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## Abstract

A formulation is proposed to analyze energetics of the global atmosphere. To see effects of wave–mean-flow interaction and Lagrangian mean meridional circulation from nonlinear and nongeostrophic senses, rate equations of potential and kinetic energies are derived from primitive equations expressed in terms of the pressure–isentrope hybrid–vertical coordinates. The present scheme does not directly exchange the zonal mean available potential energy with the eddy available potential energy but does exchange the zonal mean kinetic energy with the eddy available potential energy. The latter is contributed to by the vertical divergence of the form drag over isentropic surfaces, which is the major term of the Eliassen–Palm flux divergence.

One application is made to two-dimensional (a longitude–altitude plane) channel fluid. This system has no energy conversion between the mean and eddy kinetic energies. In the process of wave–mean-flow interactions, the mean flow amplifies waves through the advection of positive isentropic thickness anomaly toward higher portions over undulated isentropes and, accordingly, the mean kinetic energy is converted into the eddy available potential energy. The eddy available potential energy is converted into the eddy kinetic energy when the flow field deforms, conserving the mean zonal flows.

Another application is made to baroclinic instability waves. The zonal mean available potential energy is released to the zonal mean kinetic energy by driving mean meridional wind. Simultaneously the kinetic energy of mean zonal wind is converted into the eddy available potential energy through wave–mean-flow interactions. Under the geostrophic equilibrium condition, these two conversions are almost equal to each other. Geostrophic adjustments may assist conversions from the eddy available potential energy into the eddy kinetic energy. All the processes might be the main stream of dynamical energy flows at mid- and high latitudes.

## Abstract

A formulation is proposed to analyze energetics of the global atmosphere. To see effects of wave–mean-flow interaction and Lagrangian mean meridional circulation from nonlinear and nongeostrophic senses, rate equations of potential and kinetic energies are derived from primitive equations expressed in terms of the pressure–isentrope hybrid–vertical coordinates. The present scheme does not directly exchange the zonal mean available potential energy with the eddy available potential energy but does exchange the zonal mean kinetic energy with the eddy available potential energy. The latter is contributed to by the vertical divergence of the form drag over isentropic surfaces, which is the major term of the Eliassen–Palm flux divergence.

One application is made to two-dimensional (a longitude–altitude plane) channel fluid. This system has no energy conversion between the mean and eddy kinetic energies. In the process of wave–mean-flow interactions, the mean flow amplifies waves through the advection of positive isentropic thickness anomaly toward higher portions over undulated isentropes and, accordingly, the mean kinetic energy is converted into the eddy available potential energy. The eddy available potential energy is converted into the eddy kinetic energy when the flow field deforms, conserving the mean zonal flows.

Another application is made to baroclinic instability waves. The zonal mean available potential energy is released to the zonal mean kinetic energy by driving mean meridional wind. Simultaneously the kinetic energy of mean zonal wind is converted into the eddy available potential energy through wave–mean-flow interactions. Under the geostrophic equilibrium condition, these two conversions are almost equal to each other. Geostrophic adjustments may assist conversions from the eddy available potential energy into the eddy kinetic energy. All the processes might be the main stream of dynamical energy flows at mid- and high latitudes.

## Abstract

A set of mass-weighted zonal mean equations in a pressure–isentrope hybrid vertical coordinate is derived. This formulation is able to present the nonacceleration theorem in ageostrophic and finite-amplitude sense.

## Abstract

A set of mass-weighted zonal mean equations in a pressure–isentrope hybrid vertical coordinate is derived. This formulation is able to present the nonacceleration theorem in ageostrophic and finite-amplitude sense.

## Abstract

In this study, the impacts of evaporative cooling from raindrops on a tropical cyclone (TC) are examined using cloud-resolving simulations under an idealized condition. of this study showed that evaporative cooling greatly increases the kinetic energy of a TC and its size because rainbands provide a large amount of condensation heating outside the eyewall. Part II investigates characteristics of simulated rainbands in detail. Rainbands are actively formed, even outside the eyewall, in the experiment including evaporative cooling, whereas they are absent in the experiment without evaporative cooling. Rainbands propagate in the counterclockwise and radially outward direction, and such behaviors are closely related to cold pools. New convective cells are successively generated at the upstream end of a cold pool, which is referred to here as the upstream development. The upstream development organizes spiral-shaped rainbands along a low-level streamline that is azimuthally averaged and propagates them radially outward. Asymmetric flows from azimuthally averaged low-level wind advance cold pool fronts in the normal direction to rainbands, which are referred to here as cross-band propagation. The cross-band propagation deflects the movement of each cell away from the low-level streamlines and rotates it in the counterclockwise direction. Cross-band propagation plays an essential role in the maintenance of rainbands. Advancement of cold pool fronts lifts up the warm and moist air mass slantwise and induces heavy precipitation. Evaporative cooling from raindrops induces downdrafts and gives feedback to the enhancement of cold pools.

