Basic-state Flow Research Articles

Symmetric flow of a modified hadley cell model with a free surface

Numerical studies are conducted of symmetric flows in an infinite horizontal fluid layer with a constant horizontal temperature gradient. A modified rotating Hadley-cell flow configuration is devised by adopting the free-slip and thermally insulated upper boundary. For this model, an analytic solution is available as the basic state. A finite volume numerical procedure is utilized to integrate the fully nonlinear Navier-Stokes equations over broad parameter ranges of the thermal Rossby number, Ro, and the Richardson number, Ri. The Ro—Ri diagram illustrates several flow regimes. In the present framework, both the symmetric instability and Benard-type convective instability are found to occur. These are associated respectively with a negative potential vorticity in the interior and a gravitationally unstable vertical temperature gradient in the thermal boundary layer. The detailed flow structures are computed to reveal the characteristic features of these two instabilities. Time dependent responses are analyzed to examine the dominant mechanism for two-dimensional flow developments. The interaction of the symmetric flows with the basic-state flow field is scrutinized.

An Adjoint Sensitivity Study of the Efficacy of Modal and Nonmodal Perturbations in Causing Model Block Onset*

Abstract With a blocking index as the response function, the adjoint sensitivity formalism is used to assess the impact of normal modes, adjoint modes, and regional singular vectors on prediction of block onset in a two-layer model. The authors focus on three blocks excited by perturbing the model’s state vector at times preselected using the maximal perturbation that defines the direction in phase space associated with the largest possible change in the response function. The sets of normal modes, adjoint modes, and regional singular vectors (using the total energy or the L2 norm) are computed on instantaneous basic-state flows for the preselected times and sensitivity results are presented for a time window of 3 days. When ordered by decreasing values of the growth rates of the normal modes, the authors find that some distant normal modes and adjoint modes can produce larger changes in the response function than some of their leading counterparts. In contrast, the sets of regional singular vectors conta...

Nonlinear adjustment of a rotating homogeneous atmosphere to zonal momentum forcing

Idealized numerical simulations using a simple shallow water model are performed to study ageneralized Rossby adjustment problem which focuses on the nonlinear response of a rotating, uniform, homogeneous, barotropic zonal flow to meso-α and β scale zonal momentum forcing. The prescribed forcings propagate downstream at a speed (c) which is less than the basic stateflow speed (U), and represent the local effects of momentum deposition/redistribution attributableto a variety of physical processes. For small Rossby number flow and t≤ τ =2a/(U — c), the near-field response to meso-α scale forcing in the moving frame of reference is to producelocalized zonal jets of finite longitudinal and latitudinal extent whose geometries are similar tothe imposed forcing structure. The perturbation mass (height) field adjusts to the wind fieldassociated with these disturbances. Although the free surface vertical motion is dominated bytransient inertia-gravity waves at early times, well-defined localized vertical motions also formin the vicinity of the forcing center. For isolated forcing, ascending and descending verticalmotion occurs south and north of the forcing center, respectively. For dipole forcing, a fourcellpattern of vertical motion characterized by ascent in the southwest and northeast quadrantsand descent in the northwest and southeast quadrants flanks the forcing center where a pairof easterly and westerly jets form. For t >t, the exit region of the localized zonal jet producedby isolated forcing is advected downstream, carrying portions of the meridional perturbationwinds and free surface displacement fields with it. The long term asymptotic response is azonally elongated, synoptic scale jet due to the temporally continuous relative vorticity generatedby the zonal momentum forcing. A divergent cross-stream ageostrophic flow in the jetentrance region produces an isolated region of ascending vertical motion which is compensatedby weaker regions of descent to the east and west of the forcing center. The easterly jet producedby flow deceleration in the exit region of the dipole forcing is advected downstream during thesame time period. A four-cell pattern of vertical motion accompanies this easterly jet. Theresponse in the vicinity of the forcing center is an isolated meso-α scale westerly jet, withmeridionally confluent flow in its entrance region and meridionally diffluent flow in its exitregion. The ageostrophic circulation produces rising motion in the jet entrance region andsinking motion in the jet exit region. For moderately large Rossby number flow and meso-bscale dipole forcing, a mesoscale cyclone forms in response to fluid parcels being displacedsouthward into deeper fluid around a ridge in the height field. The moderately strong meso-bscale zonal wind maximum which is produced has associated vertical motions whose geometryis similar to those produced by larger meso-α scale dipole forcing. Stronger nonlinear advectionallows the meso-β scale jet to form four times sooner than the westerly jet produced by smallerRossby number meso-α scale dipole forcing.

