Abstract

A weakly nonlinear baroclinic life cycle is examined with a spherical, multilevel, primitive equation model. The structure of the initial zonal jet is chosen so that the disturbance grows very slowly, that is, linear growth rate less than 0.1 day⁻¹, and the life cycles of the disturbance are characterized by baroclinic growth and followed by barotropic decay. It is found that if the disturbance grows sufficiently slowly, the decay is baroclinic. As a result, the procedure for determining this weakly nonlinear jet is rather delicate.

The evolution of the disturbance is examined with Eliassen-Palm flux diagrams, which illustrate that the disturbance is bounded at all times by its critical surface in the model's middle and upper troposphere. The disturbance undergoes two large baroclinic gtowth/barotropic decay life cycles, after which it decays by horizontal diffusion. At the end of the first cycle, the zonally averaged zonal flow is linearly stable, suggesting that the disturbance growth during the second cycle may have arisen through nonmodal instability. This stabilization of the disturbance is due to an increase in the horizontal shear of the zonal wind, that is, the barotropic governor mechanism. It is argued that this stabilization is due to the large number of model levels.

A quasigeostrophic refractive index is used to interpret the result that as the linear growth rate of the disturbance is lowered, the ratio of equatorward to poleward wave activity propagation decreases. A parameter is defined as the ratio of the horizontal zonal wind shear to the Eady growth rate. It is found that the growing disturbance tends to be confined to regions of local minima of this parameter.

Abstract

A two-layer quasigeostrophic β-plane channel model is used to examine the role of the wave-mean flow interaction during the life cycles of baroclinic waves. Two cases are examined: a wide and a narrow jet limit. These two limits are required to satisfy the property that their instability lead to a realistic baroclinic life cycle consisting of baroclinic growth and barotropic decay. In order to characterize the properties of the zonal-wind tendency in the two cases, scaling arguments based on a study by Andrews and McIntyre are used. This scaling procedure is then used to explain the nonlocal (local) zonal-wind tendency during the realistic baroclinic life cycle for the wide (narrow) jet limit.Several differences between the properties of the two jet limits are found. For the wide jet limit, the acceleration at the center of the jet is confined to the growth stage. This contrasts the narrow jet limit where the jet is accelerated throughout the entire life cycle. These differences depend upon the lower-layer potential vorticity fluxes, which exhibit the same timing properties as the zonal-wind tendency. In addition, for both the wide and narrow jet limits, irreversible potential vorticity mixing is shown to force nonlocal and local permanent changes to the zonal wind, respectively. A comparison is also made between the vorticity flux and potential vorticity flux to determine which is a better predictor of the zonal-wind tendency. It is shown that in the wide (narrow) jet limit, the vorticity (potential vorticity) flux does better at predicting the zonal-wind tendency. It is also argued that one can use a barotropic model to study the temporal evolution of the upper-layer flow for both the narrow and wide jet limits.Last, it is shown that the properties of the inviscid calculations are retained when thermal forcing and surface Ekman friction are included. Calculations are performed with different values for the surface Ekman friction coefficient and with the thermal forcing coefficient fixed. For the wide (narrow) jet limit, it is found that the disturbance grows to a larger (smaller) total energy as the Ekman friction coefficient is increased (decreased). This behavior for the wide jet limit is explained in terms of an enhancement of the baroclinic energy conversions that overcome the barotropic governor mechanism of James and Gray.

Abstract

Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies.

In the weakly nonlinear model, asymptotic series expansions are used in conjunction with the method of multiple time scales. The stability of a forced planetary-scale stationary baroclinic Rossby wave to synoptic-scale perturbations is first examined. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. This indicates that the transient synoptic-scale perturbation has neither an amplifying nor a dissipative influence on the stationary wave. A study of the energetics shows that eddy available potential energy is transferred from the planetary-scale stationary wave to the synoptic-scale perturbation, while eddy kinetic energy is simultaneously transferred in the reverse direction.

The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. In addition, by comparing spectral model solutions with and without the higher-order modes of the weakly nonlinear model present, it is found that the evolution of the basic wave and the perturbation are extremely sensitive to the presence of these modes. This suggests that the interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present.

