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The poleward expansion of the Hadley cells is one of the most robust modeled responses to increasing greenhouse gas concentrations. There are many proposed mechanisms for expansion, and most are consistent with modeled changes in thermodynamics, dynamics, and clouds. The adjustment of the eddies and the mean flow to greenhouse gas forcings, and to one another, complicates any effort toward a deeper understanding. Here we modify the Gray Radiation and Moist Aquaplanet (GRANDMA) model to uncouple the eddy and mean flow responses to forcings. When eddy forcings are held constant, the purely axisymmetric response of the Hadley cell to a greenhouse gas–like forcing is an intensification and poleward tilting of the cell with height in response to an axisymmetric increase in angular momentum in the subtropics. The angular momentum increase drastically alters the circulation response compared to axisymmetric theories, which by nature neglect this adjustment. Model simulations and an eddy diffusivity framework demonstrate that the axisymmetric increase in subtropical angular momentum—the direct manifestation of the radiative–convective equilibrium temperature response—drives a poleward shift of the eddy stresses which leads to Hadley cell expansion. Prescribing the eddy response to the greenhouse gas–like forcing shows that eddies damp, rather than drive, changes in angular momentum, moist static energy transport, and momentum transport. Expansion is not driven by changes in baroclinic instability, as would otherwise be diagnosed from the fully coupled simulation. These modeling results caution any assessment of mechanisms for circulation change within the fully coupled wave–mean flow system.

The global superrotation index S compares the integrated axial angular momentum of the atmosphere to that of a state of solid-body corotation with the underlying planet. The index S is similar to a zonal Rossby number, which suggests it may be a useful indicator of the circulation regime occupied by a planetary atmosphere. We investigate the utility of S for characterizing regimes of atmospheric circulation by running idealized Earthlike general circulation model experiments over a wide range of rotation rates Ω, 8ΩE to ΩE/512, where ΩE is Earth’s rotation rate, in both an axisymmetric and three-dimensional configuration. We compute S for each simulated circulation, and study the dependence of S on Ω. For all rotation rates considered, S is on the same order of magnitude in the 3D and axisymmetric experiments. For high rotation rates, S ≪ 1 and S ∝ Ω−2, while at low rotation rates S ≈ 1/2 = constant. By considering the limiting behavior of theoretical models for S, we show how the value of S and its local dependence on Ω can be related to the circulation regime occupied by a planetary atmosphere. Indices of S ≪ 1 and S ∝ Ω−2 define a regime dominated by geostrophic thermal wind balance, and S ≈ 1/2 = constant defines a regime where the dynamics are characterized by conservation of angular momentum within a planetary-scale Hadley circulation. Indices of S ≫ 1 and S ∝ Ω−2 define an additional regime dominated by cyclostrophic balance and strong equatorial superrotation that is not realized in our simulations.

The quasi-biennial oscillation (QBO) is a descending pattern of winds in the stratosphere that vanishes near the top of the tropical tropopause layer, even though the vertically propagating waves that drive the QBO are thought to originate in the troposphere several kilometers below. The region where there is low QBO power despite sufficient vertically propagating wave activity to drive a QBO is known as the buffer zone. Classical one-dimensional models of the QBO are ill suited to represent buffer zone dynamics because they enforce the attenuation of the QBO via a zero-wind lower boundary condition. The formation of the buffer zone is investigated by analyzing momentum budgets in the reanalyses MERRA-2 and ERA-Interim. The buffer zone must be formed by weak wave-driven acceleration and/or cancellation of the wave-driven acceleration. This paper shows that in MERRA-2 weak wave-driven acceleration is insufficient to form the buffer zone, so cancellation of the wave-driven acceleration must play a role. The cancellation results from damping of angular momentum anomalies, primarily due to horizontal mean and horizontal eddy momentum flux divergence, with secondary contributions from the Coriolis torque and vertical mean momentum flux divergence. The importance of the damping terms highlights the role of the buffer zone as the mediator of angular momentum exchange between the QBO domain and the far field. Some far-field angular momentum anomalies reach the solid Earth, leading to the well-documented lagged correlation between the QBO and the length of day.

This paper investigates the coupling between the rotational and divergent circulations aiming to explain the observations that show that the tropical eddy momentum flux is due to correlations between divergent eddy meridional velocities and rotational eddy zonal velocities. A simple linear model in which the observed eddy divergence field is used to force the vorticity equation can reproduce quite well the observed tropical eddy momentum flux. The eddy momentum flux in the model shows little sensitivity to the basic-state winds and is mainly determined by the characteristics of the divergent forcing. Vortex stretching and divergent advection of planetary vorticity produce eddy momentum flux contributions with the same sign but the former forcing dominates. It is shown that the main factor affecting the direction of the eddy momentum flux response to both forcings is the meridional tilt of the divergence phase lines, albeit with an opposite sign to the classical relation between rotational momentum flux and streamfunction phase tilt. How this divergent structure is determined remains an open question.