Viscous fingering in periodically heterogeneous porous media. I. Formulation and linear instability

We are generally interested in viscously driven instabilities in heterogeneous porous media for a variety of applications, including chromatographic separations and the passage of chemical fronts through porous materials. Heterogeneity produces new physical phenomena associated with the interaction of the flow with the heterogeneity on the one hand, and the coupling between the flow, the concentration of a passive scalar, and the physical properties (here the viscosity) on the other. We pose and solve a model in which the permeability heterogeneity is taken to be periodic in space, thus allowing the interactions of the different physical mechanisms to be carefully studied as functions of the relevant length and time scales of the physical phenomena involved. In this paper, Paper I of a two-part study, we develop the basic equations and the parameters governing the solutions. We then focus on identifying resonant interactions between the heterogeneity and the intrinsic viscous fingering instability. We make analytical progress by limiting our attention to the case of small heterogeneity, in which case the base state flow is only slightly disturbed from a uniform flow, and to linear instability theory, in which the departures from the base state flow are taken to be small. It is found that a variety of resonances are possible. Analytic solutions are developed for short times and for the case of subharmonic resonance between the heterogeneities and the intrinsic instability modes. A parametric study shows this resonance to increase monotonically with the viscosity ratio i.e., with the strength of the intrinsic instability, and to be most pronounced for the case of one-dimensional heterogeneities layered horizontally in the flow direction, as expected on simple physical grounds. When axial variation of the permeability field is also considered, a damping of the magnitude of the response generally occurs, although we find some evidence of local resonances in the case when the axial forcing is commensurate with a characteristic dispersive time. The response exhibits a high frequency roll-off as expected. These concepts of resonant interaction are found to be useful and to carry over to the strongly nonlinear cases treated by numerical methods in Paper II [J. Chem Phys. 107, 9619 (1997)].

Dynamics of Barotropic Storm Tracks

Longitudinal variations in the upper-tropospheric time-mean flow strongly modulate the structure and amplitude of upper-tropospheric eddies. This barotropic modulation is studied using simple models of wave propagation through zonally varying basic states that consist of contours separating regions of uniform barotropic potential vorticity. Such basic states represent in a simple manner the potential vorticity distribution in the upper troposphere. Predictions of the effect of basic-state zonal variations on the amplitude and spatial structure of eddies and their associated particle displacements are made using conservation of wave action or, equivalently, the linearized ‘‘pseudoenergy’’ wave activity. The predictions are confirmed using WKB theory and linear numerical calculations. The interaction of finite-amplitude disturbances with the basic flow is also analyzed numerically using nonlinear contour-dynamical simulations. It is found that breaking nonlinear contour waves undergo irreversible amplitude attenuation, scale lengthening, and frequency lowering upon passing through a region of weak basic-state flow.

Domain-Independent Attribution. Part II: Its Value in the Verification of Dynamical Theories of Frontal Waves and Frontogenesis

Abstract Theories of frontogenesis and frontal waves describe development in terms of the interaction of a basic state or environmental flow with a frontal flow. The basic-state flow may comprise a large-scale confluent–diffluent deformation field and/or an alongfront temperature gradient. The frontal flow is seen as evolving as a result of its interaction with the environmental flow. Such theories make specific predictions about the effect of the basic-state flow on the frontal flow. To test these predictions, counterparts of the basic-state flows and frontal flows used in theoretical models must be extracted from atmospheric data. Here the concept of attribution is used to identify such counterparts. In the present context, attribution refers to the process whereby a part of the wind field is attributed to a part of the vorticity or divergence field. It is mathematically equivalent to the process by which a part of a field of electric potential is associated with an element of total charge density in el...

A 10-Year Climatology of Northern Hemisphere Tropical Cloud Plumes and Their Composite Flow Patterns

Abstract A 10-year cool season climatology of tropical cloud plumes in the Northern Hemisphere was generated by visual inspection of infrared satellite imagery. The sample included 1062 plume events during the months of October to May for the years 1974 to 1984. The results show that the westerly ducts of the tropical eastern Pacific and central Atlantic are preferred regions for tropical cloud plume development. Composite fields of streamfunction and outgoing longwave radiation for eastern Pacific plumes indicate that both low-latitude westerlies in the planetary-scale basic-state flow and the presence of synoptic-scale transients appear to be favorable for plume formation. With a knowledge of these features, some of the interannual and intraannual variability shown in the climatology can be explained.