Abstract

The nonlinear evolution of disturbances that emanate from unstable westerly and easterly jet profiles is examined with a two-layer quasi-geostrophic β-plane channel model. Significant differences arise between the solutions for westerly and easterly jets. For unstable narrow (width less than the deformation radius) westerly jets, the disturbance undergoes a sequence of life cycles characterized by barotropic growth and barotropic decay. Unstable easterly jets also give rise to a series of life cycles in which the disturbance grows and decays in a combined baroclinic/barotropic manner. In each of these cases, the disturbance structure remains close to its unstable normal mode form throughout the life cycle. This contrasts with earlier results of Feldstein and Held who find that disturbances emanating from unstable wide (width greater than the deformation radius) westerly jets undergo a change in meridional structure, enhanced lateral radiation, and a single life cycle consisting of baroclinic growth followed by barotropic decay.

The wave propagation characteristics of the westerly and easterly jets are examined in the context of linear WKB theory. It is found that the modes growing in the narrow westerly and easterly jets are reflected at turning latitudes. On the other hand, the modes of the unstable wide westerly jet are completely absorbed at critical latitudes. These properties at the bounding latitudes are used to explain differences in the life cycles.

The life cycles for westerly and easterly jets are also examined with a forced dissipative model. For both narrow westerly and easterly jets, the disturbance always evolves to a steady state. This contrasts with the multiple life cycle solutions of the wide westerly jet. Finally, the results in this study are related to the nonlinear instability of various jets in the atmosphere.

Abstract

The poleward propagation of zonal-mean relative angular momentum (M _R ) anomalies is examined using NCEP–NCAR Reanalysis data for both the winter and summer seasons of the Northern and Southern Hemisphere. This analysis is performed with a regression analysis using base latitudes in the subtropics, midlatitudes, and high latitudes. It is found that the poleward M _R anomaly propagation occurs at all latitudes, with the propagation speed being greater in the subtropics and high latitudes, compared to midlatitudes.

Other fields, such as eddy angular momentum flux convergence, eddy heat flux, friction torque, and 300-mb streamfunction, are regressed for the Northern Hemisphere winter and the Southern Hemisphere summer. The main finding is that in the subtropics and midlatitudes, the poleward M _R anomaly propagation is primarily due to high-frequency (<10 day) transient eddy angular momentum flux convergence and in high latitudes the propagation is mostly due to the summation of cross-frequency and low-frequency (>10 day) eddy angular momentum flux convergence. For the Northern Hemisphere winter, the anomalous eddy angular momentum flux convergence due to the interaction between stationary and transient eddies also contributes to the poleward M _R anomaly propagation.

The regression analysis suggests that a high-frequency transient eddy feedback is taking place that influences the poleward propagation of the M _R anomalies. However, the effectiveness of this feedback is limited by the summation of the cross-frequency and low-frequency eddy angular momentum flux convergence, as once the M _R anomaly reaches its largest amplitude, this summation of terms dominates the eddy angular momentum flux convergence and, together with the friction torque, contributes to the decay of the M _R anomaly.

Abstract

The atmospheric dynamical processes that drive intraseasonal polar motion are examined with National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis data and with pole position data from the International Earth Rotation Service. The primary methodology involves the regression of different atmospheric variables against the polar motion excitation function.

A power spectral analysis of the polar motion excitation function finds a statistically significant peak at 10 days. Correlation calculations show that this peak is associated with the 10-day, first antisymmetric, zonal wavenumber 1, normal mode of the atmosphere. A coherency calculation indicates that the atmospheric driving of polar motion is mostly confined to two frequency bands, with periods of 7.5–13 and 13–90 days. Regressions of surface pressure reveal that the 7.5–13-day band corresponds to the 10-day atmospheric normal mode and the 13–90-day band to a quasi-stationary wave.

The regressions of pole position and the various torques indicate not only that the equatorial bulge torque dominates the mountain and friction torques but also that the driving by the equatorial bulge torque accounts for a substantial fraction of the intraseasonal polar motion. Furthermore, although the 10-day and quasi-stationary wave contributions to the equatorial bulge torque are similar, the response in the pole position is primarily due to the quasi-stationary wave.