Multiscale asymptotic methods are used to derive wave activity equations for planetary- and synoptic-scale eddies and their interactions with a zonal mean flow. The eddies are assumed to be of small amplitude, and the synoptic-scale zonal and meridional length scales are taken to be equal. Under these assumptions, the zonal-mean and planetary-scale dynamics are planetary geostrophic (i.e., dominated by vortex stretching), and the interaction between planetary- and synoptic-scale eddies occurs only through the zonal mean flow or through diabatic processes. Planetary-scale heat fluxes are shown to enter the angular momentum budget through meridional mass redistribution. After averaging over synoptic length and time scales, momentum fluxes disappear from the synoptic-scale wave activity equation while synoptic-scale heat fluxes disappear from the baroclinicity equation, leaving planetary-scale heat fluxes as the only adiabatic term coupling the baroclinic and barotropic components of the zonal mean flow. In the special case of weak planetary waves, the decoupling between the baroclinic and barotropic parts of the flow is complete with momentum fluxes driving the barotropic zonal mean flow, heat fluxes driving the wave activity, and diabatic processes driving baroclinicity. These results help explain the apparent decoupling between the baroclinic and barotropic components of flow variability recently identified in observations and may provide a means of better understanding the link between thermodynamic and dynamic aspects of climate variability and change.

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., Nicholas Lutsko was supported by NSF Grant DGE 1148900 and Pablo Zurita-Gotor thanks the Cooperative Institute for Climate Science at Princeton University for support during summer 2016.

A diagnostic framework to investigate the role of processes around and during tropical cyclogenesis is presented. The key framework metric is the ratio of bulk differences of moist entropy over differences of angular momentum between an inner and outer region of a tropical disturbance or cyclone. This ratio is hypothesized to decrease and become negative as both the high-entropy core and low-level vortex in the inner region amplify during tropical cyclogenesis. The time tendency of this ratio can be split into two forcings: a moist entropy forcing and an angular momentum forcing. Each forcing can be further divided into components comprising differences in net advective fluxes and nonadvective boundary fluxes of moist entropy or angular momentum between each region. The framework provides a comprehensive way to compare the relative importance of processes leading to tropical cyclogenesis in a tractable, consistent manner. Suggestions on how to apply the framework to numerical model output are given.

An ensemble of axisymmetric model experiments with simplified physics is used to evaluate the diagnostic framework presented in Part I. The central piece of the framework is understanding what causes decreases in the ratio of bulk differences of moist entropy over differences of angular momentum between two defined regions, the boundary between the two demarcating the approximate location of the emergence of the radius of maximum wind of the developing meso-beta-scale protovortex. Within a day before tropical cyclogenesis, the moist entropy forcing results in a decrease of this ratio. Net advective fluxes act to export moist entropy from the outer region and import moist entropy into the inner region, resulting in a positive radial gradient in gross moist stability that is maximized around the time of genesis. While surface moist entropy fluxes are needed for genesis to occur, they act synergistically with the net advective fluxes to decrease the ratio before and during genesis. Within a day after tropical cyclogenesis, surface moist entropy fluxes directly amplify the positive difference in moist entropy between the inner and outer regions, and radial fluxes of angular momentum reduce the magnitude of the negative difference in angular momentum between the inner and outer regions. Both of these processes act to reduce the ratio further. The framework highlights differences in processes occurring before, during, and after genesis as the meso-beta-scale protovortex develops and intensifies.

The secondary eyewall formation (SEF) in an idealized simulation of a tropical cyclone (TC) is examined from the perspective of both the balanced and unbalanced dynamics and through the tangential wind (Vt) budget analysis. It is found that the expansion of the azimuthal-mean Vt above the boundary layer occurs prior to the development of radial moisture convergence in the boundary layer. The Vt expansion results primarily from the inward angular momentum transport by the mid- to lower-tropospheric inflow induced by both convective and stratiform heating in the spiral rainbands. In response to the Vt broadening is the development of radial inflow convergence and the supergradient flow near the top of the inflow boundary layer. Results from the Vt budget analysis show that the combined effect of the mean advection and the surface friction is to spin down Vt in the boundary layer, while the eddy processes (eddy radial and vertical advection) contribute positively to the spinup of Vt in the SEF region in the boundary layer. Therefore, eddies play an important role in the spinup of Vt in the boundary layer during SEF. The balanced Sawyer–Eliassen solution can well capture the secondary circulation in the full-physics model simulation. The radial inflow diagnosed from the Sawyer–Eliassen equation is shown to spin up Vt and maintain the vortex above the boundary layer. However, the axisymmetric balanced dynamics cannot explain the spinup of Vt in the boundary layer, which results mainly from the eddy processes.

The dynamics of modulated point vortex pairs is investigated on a rotating sphere, where modulation is chosen to reflect the conservation of angular momentum (potential vorticity). In this setting the authors point out a qualitative difference between the full spherical dynamics and the one obtained in a β-plane approximation. In particular, dipole trajectories starting at the same location evolve to completely different directions under these two treatments, despite the fact that the deviations from the initial latitude remain small. This is a strong indication for the mathematical inconsistency of the traditional β-plane approximation. At the same time, a consistently linearized set of equations of motion leads to trajectories agreeing with those obtained under the full spherical treatment. The β-plane advection patterns due to chaotic advection in the velocity field of finite-sized vortex pairs are also found to considerably deviate from those of the full spherical treatment, and quantities characterizing transport properties (e.g., the escape rate from a given region) strongly differ.