On the Dynamical Basis for the Asian Summer Monsoon Rainfall-El Niño Relationship

The dynamical basis for the Asian summer monsoon rainfall-El Niño linkage is explored through diagnostic calculations with a linear steady-state multilayer primitive equation model. The contrasting monsoon circulation during recent El Niño (1987) and La Niña (1988) years is first simulated using orography and the residually diagnosed heating (from the thermodynamic equation and the uninitialized, but mass-balanced, ECMWF analysts) as forcings, and then analyzed to provide insight into the importance of various regional forcings, such as the El Niño–related heating anomalies over the tropical Indian and Pacific Oceans. The striking simulation of the June–August (1987–1988) near-surface and upper-air tropical circulation anomalies indicates that tropical anomaly dynamics during northern summer is essentially linear even at the 150-mb level. The vertical structure of the residually diagnosed heating anomaly that contributes to this striking simulation differs significantly from the specified canonical vertical structure (used in generating 3D heating from OLR/precipitation distributions) near the tropical tropopause. The dynamical diagnostic analysis of the anomalous circulation during 1987 and 1988 March–May and June–August periods shows the orographically forced circulation anomaly (due to changes in the zonally averaged basic-state flow) to be quite dominant in modulating the low-level moisture-flux convergence and hence monsoon rainfall over Indochina. The El Niño–related persistent (spring-to-summer) heating anomalies over the tropical Pacific and Indian Ocean basins, on the other hand, mostly regulate the low-level westerly monsoon flow intensity over equatorial Africa and the northern Indian Ocean and, thereby, the large-scale moisture flux into Sahel and Indochina. The anomalous summer monsoon rainfall over Asian/African longitudes in turn, forces modest surface westerlies over the equatorial western and south tropical Pacific, which contribute positively to the ongoing El Niño's development.

Short‐wave length instabilities on coastal jets and fronts

The stability of a coastal jet and front is investigated using the primitive equations applied to a continuously stratified flow in geostrophic balance. A linear stability analysis successfully explains the growth of two modes of instability with distinctly different horizontal scales. A long‐wavelength mode (fastest‐growing wavelength of 0(100 km)) is found which is a modified version of a traditional baroclinic instability. A second, rapidly growing frontal instability also exists. For a realistic basic state density and flow structure, this mode has its fastest growth at short wavelengths (0(20 km)), e‐folds in less than 1.5 days and propagates rapidly in the direction of the mean flow. The frontal instability grows primarily by extracting the available potential energy of the mean flow via a baroclinic instability mechanism. A small contribution from vertical Reynolds stress is also found, but the transfer via horizontal Reynolds stress is from the eddy to the mean kinetic energy. Further evidence shows that the frontal instability is not a result of horizontal shear instability nor is it an inertial instability. The frontal mode is trapped to the surface front and its influence is confined to the upper water column (z ≲ 70 m). A significant subsurface vertical velocity maximum (20 m d−1 at 30 m) is associated with a frontal instability with a reasonable, as judged by satellite sea surface temperature observations, surface temperature perturbation of 0.35°C. The linear stability predictions are verified by and compared with results from a time‐dependent, three‐dimensional, nonlinear ocean circulation model. Finally, the frontal instability is discussed in the context of other recent stability analyses that yield high‐wavenumber modes.

Rapid Perturbation Growth on Spatially and Temporally Varying Oceanic Flows Determined Using an Adjoint Method: Application to the Gulf Stream

The stability of the Gulf Stream flow predicted by a nonlinear quasigeostrophic model is examined by employing an iterative method, which uses both the tangent linear equations and the adjoint tangent linear equations of the quasigeostrophic model. The basic state flow is the model's representation of the Gulf Stream as observed during January and February 1988. The growth of perturbation energy is examined as a measure of disturbance growth and linear perturbations are found that are optimal in the sense that they maximize the growth of perturbation energy. The structures of optimal perturbations are compared with the structure of the normal modes. The optimal perturbations are found to be mere localized and to grow much more rapidly than the normal modes. Optimal perturbations are of interest because they can be used to plan tight constructive upper bounds on the growth of perturbations to ocean currents such as the Gulf Stream, and they provide valuable information about the predictability of such flows. Initially the stability of a basic-state flow that is stationary in time is considered. The inclusion of time dependence in the basic state is straightforward using the method adopted here, and it is found that the time evolution of the basic-state flow can have a large influence on the structure and preferred location of the optimal perturbation.