## Abstract

In this study, the impacts of evaporative cooling from raindrops on a tropical cyclone (TC) are examined using cloud-resolving simulations under an idealized condition. of this study showed that evaporative cooling greatly increases the kinetic energy of a TC and its size because rainbands provide a large amount of condensation heating outside the eyewall. Part II investigates characteristics of simulated rainbands in detail. Rainbands are actively formed, even outside the eyewall, in the experiment including evaporative cooling, whereas they are absent in the experiment without evaporative cooling. Rainbands propagate in the counterclockwise and radially outward direction, and such behaviors are closely related to cold pools. New convective cells are successively generated at the upstream end of a cold pool, which is referred to here as the upstream development. The upstream development organizes spiral-shaped rainbands along a low-level streamline that is azimuthally averaged and propagates them radially outward. Asymmetric flows from azimuthally averaged low-level wind advance cold pool fronts in the normal direction to rainbands, which are referred to here as cross-band propagation. The cross-band propagation deflects the movement of each cell away from the low-level streamlines and rotates it in the counterclockwise direction. Cross-band propagation plays an essential role in the maintenance of rainbands. Advancement of cold pool fronts lifts up the warm and moist air mass slantwise and induces heavy precipitation. Evaporative cooling from raindrops induces downdrafts and gives feedback to the enhancement of cold pools.

## Abstract

A transport equation based on mass-weighted isentropic zonal means applies to the diagnosis for the meridional ozone transport in the troposphere and stratosphere. The mean and eddy ozone fluxes are estimated from the global distributions of the temperature, wind, and ozone.

In comparison with the conventional Eulerian mean and transformed Eulerian mean (TEM), the present diagnosis has advantages for the expression of eddy transport terms. The adiabatic eddy flux is separated from the diabatic eddy flux, which is parallel to the isentropic surface. The analysis shows that the eddy flux is almost adiabatic except that it is significantly affected by diabatic effects near the lower troposphere. Another advantage lies in the mean meridional transport. Although it is almost similar to the TEM, significant differences can be found near the Antarctic polar vortex due to nongeostrophic effects. Furthermore, the isentropic diagnosis expresses a strong equatorward flux near the lower boundary, while the TEM hardly does this because of inadequate treatment of the lower-boundary conditions.

The life cycle of ozone can be understood through the exact estimation of the transport terms. Although the stratospheric meridional transport is mainly performed by the Brewer–Dobson circulation, the strong poleward eddy ozone flux is caused by planetary wave breaking, especially in the winter hemisphere. In the extratropics, the ozone subsides from the stratosphere to the troposphere by mean downward motions, mainly diffused to the lower latitudes probably due to strong baroclinic waves and effectively lost through chemical processes in the lower troposphere.

## Abstract

A transport equation based on mass-weighted isentropic zonal means applies to the diagnosis for the meridional ozone transport in the troposphere and stratosphere. The mean and eddy ozone fluxes are estimated from the global distributions of the temperature, wind, and ozone.

In comparison with the conventional Eulerian mean and transformed Eulerian mean (TEM), the present diagnosis has advantages for the expression of eddy transport terms. The adiabatic eddy flux is separated from the diabatic eddy flux, which is parallel to the isentropic surface. The analysis shows that the eddy flux is almost adiabatic except that it is significantly affected by diabatic effects near the lower troposphere. Another advantage lies in the mean meridional transport. Although it is almost similar to the TEM, significant differences can be found near the Antarctic polar vortex due to nongeostrophic effects. Furthermore, the isentropic diagnosis expresses a strong equatorward flux near the lower boundary, while the TEM hardly does this because of inadequate treatment of the lower-boundary conditions.