The motion of a mass undergoing free horizontal motion on a planet’s surface is analyzed in an inertial frame by using a potential well presentation. The following results from the conventional analysis in rotating coordinates are also found in inertial coordinates. Under typical circumstances the mass oscillates about the latitude where its angular momentum per unit mass matches that of the planet’s surface. For masses with nonzero angular momentum, conservation of angular momentum bounds the mass away from the pole. Motion with zero angular momentum is confined to a fixed meridian plane on which the mass may oscillate across the pole. Motion across the equator is possible only for masses with sufficient energy. Masses with angular momentum per unit mass greater than that of the planet at the equator oscillate about the equator with a limiting period determined by the excess angular momentum.

This paper reports a comprehensive diagnostic analysis of mass and angular momentum (AM) circulations and their budgets in boreal winter using the 32-yr daily NCEP–Department of Energy (DOE) reanalysis (1979–2010). The diagnosis is performed using instantaneous total flows before taking time and zonal average without decomposition of time mean and transient flows and separation of zonal mean and wavy flows. The analysis reveals that embedded in a broad hemispheric thermally direct meridional mass circulation in each hemisphere are three distinct but interconnected thermally direct meridional cells. They are the tropical Hadley cell, the stratospheric cell, and the extratropical zonally asymmetric Hadley cell. The tropical Hadley cell corresponds to the Hadley cell of the classic three-cell model whereas the extratropical Hadley cell and the stratospheric cell correspond to the eddy-driven extratropical residual circulation. The joint consideration of meridional mass and AM circulations helps to substantiate Hadley’s original view that the hemispheric-wide thermally direct meridional circulation can have broad surface easterly in the tropics and westerly in the extratropics. Because the mass circulation cannot have a net divergence anywhere in long time mean and the earth’s AM decreases toward the poles, the companion AM transport in the equatorward cold air branch inevitably has to be divergent. The downward transfer of westerly AM to the cold air branch by the pressure torque associated with westward tilted baroclinic waves dominates such divergence in the extratropics, explaining the prevailing surface westerly there. In the tropics and polar region where the meridional circulation is nearly zonally symmetric, the dominance of this divergence results in a surface easterly there.

The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments. From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process. From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.

The mean meridional circulation of the atmosphere is presented using the mass (more specifically, the pressure corresponding to the mass) above the isentrope of interest as the vertical coordinate. In this vertical coordinate, the mass-weighted mean circulation is exactly balanced by entropy sources and sinks with no eddy flux contribution as in the isentropic coordinate, and the coordinate can be readily generalized to the mass above moist isentropes or other quasi-conservative tracers by construction. The corresponding Eliassen–Palm (EP) flux divergence for the zonal-mean angular momentum is formulated in a hybrid isobaric–isentropic form, extending the conventional transformed Eulerian-mean (TEM) formulation to finite-amplitude nongeostrophic eddies on the sphere. In the small-amplitude limit, the hybrid isobaric–isentropic formulation reduces to the TEM formulation. Applying to the NCEP–U.S. Department of Energy (DOE) Reanalysis 2, the new formulation resolves the deficiency of the conventional TEM formulation for the near-surface flow, where the isentropic surface intersects the ground, and the mean circulation agrees well with the TEM above the near-surface layer. In the small-amplitude limit, this improvement near the surface can be partially attributed to the isentropic static stability over the isobaric counterpart, as the mass density in the near-surface isentropic layers gradually approaches zero. Also, the mean mass streamfunction can be approximately obtained from the EP flux divergence except for the deep tropics or the near-surface flow, highlighting the dominant control of potential vorticity mixing for the subtropics-to-pole mean circulations. It is then expected to provide a valuable diagnostic framework not only for global circulation theory, but also for atmospheric transport in the troposphere.

In this study the authors analyze and interpret the effects of parameterized diffusion on the nearly steady axisymmetric numerical simulations of hurricanes presented in a recent study. In that study it was concluded that horizontal diffusion was the most important control factor for the maximum simulated hurricane intensity. Through budget analysis it is shown here that horizontal diffusion is a major contributor to the angular momentum budget in the boundary layer of the numerically simulated storms. Moreover, a new scale analysis recognizing the anisotropic nature of the parameterized model diffusion shows why the horizontal diffusion plays such a dominant role. A simple analytical model is developed that captures the essence of the effect. The role of vertical diffusion in the boundary layer in the aforementioned numerical simulations is more closely examined here. It is shown that the boundary layer in these simulations is consistent with known analytical solutions in that boundary layer depth increases and the amount of “overshoot” (maximum wind in excess of the gradient wind) decreases with increasing vertical diffusion. However, the maximum wind itself depends mainly on horizontal diffusion and is relatively insensitive to vertical diffusion; the overshoot variation with vertical viscosity mainly comes from changes in the gradient wind with vertical viscosity. The present considerations of parameterized diffusion allow a new contribution to the dialog in the literature on the meaning and interpretation of the Emanuel potential intensity theory.