Additional calculations of regressed power spectra and meridional heat fluxes indicate that the atmospheric wave pattern that drives polar motion is itself excited by synoptic-scale eddies. Regressions of pole position with separate torques from either hemisphere show that most of the pole displacement arises from the equatorial bulge torque from the winter hemisphere. Together with the above findings on wave–wave interactions, these results suggest that synoptic-scale eddies in the winter hemisphere excite the quasi-stationary wave, which in turn drives the polar motion through the equatorial bulge torque.

Abstract

The atmospheric dynamical processes associated with intraseasonal length-of-day (LOD) variability during the austral winter are examined with National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis and outgoing longwave radiation (OLR) data. The method adopted is to regress the relevant fields against the LOD tendency. All quantities in this study are bandpassed through a 30–70-day filter.

The findings from an analysis of the OLR and 200-mb eddy streamfunction fields are consistent with the idea that large intraseasonal LOD fluctuations coincide with an active Madden–Julian oscillation (MJO). Further analysis suggests that the eddy response to the MJO heating drives both an anomalous meridional circulation that excites the anomalous global friction torque, and an eddy field that has the appropriate location relative to the topography for generating the anomalous global mountain torque. These results were obtained by calculating regressions of the anomalous eddy angular momentum flux convergence, mass streamfunction, surface stress, and surface pressure fields, and each term in the lowest sigma level relative angular momentum budget.

The anomalous global friction and mountain torques are found to be of similar magnitude, with the former leading the latter by eight days. The largest contribution toward the anomalous global friction (mountain) torque comes from Australia and the surrounding ocean (the Andes).

Abstract

This investigation examines the dynamical processes that drive the anomalous friction torque associated with intraseasonal length-of-day fluctuations. Diagnostic analyses with National Centers for Environmental Protection–National Center for Atmospheric Research reanalysis and National Oceanic and Atmospheric Administration outgoing longwave radiation data are performed. The approach adopted is to use the mean meridional circulation (MMC) as a proxy for the friction torque, and then to examine the MMC that is driven both by eddy fluxes and zonal mean diabatic heating.

The following simple picture emerges from this analyses. For the austral winter (May through September), the anomalous friction torque in both hemispheres is driven by anomalous zonal mean convection. For the boreal winter (November through March), the anomalous friction torque in the Northern Hemisphere is driven primarily by eddy fluxes, whereas in the Southern Hemisphere the anomalous friction torque is also driven by anomalous zonal mean convection. However, the dynamics associated with this convection for the Southern Hemisphere boreal winter may be rather subtle, as the results suggest that this convection may in turn be driven by eddies within the Northern Hemisphere.

Abstract

The dynamical processes that drive intraseasonal equatorial atmospheric angular momentum (EAAM) fluctuations in a 4000-day aquaplanet GCM run are examined. The all-ocean lower boundary has a sea surface temperature field that is both independent of longitude and symmetric across the equator. Because of the absence of topography, the model includes an equatorial bulge and friction torque, but not a mountain torque. The methodology adopted is to regress variables such as surface pressure, streamfunction, precipitation, and the two torques against individual components and the amplitude of the EAAM vector.

The results indicate that the phase of the EAAM vector is associated with the westward propagation of a zonal wavenumber-1 midlatitude Rossby wave. This wave has characteristics that closely match those of a normal mode of the GCM and also those of the first antisymmetric rotational mode of the shallow water model on the sphere. Fluctuations in the amplitude of the EAAM vector are found to be related to the presence of a zonal wavenumber-1 mixed Rossby–gravity wave in the Tropics. The structure of the precipitation anomalies suggests that the latent heat release associated with the mixed Rossby–gravity wave excites poleward Rossby wave propagation, which alters the EAAM amplitude. The above dynamical processes are also found to determine the phase and amplitude of the equatorial bulge torque. It is this torque that dominates the driving of the EAAM. Lastly, the properties of the friction torque are discussed.

Abstract

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.