Transport of a sediment layer due to a laminar, stratified flow

It is known that a bed of settled particles resuspends under the action of shear caused by a laminar flow. Earlier papers investigated such a resuspension in a fully-developed Hagen-Poiseuille channel flow and in a gravity-driven film flow along an inclined plate. The theoretical results were compared with experiments which, however, disagree for larger flow-rates. In this paper we study the propagation of a change of height of a resuspended sediment, e.g., the beginning (onset) or the end of a particle layer. We apply the previously developed model for the base-state flow and find by means of the theory of kinematic waves that both a sudden onset and a sudden end of a resuspended layer in either a fully-developed Hagen-Poiseuille channel flow or a two-dimensional gravity-driven film flow move as a combination of kinematic shocks and kinematic waves. Experimental observations of the motion of a sudden end of a resuspended layer in a channel flow correspond well with the theory if the flow-rate is small but show distinct discrepancies from the theoretical predictions for larger flow-rates.

Monsoon Disturbances, Intraseasonal Oscillations, Teleconnection Patterns, Blocking, and Storm Tracks of the Global Atmosphere during January 1979: Linear Theory

The results of a study are presented that indicate that a wide variety of atmospheric disturbances, including those associated with storm tracks and blocking in both hemispheres, quasi-stationary global teleconnection patterns, and localized monsoon disturbances, as well as intraseasonal oscillations, may be generated through the instability of the three-dimensional global basic state for January 1979 including a wave-CISK cumulus heating parameterization. The analysis has been conducted with a two-level primitive equation eigenvalue model, and the growing disturbances for various specifications of the strengths of the cumulus heating have been analyzed. Within the parameter range studied, inclusion of explicit moisture in the basic state has little effect on the structures of the storm track and onset-of-blocking modes in both hemispheres, but it increases growth rates as expected. It is also responsible for generating a significant amplitude of the tropical shear streamfunction of low-frequency and quasi-stationary teleconnection pattern modes, particularly in the Australian/South Pacific region where a coupling to the Australian monsoon appears to occur. Remarkable localized quasi-stationary monsoon disturbances of fairly small scale are found, which tend to produce either break or active periods of the Australian monsoon depending on their phase. The CISK heating focuses these modes in the Australian region and increases their growth rates. A group of intraseasonal oscillation modes with quite complex structures and periods between about 20 and 60 days is also found. They have eastward-propagating velocity potentials, peaking in the equatorial regions with a zonal wavenumber 1, and possibly 2, envelope wave within which are embedded smaller-scale structures. They have equivalent barotropic streamfunctions in extratropical regions with a baroclinic structure, typical of the first internal mode, in the tropical regions. At certain phases they can produce break or active periods of the Australian monsoon. Both a three-dimensional large-scale basic-state flow and a cumulus heating parameterization appear to be necessary for generating, through instability, intraseasonal oscillation modes with realistic structures.

On radiating baroclinic instability of zonally varying flow

The baroclinic instability characteristics of zonally varying flow are examined in a quasigeostrophic, two-layer, beta-plane model. The most unstable eigenmode is determined numerically by solving a one-dimensional initial value problem. Emphasis is placed on determining how the basic state vertically averaged wind, U B , local maximum in vertical wind shear, Δ U T , and length of the locally unstable region, λ L , combine to yield local instabilities whose energy fluxes radiate deep into the locally neutral far field. The existence of such zonally radiating instabilities (RIs), which represent a transition between trapped and global instabilities, requires that λ L not exceed some critical value and that Δ U T / U B lie within a certain range. In sharp contrast to the trapped and global instabilities, the RIs have horizontal wavelengths that increase dramatically with distance from the locally unstable region. If λ L and Δ U T / U B are both sufficiently small, the local instability that emerges is characterized by a vertical asymmetry in its horizontal spatial structure; the disturbance in the upper layer has a longer zonal wavelength than its counterpart in the lower layer. For slowly varying basic states, analysis of the local disturbance energetics reveals that the baroclinic energy conversion predominates within the locally unstable region. For basic states that vary rapidly in the downstream direction, the barotropic energy conversion associated with the horizontal deformation field may predominate over the baroclinic conversion depending on the relative importance of Δ U T and U B . For RIs, the energy budget outside the locally unstable region is primarily due to the advection of total energy and the convergence of mechanical energy flux. Calculations of the basic state tendencies show that the net effect of the local (trapped or radiating) instabilities is to redistribute energy from the baroclinic to the barotropic component of the basic state flow. The fluxes produced by the trapped modes reduce the vertical shear downstream of the jet center, while the fluxes produced by the radiating modes reduce the vertical shear both downstream and near the jet center. DOI: 10.1034/j.1600-0870.1993.00005.x