Tropical cyclones intensify and are maintained by surface enthalpy fluxes that result from the thermodynamics disequilibrium that exists between the tropical oceans and atmosphere. While this general result has been known for at least a half century, the detailed nature of feedbacks between thermodynamic and dynamic processes in tropical cyclones remains poorly understood. In particular, the spatial relationship between surface fluxes and the radial entropy distribution apparently does not act to amplify the entropy gradient and therefore the surface winds. In previous work, this problem was addressed by accounting for the radial distribution of convective fluxes of entropy out of the boundary layer; this led to the conclusion that a radial gradient of such convective fluxes is necessary for intensification. Part I showed that the assumption of constant outflow temperature is incorrect and argued that the thermal stratification of the outflow is set by small-scale turbulence that limits the Richardson number. The assumption of Richardson number criticality of the outflow allows one to derive an equation for the variation of outflow temperature with angular momentum; this in turn leads to predictions of vortex structure and intensity that agree well with tropical cyclones simulated using a full-physics axisymmetric model. Here it is shown that the variation of outflow temperature with angular momentum also permits the vortex to intensify with time even in the absence of radial gradients of entrainment into the boundary layer. An equation is derived for the rate of intensity change and compared to simple models and to simulations using a full-physics model.

Extant theoretical work on the steady-state structure and intensity of idealized axisymmetric tropical cyclones relies on the assumption that isentropic surfaces in the storm outflow match those of the unperturbed environment at large distances from the storm’s core. These isentropic surfaces generally lie just above the tropopause, where the vertical temperature structure is approximately isothermal, so it has been assumed that the absolute temperature of the outflow is nearly constant. Here it is shown that this assumption is not justified, at least when applied to storms simulated by a convection-resolving axisymmetric numerical model in which much of the outflow occurs below the ambient tropopause and develops its own stratification, unrelated to that of the unperturbed environment. The authors propose that this stratification is set in the storm’s core by the requirement that the Richardson number remain near its critical value for the onset of small-scale turbulence. This ansatz is tested by calculating the Richardson number in numerically simulated storms, and then showing that the assumption of constant Richardson number determines the variation of the outflow temperature with angular momentum or entropy and thereby sets the low-level radial structure of the storm outside its radius of maximum surface winds. Part II will show that allowing the outflow temperature to vary also allows one to discard an empirical factor that was introduced in previous work on the intensification of tropical cyclones.

Solutions of an axially symmetric inviscid shallow-water model (SWM) on the earth forced by equinoctial differential heating are constructedusing numerical integration of the time-dependent equationsand analysis of their steady states. The study also maps the physical initial conditions and parameter values for which the solutions approach steady states at long times, demonstrating strong dependence of the SWM on initial conditions. The model admits states of uniform angular momentum, including superrotation, in the tropics and radiative equilibrium at high latitudes. The asymptotic properties of the subtropical jets and tropical fluxes are explicitly calculated and it is shown that all solutions of the previously studied nearly inviscid theories are particular solutions of the present theory. The model’s results relate the location and intensity of the subtropical jet in the steady states to properties of the SWM on a sphere, such as the conservation of angular momentum. The exact form of the differential heating is secondary in determining these properties and its main role is to transform any initial state to the vicinity of the steady states. When mass is assumed to be supplied to the fluid from an underlying motionless layer (this model is termed the 1Ω-SWM), the angular momentum in the tropics is not uniform (so the local Rossby number is smaller than 1),theheightofthetropopauseisnearlyuniformthere,thesteadystates donotdependon theinitialconditions, and the zonal velocity vanishes on the equator. Accurate and simple estimates that are determined only by the value of a thermal Rossby number are derived in this case for the location and intensity of the subtropical jet.

Previous studies have suggested that gravity waves can transport a significantly large amount of angular momentum away from tropical cyclones, as much as 10% of the core angular momentum per hour. These previous studies used the shallow-water equations to model gravity waves radiating outward from rapidly rotating inner-core asymmetries. This issue is reinvestigated with a three-dimensional, nonhydrostatic, linear model of the vortex-anelastic equations. The response of balanced, axisymmetric vortices modeled after tropical cyclones to rotating asymmetric heat sources is examined to assess angular momentum transport by gravity waves radiating away from the core region of the vortices. Calculations show that gravity waves do transport angular momentum away from the vortex core; however, the amount transported is several orders of magnitude smaller than recent estimates.

