure gradients. In this paper, we design a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice. A detailed Chapman-Enskog analysis is presented to illustrate all the necessary constraints in reproducing the isothermal Navier-Stokes equations. The remaining degrees of freedom are carefully analyzed to derive a model that accommodates mesoscopic computation of all the velocity and pressure gradients from the nonequilibrium moments. This way of vorticity calculation naturally ensures a second-order accuracy, which is also proven through an asymptotic analysis. We thus show, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM. The resulting model is then validated in simulations of a three-dimensional decaying Taylor-Green flow, a lid-driven cavity flow, and a uniform flow passing a fixed sphere. Furthermore, it is shown that the mesoscopic vorticity computation can be realized even with single relaxation parameter.

Simulated sensitivity of tropical cyclone track to the moisture in an idealized monsoon gyre

In this study, the sensitivity of tropical cyclone (TC) track to the moisture condition in a nearby monsoon gyre (MG) is investigated. Numerical simulations reveal that TC track is highly sensitive to the spatial distribution of relative humidity (RH). In an experiment conducted with higher (lower) RH in the eastern (western) semicircle of an MG, the TC experiences a sharp northward turning. In contrast, when the RH pattern is reversed, the simulated TC does not show a sharp northward turning. The RH distribution modulates the intensity and structure of both the TC and MG, so that when the TC is initially embedded in a moister environment, convection is enhanced in the outer core, which favors an expansion of the outer core size. A TC with a larger outer size has greater beta-effect propagation, favoring a faster westward translational speed. Meanwhile, higher RH enhances the vorticity gradient within the MG and promotes a quicker attraction between the TC and MG centers through vorticity segregation process. These cumulative effects cause the TC to collocate with the MG center. Once the coalescence process takes place, the energy dispersion associated with the TC and MG is enhanced, which rapidly strengthens southwesterly flows on the eastern flanks. The resulting steering flow leads the TC to take a sharp northward track.

Lower-Tropospheric Eddy Momentum Fluxes in Idealized Models and Reanalysis Data

Abstract In Earth’s atmosphere eddy momentum fluxes (EMFs) are largest in the upper troposphere, but EMFs in the lower troposphere, although modest in amplitude, have an intriguing structure. To document this structure, the EMFs in the lower tropospheres of a two-layer quasigeostrophic model, a primitive equation model, and the Southern Hemisphere of a reanalysis dataset are investigated. The lower-tropospheric EMFs are very similar in the cores of the jets in both models and the reanalysis data, with EMF divergence (opposing the upper-tropospheric convergence) due to relatively long waves with slow eastward phase speeds and EMF divergence (as in the upper troposphere) due to shorter waves with faster eastward phase speeds. As the two-layer model is able to capture the EMF divergence by long waves, a qualitative picture of the underlying dynamics is proposed that relies on the negative potential vorticity gradient in the lower layer of the model. Eddies excited by baroclinic instability mix efficiently through a wide region in the lower layer, centered on the latitude of maximum westerlies and encompassing the lower-layer critical latitudes. Near these critical latitudes, the mixing is enhanced, resulting in increased EMF convergence, with compensating EMF divergence in the center of the jet. The EMF convergence at faster phase speeds is due to deep eddies that propagate on the upper-tropospheric potential vorticity gradient.

A climatology of Rossby wave generation in the middle atmosphere of the Southern Hemisphere from MERRA reanalysis

AbstractA climatological characterization of Rossby wave generation events in the middle atmosphere of the Southern Hemisphere is conducted using 20 years of Modern‐Era Retrospective Analysis for Research and Applications (MERRA) reanalysis. An automatic detection technique of wave generation events is developed and applied to MERRA reanalysis. The Rossby wave generation events with wave period of 1.25 to 5.5 days and zonal wave number from one to three dominate the Eliassen‐Palm flux divergence around the stratopause at high latitudes in the examined 20 year period. These produce an eastward forcing of the general circulation between May and mid‐August in that region. Afterward from mid‐August to the final warming date, Rossby wave generation events are still present but the Eliassen‐Palm flux divergence in the polar stratopause is dominated by low‐frequency Rossby waves that propagate from the troposphere. The Rossby wave generation events are associated with potential vorticity gradient inversion, and so they are a manifestation of the dominant barotropic/baroclinic unstable modes that grow at the cost of smearing the negative meridional gradient of potential vorticity. The most likely region of wave generation is found between 60° and 80°S and at a height of 0.7 hPa, but events were detected from 40 hPa to 0.3 hPa (which is the top of the examined region). The mean number of events per year is 24, and its mean duration is 3.35 days. The event duration follows an exponential distribution.

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.