The Robustness of Barotropic Unstable Modes in a Zonally Varying Atmosphere

Abstract The unstable normal modes of the barotropic vorticity equation, linearized around an observed zonally varying atmospheric flow, have been related to patterns of observed low-frequency variability. The sensitivity of this problem to changes in the model truncation and diffusion and to details of the basic state flow are examined. Normal modes that are highly sensitive to these changes are found to be of minimal relevance to the low-frequency variability of the atmosphere. A new numerical method capable of efficiently finding a number of the most unstable modes of large eigenvalue problems is used to examine the effects of model truncation on the instability problem. Most previous studies are found to have utilized models of insufficiently high resolution. A small subset of unstable modes is found to be robust to changes in truncation. Sensitivity to changes in diffusion in a low-resolution model can partially reproduce the truncation results. Sensitivity to the basic state is examined using a matr...

The Interaction of Planetary-Scale Tropical Easterly Waves with Topography: A Mechanism for the Initiation of Tropical Cyclones

The interaction of a basic state flow consisting of a planetary-scale easterly wave superimposed on a uniform easterly zonal wind with an isolated topographic feature is examined by numerical integration of the shallow water equations in an equatorial beta-plane channel. The topographic parameters are chosen to represent the Sierra Madre Mountains of Mexico. The zonal wavelength and phase speeds of the basic state easterly waves are chosen to correspond with previously published observations. The topographic modification of a slow Rossby mode in which the basic state vorticity maximum is located near 15° latitude is characterized by the generation of a cyclonic vorticity maximum in the lee of the mountain, which extends the entire length of the ridge, and a secondary maximum which propagates downstream. A fast mixed Rossby–gravity mode in which the vorticity maximum is located at the equator interacts less strongly with the mountain, with a lee vorticity maximum that is confined near the southern portion of the ridge and an absence of a secondary vorticity maximum downstream. The relative vorticity maxima generated by the interaction of nonzonal easterly flow may serve as the locations for tropical cyclogenesis and help explain the tropical cyclone outbreaks that are common off the coast of Mexico.

Stability of a coastal upwelling front: 1. Model development and a stability theorem

A two‐layer shallow water equation model is used to investigate the linear stability of a coastal upwelling front. The model features a surface front parallel to a coastal boundary and bottom topography which is an arbitrary function of the cross‐shelf coordinate. Global conservation statements for energy, momentum and potential vorticity are examined to help elucidate the instability mechanism. By combining these conservation statements, a general stability theorem is established which allows the a priori determination of the stability of a coastal upwelling front. The necessary conditions for instability derived for these ageostrophic flows differ from traditional quasi‐geostrophic criteria. The stability theorem suggests that a coastal upwelling front may be unstable no matter what the basic state flow configuration is. Confirmation of the existence of these unstable waves, a description of their characteristics and a comparison of their properties to observations are presented in a companion paper.

Stability of a coastal upwelling front: 2. Model results and comparison with observations

A two‐layer shallow water equation model is used to investigate the linear stability of a coastal upwelling front. The model features a surface front parallel to a coastal boundary and bottom topography which is an arbitrary function of the cross‐shelf coordinate. The existence of unstable waves on the model coastal upwelling front, as suggested by the general stability theorem developed in a companion paper, is confirmed by solving directly the linearized equations of motion. The unstable wave motions are frontally trapped and dominant in the upper layer. The wave propagates phase in the direction of the basic state flow, and the primary energy conversion is via baroclinic instability. The effect of varying the model parameters is presented. Moving the front closer than ∼2 Rossby radii to the coastal boundary results in a decrease in the growth rate of the fastest growing wave. Increasing the overall vertical shear of the basic state flow, by either decreasing the lower layer depth or increasing the steepness of the interface, results in an increase in the growth of the fastest growing wave. A bottom sloping in the same sense as the interface results in a decrease of the growth rates and alongfront wave numbers of the unstable waves in the system. Linearized bottom friction is included in the stability model and results in a decrease in the growth rates of the unstable waves by extracting energy from the system. Since the unstable mode is strongest in the upper layer, bottom friction will not stabilize the upwelling front. A comparison between the predictions from the simple two‐layer model and observed alongfront variability for three areas of active upwelling is presented. Reasonable agreement is found, suggesting that the observed alongfront variability can be interpreted in terms of the instability of a coastal upwelling front.