Several studies have shown that the intensity of numerically simulated tropical cyclones can exceed (by 50%) a theoretical upper limit. To investigate the cause, this study evaluates the underlying components of Emanuel’s commonly cited analytic theory for potential intensity (herein referred to as E-PI). A review of the derivation of E-PI highlights three primary components: a dynamical component (gradient-wind and hydrostatic balance); a thermodynamical component (reversible or pseudoadiabatic thermodynamics, although the pseudoadiabatic assumption yields greater intensity); and a planetary boundary layer (PBL) closure (which relates the horizontal gradients of entropy and angular momentum at the top of the PBL to fluxes and stresses at the ocean surface). These three components are evaluated using output from an axisymmetric numerical model. The present analysis finds the thermodynamical component and the PBL closure to be sufficiently accurate for several different simulations. In contrast, the dynamical component is clearly violated. Although the balanced portion of the flow (υg, to which E-PI applies) appears to also exceed E-PI, it is shown that this difference is attributable to the method used to calculate υg from the model output. Evidence is shown that υg for a truly balanced cyclone does not exceed E-PI. To clearly quantify the impact of unbalanced flow, a more complete analytic model is presented. The model is not expressed in terms of external conditions and thus cannot be used to predict maximum intensity for a given environment; however, it does allow for evaluation of the relative contributions to maximum intensity from balanced and unbalanced (i.e., inertial) terms in the governing equations. Using numerical model output, this more complete model is shown to accurately model maximum intensity. Analysis against observations further confirms that the effects of unbalanced flow on maximum intensity are not always negligible. The contribution to intensity from unbalanced flow can become negligible in axisymmetric models as radial turbulence (i.e., viscosity) increases, and this explains why some previous studies concluded that E-PI was an accurate upper bound for their simulations. Conclusions of this study are also compared and contrasted to those from previous studies.

The effect of wind-induced surface heat exchange (WISHE) on axisymmetric, solstitial Hadley circulations is examined for forcings strong enough to produce meridional flow that nearly conserves absolute angular momentum in the free troposphere. Such forcings are known to produce an off-equatorial ascent zone in the summer hemisphere where the convergence of zonal momentum is balanced by drag on surface westerlies. Here, a convective quasi-equilibrium model with two vertical modes is used to show that enhanced surface entropy fluxes induced by these westerlies can intensify and shift both this ascent zone and the subcloud-layer entropy peak toward the equator. The equatorward shift of the subcloud entropy peak is associated with a reduction in the forcing amplitude needed to produce angular momentum–conserving (AMC) meridional flow. A previous theory of frontogenesis in tropical cyclones is adapted to axisymmetric Hadley circulations to show how WISHE shifts the peak subcloud entropy toward the equator. These effects also occur for forcings that vary in a seasonal cycle, with the precise effect of WISHE depending on the peak amplitude of the forcing. For weak seasonally varying forcings, WISHE can abruptly increase the intensity of a local, viscous circulation, whereas for forcings of intermediate strength WISHE produces a transition to AMC flow when such a transition would not otherwise occur. For the strongest forcings, WISHE shifts the transition to AMC flow to a time earlier in the seasonal cycle. The possible relevance of these results to monsoon dynamics is discussed, as are possible effects of processes not represented in these axisymmetric models.

The axial angular momentum (AAM) budget of zonal atmospheric annuli extending from the surface to a given height and over meridional belts is discussed within the framework of conventional and transformed Eulerian mean (TEM) theory. Conventionally, it is only fluxes of AAM through the boundaries and/or torques at the surface that are able to change the AAM of an annulus. TEM theory introduces new torques in the budget related to the vertically integrated Eliassen–Palm flux divergence and also new AAM fluxes of the residual difference circulation. Some of these torques are displayed for various annuli. In particular, the application of TEM theory generates a large positive torque at tropospheric upper boundaries in the global case. This torque is much larger than the global mountain and friction torques but is cancelled exactly by the new vertical AAM fluxes through the upper boundary. It is concluded that the TEM approach complicates the analysis of AAM budgets but does not provide additional insight. Isentropic pressure torques are believed to be similar to the TEM torques at the upper boundary of an annulus. The isentropic pressure torques are evaluated from data and found to differ in several respects from the TEM torques.

For an imposed thermal forcing localized off the equator, it is known that conservation of absolute angular momentum in axisymmetric flow produces a nonlinear response once the forcing exceeds a critical amplitude. It is shown here that, for a moist atmosphere in convective quasi-equilibrium, the combination of wind-dependent ocean surface enthalpy fluxes and zonal momentum advection can provide a separate feedback that causes the meridional flow to evolve nonlinearly as a function of a sea surface temperature (SST) forcing, even if an angular momentum–conserving response is not achieved. This wind–evaporation feedback is examined in both an axisymmetric primitive equation model and a simple model that retains only a barotropic and single baroclinic mode. Only SST forcings that do not produce an angular momentum–conserving response are examined here. The wind–evaporation feedback is found to be inhibited in models with linear dynamics because the barotropic component of the Hadley circulation, which is coupled to the baroclinic circulation via surface drag, keeps surface winds small compared to upper-level winds. In models with nonlinear dynamics, the convergence of zonal momentum into the ascending branch of the cross-equatorial Hadley cell can create barotropic westerlies that constructively add to the baroclinic wind at the surface, thereby eliminating the inhibition of the wind–evaporation feedback. The possible relevance of these results to the onset of monsoons is discussed.

