# Search Results

## You are looking at 1 - 10 of 63 items for

- Author or Editor: Steven B. Feldstein x

- All content x

## 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 Rossbyâ€“gravity wave in the Tropics. The structure of the precipitation anomalies suggests that the latent heat release associated with the mixed Rossbyâ€“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 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 Rossbyâ€“gravity wave in the Tropics. The structure of the precipitation anomalies suggests that the latent heat release associated with the mixed Rossbyâ€“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

This study examines whether both the trend and the increase in variance of the Northern Hemisphere winter annular mode during the past 30 years arise from atmospheric internal variability. To address this question, a synthetic time series is generated that has the same intraseasonal stochastic properties as the annular mode. By generating a distribution of linear trend values for the synthetic time series, and through a chi-square statistical analysis, it is shown that this trend and variance increase are well in excess of the level expected from internal variability of the atmosphere. This implies that both the trend and the variance increase of the annular mode are due either to coupling with the hydrosphere and/or cryosphere or to driving external to the climate system. This behavior contrasts that of the first 60 years of the twentieth century, for which it is shown that all of the interannual variability of the annular mode can be explained by atmospheric internal variability.

## Abstract

This study examines whether both the trend and the increase in variance of the Northern Hemisphere winter annular mode during the past 30 years arise from atmospheric internal variability. To address this question, a synthetic time series is generated that has the same intraseasonal stochastic properties as the annular mode. By generating a distribution of linear trend values for the synthetic time series, and through a chi-square statistical analysis, it is shown that this trend and variance increase are well in excess of the level expected from internal variability of the atmosphere. This implies that both the trend and the variance increase of the annular mode are due either to coupling with the hydrosphere and/or cryosphere or to driving external to the climate system. This behavior contrasts that of the first 60 years of the twentieth century, for which it is shown that all of the interannual variability of the annular mode can be explained by atmospheric internal variability.

## 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 Protectionâ€“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

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 Protectionâ€“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 atmospheric dynamical processes that drive intraseasonal polar motion are examined with National Centers for Environmental Predictionâ€“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 7.5â€“13 and 13â€“90 days. Regressions of surface pressure reveal that the 7.5â€“13-day band corresponds to the 10-day atmospheric normal mode and the 13â€“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 waveâ€“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 that drive intraseasonal polar motion are examined with National Centers for Environmental Predictionâ€“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 7.5â€“13 and 13â€“90 days. Regressions of surface pressure reveal that the 7.5â€“13-day band corresponds to the 10-day atmospheric normal mode and the 13â€“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 waveâ€“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 poleward propagation of zonal-mean relative angular momentum (*M*
_{R}) anomalies is examined using NCEPâ€“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 poleward propagation of zonal-mean relative angular momentum (*M*
_{R}) anomalies is examined using NCEPâ€“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

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^{âˆ’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 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^{âˆ’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

This study uses National Centers for Environmental Predictionâ€“National Center for Atmospheric Research reanalysis data to investigate the extent to which interannual zonal index (ZI) fluctuations occur in the atmosphere and whether interannual ZI fluctuations can be accounted for by climate noise associated with the intraseasonal ZI. By using an empirical orthogonal function analysis, it is shown that the ZI is indeed a prominent form of interannual variability, because the interannual ZI corresponds to EOF1 (EOF2) for the winter (summer) seasons of both hemispheres. Also, by application of spectral, correlation, and *Ï‡*
^{2} analyses, it is shown that interannual ZI variability can be interpreted as arising from climate noise.

## Abstract

This study uses National Centers for Environmental Predictionâ€“National Center for Atmospheric Research reanalysis data to investigate the extent to which interannual zonal index (ZI) fluctuations occur in the atmosphere and whether interannual ZI fluctuations can be accounted for by climate noise associated with the intraseasonal ZI. By using an empirical orthogonal function analysis, it is shown that the ZI is indeed a prominent form of interannual variability, because the interannual ZI corresponds to EOF1 (EOF2) for the winter (summer) seasons of both hemispheres. Also, by application of spectral, correlation, and *Ï‡*
^{2} analyses, it is shown that interannual ZI variability can be interpreted as arising from climate noise.

## Abstract

A two-layer quasigeostrophic Î²-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

A two-layer quasigeostrophic Î²-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

The dynamical processes that drive intraseasonal equatorial atmospheric angular momentum (EAAM) fluctuations are examined with the National Centers for Environmental Predictionâ€“National Center for Atmospheric Research (NCEPâ€“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 Rossbyâ€“gravity waves and also by waveâ€“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 waveâ€“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 waveâ€“wave interaction to planetary scales.

## Abstract

The dynamical processes that drive intraseasonal equatorial atmospheric angular momentum (EAAM) fluctuations are examined with the National Centers for Environmental Predictionâ€“National Center for Atmospheric Research (NCEPâ€“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 Rossbyâ€“gravity waves and also by waveâ€“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 waveâ€“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 waveâ€“wave interaction to planetary scales.

## 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

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.