The life cycle of ozone can be understood through the exact estimation of the transport terms. Although the stratospheric meridional transport is mainly performed by the Brewer–Dobson circulation, the strong poleward eddy ozone flux is caused by planetary wave breaking, especially in the winter hemisphere. In the extratropics, the ozone subsides from the stratosphere to the troposphere by mean downward motions, mainly diffused to the lower latitudes probably due to strong baroclinic waves and effectively lost through chemical processes in the lower troposphere.

## Abstract

Cloud-resolving simulations of an ideal tropical cyclone (TC) on an *f* plane are performed to investigate the effects of evaporative cooling on the evolution and structure of a TC. Evaporative cooling has markedly different impacts on the TC development and structure than melting/sublimation cooling because of the formation of rainbands. Evaporative cooling suppresses the organization of a TC at the early development stage. Evaporative cooling effectively forms convective downdrafts that cool and dry the boundary layer. Stabilizing the TC boundary layer reduces convective available potential energy (CAPE) around the eyewall by about 40% and slows the development. However, at the mature stage evaporative cooling steadily develops the TC for a longer period and enlarges the TC size because of rainbands, which are formed by the cold pool associated with evaporative cooling outside the eyewall. The large amounts of latent heating greatly induce the secondary circulation and transport large absolute angular momentum inward around the midtroposphere, resulting in the steady development of the TC. After a three-day integration, both the area-averaged precipitation and the kinetic energy become greater than when evaporative cooling is excluded.

## Abstract

Cloud-resolving simulations of an ideal tropical cyclone (TC) on an *f* plane are performed to investigate the effects of evaporative cooling on the evolution and structure of a TC. Evaporative cooling has markedly different impacts on the TC development and structure than melting/sublimation cooling because of the formation of rainbands. Evaporative cooling suppresses the organization of a TC at the early development stage. Evaporative cooling effectively forms convective downdrafts that cool and dry the boundary layer. Stabilizing the TC boundary layer reduces convective available potential energy (CAPE) around the eyewall by about 40% and slows the development. However, at the mature stage evaporative cooling steadily develops the TC for a longer period and enlarges the TC size because of rainbands, which are formed by the cold pool associated with evaporative cooling outside the eyewall. The large amounts of latent heating greatly induce the secondary circulation and transport large absolute angular momentum inward around the midtroposphere, resulting in the steady development of the TC. After a three-day integration, both the area-averaged precipitation and the kinetic energy become greater than when evaporative cooling is excluded.

## Abstract

A cascade-type energy conversion diagram is proposed for the purpose of diagnosing the atmospheric general circulation based on wave–mean flow interactions. Mass-weighted isentropic zonal means facilitate the expression of nongeostrophic wave effects, conservation properties, and lower boundary conditions. To gain physical insights into energetics based on the nonacceleration theorem, the wave energy *W* is defined as the sum of the eddy available potential energy *P _{E}* and the eddy kinetic energy

*K*.

_{E}The mainstream of the energy cascade is as follows: The diabatic heating produces the zonal mean available potential energy *P _{Z}*, which is converted into the zonal mean kinetic energy

*K*through the mean meridional circulation. The

_{Z}*K*is mainly converted to

_{Z}*W*through zonal wave–mean flow interactions and the rest is dissipated through friction. Not only the dynamical conversion but also the diabatic heating generates

*W*, which is dissipated through friction.

A diagnosis package is designed to analyze actual atmospheric data on the standard pressure surfaces. A validation study of the package is made by using the output from a general circulation model. The scheme accurately expresses tendencies of the zonal mean and eddy available potential energy equations, showing the diagnosis capability. On shorter time scales, *P _{E}* changes in accordance with

*K*, good correlation indicating the relevance of the definition of wave energy.

_{E}A preliminary study is made of the climate in December–February (DJF), and June–August (JJA), using the NCEP–NCAR reanalysis. The dynamical wave energy generation rate *C*(*K _{Z}*,

*W*) is about 60% of the conversion rate

*C*(

*P*,

_{Z}*K*), which means that

_{Z}*K*is dissipated through friction at a rate of about 40%. In the extratropics,

_{Z}*C*(

*K*,

_{Z}*W*) is almost equal to

*C*(

*P*,

_{Z}*K*), as is expected from quasigeostrophic balance. In the subtropics, however,

_{Z}*C*(

*K*,

_{Z}*W*) is much smaller than

*C*(

*P*,

_{Z}*K*), which suggests the importance of nongeostrophic effects on the energetics. The energetics is substantially different between the two solstices. Both

_{Z}*C*(

*P*,

_{Z}*K*) and

_{Z}*C*(

*K*,

_{Z}*W*) are about 30% larger in DJF than those in JJA, reflecting differences in wave activity. Stationary waves contribute considerably to energy conversions in the Northern Hemispheric winter, while baroclinic instability waves do more in the Southern Hemispheric winter than in the Northern Hemispheric winter.