An idealized analytical model of the barotropic potential vorticity (PV) staircase is constructed, constrained by global conservation of absolute angular momentum, perfect homogenization of PV in mixing zones between (prograde) westerly jets, and the requirement of barotropic stability. An imposed functional relationship is also assumed between jet speed and latitudinal separation using a multiple of the “dynamical Rossby wave” Rhines scale inferred from the strength of westerly jets. The relative simplicity of the barotropic system provides a simple relation between absolute angular momentum and PV (or absolute vorticity). A family of solutions comprising an arbitrary number of jets is constructed and is used to illustrate the restriction of jet spacing and strength imposed by the constraints of global conservation of angular momentum and barotropic stability. Asymptotic analysis of the theoretical solution indicates a limiting ratio of jet spacing to the dynamical Rhines scale equal to the square root of 6, meaning that westerly jets are spaced farther apart than predicted by the dynamical Rhines scale. It is inferred that an alternative “geometrical” Rhines scale for jet spacing can be obtained from conservation of absolute angular momentum on the sphere if the strength of zonal jets is known from other considerations. Numerical simulations of the full (nonaxisymmetric) equations reveal a pattern of zonal jet evolution that is consistent with our construction of ideal PV staircases in spherical geometry (which can be considered as limiting cases), as well as with the asymptotic analysis of a geometrical Rhines scale. The evolution of the PV staircase originating from an upscale cascade of energy in the barotropic model is therefore seen to depend on conservation of energy (for the strength of jets) and conservation of absolute angular momentum (for the spacing and number of jets). Further analysis of the numerical results confirms a “Taylor identity” relating the flux of eddy potential vorticity to mean-flow acceleration. Eddy fluxes are responsible for the occasional transitions between mode number as well as for maintaining the sharp westerly jets against small-scale dissipation. Suggestions are made for extending the theoretical model to PV staircases that are asymmetric between hemispheres or with latitudinal variation of amplitude, as modeled in the shallow-water system.

Theories of topographic instability predict growth of perturbations of mean flow and wave modes due to their interaction with mountains under favorable conditions. Mountain torques form an important part of this interaction. It has been suggested that topographic instabilities contribute significantly to the subseasonal variability of the atmosphere but observational tests of topographic instability mechanisms have not yet been performed. Greenland is selected as a test bed because of its isolation, simple shape, and appropriate size. The observed flow development during mountain torque events is investigated in terms of a regression analysis. Changes of axial angular momentum and zonal mean wind with respect to the torques are monitored for domains covering Greenland since the acceleration (deceleration) of the regional zonal flow in response to a positive (negative) torque is a key feature of topographic instability. In particular, southern and northern analysis domains are considered separately in order to test “dipole” instability theories in addition to “monopole” situations where the meridional extent of the pressure perturbations is similar to that of Greenland. Moreover, zonal bands are used as analysis domains. It is found that the response of the zonal wind to the torques is quite small and not systematic. There is no evidence of monopole or dipole topographic instability. A less detailed analysis for the Tibetan Plateau leads to the same result. Reasons for these negative outcomes are discussed as are shortcomings of the tests.

The diurnal and subdiurnal variations of the mass and wind terms of the axial atmospheric angular momentum (AAM) are explored using a 1-yr integration of the Laboratoire de Météorologie Dynamique (LMDz) GCM, twelve 10-day ECMWF forecasts, and some ECMWF analysis products. In these datasets, the wind and mass AAMs present diurnal and semidiurnal oscillations for which tendencies far exceed the total torque. In the LMDz GCM, these diurnal and semidiurnal oscillations are associated with axisymmetric (s = 0) and barotropic circulation modes that resemble the second gravest (n = 2) eigensolution of Laplace’s tidal equations. This mode induces a Coriolis conversion from the wind AAM toward the mass AAM that far exceeds the total torque. At the semidiurnal period, this mode dominates the axisymmetric and barotropic circulation. At the diurnal period, this n = 2 mode is also present, but the barotropic circulation also presents a mode resembling the first gravest n = 1 eigensolution of the tidal equations. This last mode does not produce anomalies in the mass and wind AAMs. A shallow-water axisymmetric model driven by zonal mean zonal forces, for which the vertical integral equals the zonal mean zonal stresses issued from the GCM, is then used to interpret these results. This model reproduces well the semidiurnal oscillations in mass and wind AAM, and the semidiurnal mode resembling the n = 2 eigensolution that produces them, when the forcing is distributed barotropically in the vertical direction. This model also reproduces diurnal modes resembling the n = 1 and n = 2 eigensolutions when the forcings are distributed more baroclinically. Among the dynamical forcings that produce these modes of motion, it is found that the mountain forcing and the divergence of the AAM flux are equally important and are more efficient than the boundary layer friction. In geodesy, the large but opposite signals in the mass and wind AAM due to the n = 2 modes can lead to large errors in the evaluation of the AAM budget. The n = 2 responses in surface pressure can affect the earth ellipcity, and the n = 1 diurnal response can affect the geocenter position. For the surface pressure tide, the results suggest that the dynamical forcings of the zonal-mean zonal flow are a potential cause for its s = 0 component.