The sedimentation of nondilute suspensions in inclined settlers

The base-state convective flows, which are set up when a nondilute sedimenting suspension is placed beneath an inclined wall, are analyzed theoretically using a two-fluid model. Their hydrodynamic stability and the corresponding spatial growth of small two-dimensional disturbances at the clear fluid–suspension interface are then determined over the entire range of the governing parameters through numerical solutions of the relevant Orr–Sommerfeld equations. Two mechanisms for the growth of instability waves at the interface are identified. The results demonstrate that the base-state flow becomes more unstable as inertial effects in the base state become more pronounced and thus, contrary to what has been suggested by earlier investigators, there is no restabilization as the base state approaches the inviscid limit. Increasing the concentration of the suspension is found to have a stabilizing effect on the two-phase interface, particularly when inertial effects dominate in the base state. Similarly, increasing the angle of inclination enhances the stability of the interface when viscous forces are dominant in the base flow.

Instabilities caused by oscillating accelerations normal to a viscous fluid-fluid interface

Two incompressible viscous fluids with different densities meet at a planar interface. The fluids are subject to an externally imposed oscillating acceleration directed normal to the interface. The resulting basic-state flow is motionless with an internal pressure oscillation. We discuss the linear evolution of perturbations to this basic state. General viscosities and densities for the two fluids are considered but a Boussinesq equal-viscosity approximation is discussed in particular detail. For this case we show that the linear evolution of a perturbation to the interface subject to an arbitrary oscillating acceleration is governed by a single integro-differential equation. We apply a Floquet analysis to the fluid system for the case of sinusoidal forcing. Parameter regions of subharmonic, harmonic, and untuned modes are delineated. The critical Stokes-Reynolds number is found as a function of the surface tension and the difference in density and viscosity between the two fluids. The most unstable perturbation wavelengths are determined. For zero surface tension these are found to be short, on the order of a small multiple of the Stokes viscous lengthscale. The critical Stokes-Reynolds number and the most unstable perturbation wavelengths are found to be insensitive to the degree of density and viscosity differences between the two fluids.

Alternative theories of atmospheric teleconnections and low‐frequency fluctuations

Observational studies have revealed a rich low‐frequency structure in the atmosphere. A review of the theories, observations, and model studies of this low‐frequency atmospheric variability is presented. On time scales of weeks or longer the atmosphere appears to possess distinct oscillatory behavior in well‐defined and persistent “centers of action.” This behavior is also an endemic feature of surrogate atmospheric data sets emerging from experiments with complicated climate models. Many theories have attempted to determine the dominant physical processes responsible for the low‐frequency variance but have usually failed when compared carefully with observations. For example, simple linear steady state and Rossby wave dispersion theories have been used in an attempt to explain the observed global response to low‐latitude perturbation. However, the observed structures of mature anomalies are often quite distinct from the vertical structures of disturbances predicted in these theories. Also, in general circulation and model studies, the sign of the nonlinear response is not simply related to the sign of the forcing as predicted by linear steady state theories. It is argued that the theories fail because either the full three‐dimensional complexity of the basic state is not considered or its inherent instability structure is not recognized or is, in fact, ignored. It is shown that three‐dimensional instability theory provides a natural generalization and marriage of the zonally averaged instability theory of Charney and Eady and the Rossby wave dispersion theory of Rossby and Yeh. As such, it provides a formalism which may be used to understand a wide variety of atmospheric fluctuations including the locations of eddy flux covariance maxima and storm tracks in both the tropics and extratropics and the generation of blocking, teleconnection patterns, and other quasi‐stationary anomaly features. Attention is focused on two particular mechanisms within this formalism for the formation of quasi‐stationary low‐frequency fluctuations. One of these is the baroclinic‐barotropic dipole instability mechanism in which the formation of quasi‐stationary mature anomalies is initiated by the upstream development of mid‐latitude eastward propagating dipole wave trains which arise through the combined baroclinic‐barotropic instability of the three‐dimensional atmospheric flow. The other is the westerly duct mechanism in which the initiation of low‐frequency variability is caused by tropical disturbances. According to this hypothesis, the longitudinal variation of the basic state flow near the equator causes a ducting of wave energy generated in the tropics to specific zones in the upper tropospheric westerlies; these zones then act as source regions for the emanation of waves into the extratropics. Furthermore, this duct also acts as a waveguide for extratropical modes propagating into or through the tropics.