## Abstract

A cascade-type energy conversion diagram is proposed for the purpose of diagnosing the atmospheric general circulation based on wave–mean flow interactions. Mass-weighted isentropic zonal means facilitate the expression of nongeostrophic wave effects, conservation properties, and lower boundary conditions. To gain physical insights into energetics based on the nonacceleration theorem, the wave energy *W* is defined as the sum of the eddy available potential energy *P _{E}* and the eddy kinetic energy

*K*.

_{E}The mainstream of the energy cascade is as follows: The diabatic heating produces the zonal mean available potential energy *P _{Z}*, which is converted into the zonal mean kinetic energy

*K*through the mean meridional circulation. The

_{Z}*K*is mainly converted to

_{Z}*W*through zonal wave–mean flow interactions and the rest is dissipated through friction. Not only the dynamical conversion but also the diabatic heating generates

*W*, which is dissipated through friction.

A diagnosis package is designed to analyze actual atmospheric data on the standard pressure surfaces. A validation study of the package is made by using the output from a general circulation model. The scheme accurately expresses tendencies of the zonal mean and eddy available potential energy equations, showing the diagnosis capability. On shorter time scales, *P _{E}* changes in accordance with

*K*, good correlation indicating the relevance of the definition of wave energy.

_{E}A preliminary study is made of the climate in December–February (DJF), and June–August (JJA), using the NCEP–NCAR reanalysis. The dynamical wave energy generation rate *C*(*K _{Z}*,

*W*) is about 60% of the conversion rate

*C*(

*P*,

_{Z}*K*), which means that

_{Z}*K*is dissipated through friction at a rate of about 40%. In the extratropics,

_{Z}*C*(

*K*,

_{Z}*W*) is almost equal to

*C*(

*P*,

_{Z}*K*), as is expected from quasigeostrophic balance. In the subtropics, however,

_{Z}*C*(

*K*,

_{Z}*W*) is much smaller than

*C*(

*P*,

_{Z}*K*), which suggests the importance of nongeostrophic effects on the energetics. The energetics is substantially different between the two solstices. Both

_{Z}*C*(

*P*,

_{Z}*K*) and

_{Z}*C*(

*K*,

_{Z}*W*) are about 30% larger in DJF than those in JJA, reflecting differences in wave activity. Stationary waves contribute considerably to energy conversions in the Northern Hemispheric winter, while baroclinic instability waves do more in the Southern Hemispheric winter than in the Northern Hemispheric winter.

## Abstract

The present study develops a diagnostic framework for investigating the three-dimensional (3D) structure of mass-weighted isentropic time-mean (T-MIM) meridional circulations and conducts a preliminary analysis of the winter hemispheres. The T-MIM meridional velocity can unfold, in the zonal direction, time-averaged two-dimensional (2D) mass-weighted isentropic zonal means. Furthermore, the T-MIM velocity can be decomposed into the unweighted isentropic time-mean (uTM) velocity and the temporal eddy-correlated transport velocity, the so-called bolus velocity. The bolus velocity greatly contributes to the 2D extratropical direct circulation in the troposphere and to the Brewer–Dobson circulation in the stratosphere. The 3D bolus velocity seems to reflect the geographical distributions of baroclinic instability wave activity. In the boreal winter, both low-level equatorward flows and upper-level poleward flows are located around the North Pacific and North Atlantic storm tracks. In the austral winter, low-level equatorward flows extend zonally across the midlatitudes. In the subtropics, the 3D bolus velocity is found to be significant in the upper branch of the Hadley circulation. A zonal momentum equation is formulated to examine the 3D momentum balance of the meridional circulation in the T-MIM framework. In the extratropics, the uTM and bolus meridional velocities are in geostrophic balance with the stationary and transient components of the 3D Eliassen–Palm (EP) flux divergence, respectively. The pressure gradient force of transient baroclinic instability waves balances with the low-level equatorward flows of the bolus velocity in the storm tracks.