An idealized analytical model and numerical large-eddy simulations are used to explore fluid-dynamic mechanisms by which tornadoes may be intensified near the surface relative to conditions aloft. The analytical model generalizes a simple model of Barcilon and Fiedler and Rotunno for a steady supercritical end-wall vortex to more general vortex corner flows, angular momentum distributions, and time dependence. The model illustrates the role played by the corner flow swirl ratio in determining corner flow structure and intensification; predicts an intensification of near-surface swirl velocities relative to conditions aloft of Iυ ∼ 2 for supercritical end-wall vortices in agreement with earlier analytical, numerical, and laboratory results; and suggests how larger intensification factors might be achieved in some more general corner flows. Examples of the latter are presented using large-eddy simulations. By tuning the lateral inflow boundary conditions near the surface, quasi-steady vortices exhibiting nested inner and outer corner flows and Iυ ∼ 4 are produced. More significantly, these features can be produced without fine tuning, along with an additional doubling (or more) of the intensification, in a broad class of unsteady evolutions producing a dynamic corner flow collapse. These scenarios, triggered purely by changes in the far-field near-surface flow, provide an attractive mechanism for naturally achieving an intense near-surface vortex from a much larger-scale less-intense swirling flow. It is argued that, applied on different scales, this may sometimes play a role in tornadogenesis and/or tornado variability. This phenomenon of corner flow collapse is considered further in a companion paper.

The life cycle of the 2 June 1995 Dimmitt, Texas, tornado cyclone, observed during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX), is described. The tornado cyclone here is defined as a significantly axisymmetric flow larger than the visible tornado and characterized by increasing angular momentum with increasing radius. Its life cycle included three phases with somewhat differing evolution of angular momentum, herein called intensifying, transition, and weakening. During the intensifying stage, the funnel and debris cloud gradually increased in size. The azimuthally averaged secondary circulation of the larger-scale tornado cyclone, as determined using high-resolution single-Doppler data obtained by a mobile radar, was primarily inward and upward, consistent with the presence of a wall cloud outside the tornado. The azimuthally averaged angular momentum increased monotonically away from the tornado, so inward advection allowed the angular momentum to increase slowly with time in part of the tornado cyclone. During the transition phase, downdrafts began to occur within the tornado cyclone. The transport of angular momentum by the secondary circulation nearly was offset by eddy flux convergence of angular momentum so that the azimuthally averaged angular momentum tendency was only weakly negative at most radii. The tornado was visually impressive during this stage, featuring a 400-m diameter debris cloud extending to cloud base, while the surrounding wall cloud shrank and eroded. During the weakening phase, the funnel and debris cloud gradually shrank, and the funnel went through a rope stage prior to disappearing. The weakening phase was characterized by extensive downdrafts at all radii outside the tornado, and large-scale near-ground outflow as observed by mobile mesonet systems in a portion of the tornado cyclone. The secondary circulation acted to transport smaller angular momentum downward from aloft, and outward along the ground. All terms of the angular momentum budget became negative throughout most of the low-level (0–800-m AGL) tornado cyclone during the weakening phase. Several hypotheses for this evolution are evaluated, including changes in water loading in the tornado cyclone, cooling of the near-ground air, and the distribution of tangential velocity with height with its concomitant influence on the nonhydrostatic vertical pressure gradient force.

Fully developed superrotation—60 times faster than the planetary rotation (243 days)—is simulated using a Venus-like atmospheric general circulation model (AGCM). The angular momentum of the superrotation is pumped up by the meridional circulation with the help of waves, which accelerate the equatorial zonal flow. The waves generated by solar heating and shear instability play a crucial role in the atmospheric dynamics of the Venusian superrotation. Vertical and horizontal momentum transports of thermal tides maintain the equatorial superrotation in the middle atmosphere, while equatorward eddy momentum flux due to shear instability raises the efficiency of upward angular momentum transport by the meridional circulation in the lower atmosphere. In addition to the superrotation, some waves simulated in the cloud layer are consistent with the observations. The planetary-scale Kelvin wave identified as the near-infrared (NIR) oscillation with periods of 5–6 days is generated by the shear instability near the cloud base, and the temperature structure of the diurnal tide is similar to the infrared (IR) observation near the cloud top. Sensitivities to the bottom boundary conditions are also examined in this paper, since the surface physical processes are still unknown. The decrease of the equator–pole temperature difference and the increase of the surface frictional time constant result in the weaknesses of the meridional circulation and superrotation. In the cases of the weak superrotation, the vertical angular momentum transport due to the meridional circulation is inefficient and the equatorward eddy angular momentum transport is absent near 60-km altitude.

This paper introduces the concept of potential momentum, which is a nonlocal measure of the thermal structure that has momentum units. Physically, it may be interpreted as the zonal momentum that the flow would realize through an adiabatic redistribution of mass that made the isentropic thickness uniform poleward of a reference latitude. At the surface, a poleward temperature gradient is equivalent to an easterly reservoir of potential momentum. Potential momentum gives a global picture of the thermal field that also takes into account the meridional structure. When the mean flow is redefined in terms of the total momentum (the standard zonal momentum plus this newly defined potential momentum), the mean-flow response to the eddy forcing can be formulated locally. This allows one to relate in equilibrium the eddy absorption and the restoration of the mean flow. Using the concept of potential momentum, vertical propagation can be related to thermal forcing by means of an equation analogous to the relation between meridional propagation and surface friction. Based on these ideas, it is argued that the time-mean eddy propagation is largely constrained by the strength and structure of the forcing. The new formalism is applied to a forced–dissipative two-layer model to study the dependence of meridional and vertical propagation and of the global circulation on changes in the diabatic and frictional forcing time scales. It is found that baroclinic adjustment, in the form of a fixed potential vorticity (PV) gradient, is a good approximation because the intensity of the circulation only depends weakly on the forcing time scale. Another remarkable result is that, owing to the robustness of this PV gradient, thermal homogenization is always enhanced with stronger friction.

The dynamical processes that drive intraseasonal equatorial atmospheric angular momentum (EAAM) fluctuations are examined with the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data. The primary methodology involves the regression of relevant variables including the equatorial bulge, mountain, and friction torques, surface pressure, streamfunction, and outgoing longwave radiation, against the time derivative of the two components and the amplitude of the EAAM vector. The results indicate that the observed 10-day westward rotation of the EAAM vector corresponds to the propagation of a zonal wavenumber-1, antisymmetric, Rossby wave normal mode. Additional findings suggest that fluctuations in the amplitude of the EAAM vector are driven by poleward-propagating Rossby waves excited by the latent heating within equatorial mixed Rossby–gravity waves and also by wave–wave interaction among planetary waves. Both of these processes can induce surface pressure anomalies that amplify the EAAM vector via the equatorial bulge torque. The Antarctic and Greenland mountain torques were found to drive large fluctuations in the amplitude of the EAAM vector. Both the friction torque and wave–zonal-mean flow interaction were shown to dampen the EAAM amplitude fluctuations. A comparison of the EAAM dynamics in the atmosphere with that in an aquaplanet GCM suggests that the mountain torque also drives fluctuations in the phase speed of the atmospheric wave field associated with the EAAM vector, and it confines the wave–wave interaction to planetary scales.

The concept of downward control proposes a mechanism for the impact of the stratospheric circulation on the troposphere. Momentum forcing at upper-stratospheric levels induces a meridional circulation that eventually reaches the surface. So far, a lack of sufficiently accurate data hindered an observational test of this downward propagation. The concept is extended in this paper by looking at the effect of angular momentum forcing in prescribed regions in the lower stratosphere on the tropospheric circulation. In that case, the European Centre for Medium-Range Weather Forecasts Reanalysis Project (ERA) data can be used to investigate the atmospheric response to forcing in a prescribed domain. It is found that these forcing events are quite short lived and that angular momentum flux convergence in the prescribed domain is highly correlated with convergence outside this forcing area. Typically, these fields of convergence and also divergence extend to the surface in a quasibarotropic manner outside the Tropics. This structure of the forcing is not compatible with the assumptions of the downward control concept. The observed related meridional circulation therefore differs widely from that predicted. In particular, there is no obvious descent of the circulation to the ground. Even so, such forcing events are accompanied by an intensive exchange of angular momentum between stratosphere and troposphere. The confinement of the forcing to the selected forcing domain is reasonably strict in the Tropics. A relatively narrow tongue of angular momentum is growing at the equator underneath the forcing area. Frictional torques play a role in this development. Altogether, the forcing events as selected involve a strong angular momentum exchange between stratosphere and troposphere but are not suited for a test of the downward control concept. Alternatives are discussed.

The stochastic model of Weickmann et al. for the global angular momentum budget is modified to become applicable to latitude belts. In particular, a Langevin equation is added for the flux divergence of angular momentum in a belt. The friction torque Tf is assumed to be purely damping with respect to angular momentum M. The mountain torque To is generated by red noise but also damps angular momentum directly as suggested by recent stochastic models. The model parameters are tuned such that the variances of all model variables come close to the observations. The corresponding equations for the covariance functions of all variables are solved analytically. The results are compared to observations for selected belts. It is found that the model captures the observed decay rates of all covariance functions. The covariance of the flux divergence and the angular momentum is simulated successfully for positive lags but rarely for negative ones. The covariance of friction torque and angular momentum is reproduced reasonably well. The model is also successful with respect to the covariance of mountain torque and M in the Tropics, but there are large discrepancies at midlatitudes because the observed mountain torque events are accompanied by flux divergences in these belts.

Since Earth is more nearly an oblate spheroid than a sphere, it is of at least theoretical interest to develop the atmospheric equations of motion in spheroidal coordinates. In this system the horizontal unit vectors are oriented eastward and northward along the surfaces of ellipsoids, while the orthogonal unit vector is oriented vertically along the surfaces of intersecting confocal hyperboloids. Using the theory of orthogonal curvilinear coordinates, the spheroidal equations of relative atmospheric motion are derived from the vector equation of absolute motion. With the exception of two terms in the meridional and vertical equations of motion that are unique to the spheroidal system, all of the metric and rotational terms in the spheroidal system correspond to those found in the familiar spherical formulation, but now have coefficients that are functions of both the spheroidal latitude and elevation. The unique spheroidal terms arise from the resolution of the difference between the directions of apparent gravity and Newtonian gravitation, which is neglected in the spherical formulation. The complete spheroidal equations conserve both absolute angular momentum and total kinetic energy, and in the limit as Earth’s focal distance or eccentricity approaches zero, reduce to the familiar spherical equations in both the general and hydrostatic cases. The differences between solutions of the spheroidal and spherical equations are not expected to be significant in most applications, although there is the possibility of the accumulation of systematic differences in long-term integrations.