## Abstract

The present study develops a diagnostic framework for investigating the three-dimensional (3D) structure of mass-weighted isentropic time-mean (T-MIM) meridional circulations and conducts a preliminary analysis of the winter hemispheres. The T-MIM meridional velocity can unfold, in the zonal direction, time-averaged two-dimensional (2D) mass-weighted isentropic zonal means. Furthermore, the T-MIM velocity can be decomposed into the unweighted isentropic time-mean (uTM) velocity and the temporal eddy-correlated transport velocity, the so-called bolus velocity. The bolus velocity greatly contributes to the 2D extratropical direct circulation in the troposphere and to the Brewer–Dobson circulation in the stratosphere. The 3D bolus velocity seems to reflect the geographical distributions of baroclinic instability wave activity. In the boreal winter, both low-level equatorward flows and upper-level poleward flows are located around the North Pacific and North Atlantic storm tracks. In the austral winter, low-level equatorward flows extend zonally across the midlatitudes. In the subtropics, the 3D bolus velocity is found to be significant in the upper branch of the Hadley circulation. A zonal momentum equation is formulated to examine the 3D momentum balance of the meridional circulation in the T-MIM framework. In the extratropics, the uTM and bolus meridional velocities are in geostrophic balance with the stationary and transient components of the 3D Eliassen–Palm (EP) flux divergence, respectively. The pressure gradient force of transient baroclinic instability waves balances with the low-level equatorward flows of the bolus velocity in the storm tracks.

## Abstract

Mechanisms that control the formation and decay of meridional gradients in stratospheric trace species in the subtropics and around the polar vortex are investigated using a gradient genesis equation that uses mass-weighted isentropic zonal means. Application of this method to global nitrous oxide (N_{2}O) data output from a global chemical transport model shows that mean vertical transport increases the meridional tracer gradient from the subtropics to midlatitudes through the shearing deformation, particularly related to overturning of the Brewer–Dobson circulation. Mean meridional transport advects the subtropical tracer gradient toward midlatitudes, while the eddy stairstep effect, steepening at the edge of the well-mixed region because of a meridional gradient in the diffusion coefficient, increases the tracer gradient in the subtropics and around the polar vortex. Mechanisms controlling the evolution of the tracer gradients in the subtropics differ between spring and autumn. The autumnal subtropical tracer gradient maximum is generated mainly from shearing deformation of the mean vertical transport, but less from mean and eddy meridional fluxes. In spring, the eddy stairstep effect also contributes to the generation of the subtropical tracer gradient maximum. Strong divergence forces stretching deformation that causes the springtime subtropical tracer gradient to decay. The gradient genesis mechanism around the Antarctic polar vortex is significantly different from that in the subtropics. Development of the tracer gradient around the Antarctic polar vortex is mostly controlled by mean meridional stretching motion in the middle stratosphere. Vertical advection and eddy smoothing effects flatten the tracer gradient as the polar vortex decays.

## Abstract

Mechanisms that control the formation and decay of meridional gradients in stratospheric trace species in the subtropics and around the polar vortex are investigated using a gradient genesis equation that uses mass-weighted isentropic zonal means. Application of this method to global nitrous oxide (N_{2}O) data output from a global chemical transport model shows that mean vertical transport increases the meridional tracer gradient from the subtropics to midlatitudes through the shearing deformation, particularly related to overturning of the Brewer–Dobson circulation. Mean meridional transport advects the subtropical tracer gradient toward midlatitudes, while the eddy stairstep effect, steepening at the edge of the well-mixed region because of a meridional gradient in the diffusion coefficient, increases the tracer gradient in the subtropics and around the polar vortex. Mechanisms controlling the evolution of the tracer gradients in the subtropics differ between spring and autumn. The autumnal subtropical tracer gradient maximum is generated mainly from shearing deformation of the mean vertical transport, but less from mean and eddy meridional fluxes. In spring, the eddy stairstep effect also contributes to the generation of the subtropical tracer gradient maximum. Strong divergence forces stretching deformation that causes the springtime subtropical tracer gradient to decay. The gradient genesis mechanism around the Antarctic polar vortex is significantly different from that in the subtropics. Development of the tracer gradient around the Antarctic polar vortex is mostly controlled by mean meridional stretching motion in the middle stratosphere. Vertical advection and eddy smoothing effects flatten the tracer gradient as the polar vortex decays.

## Abstract

The Lagrangian characteristics of vertical motions around the Antarctic polar vortex are investigated using a general circulation model (GCM) and various analysis methods. A trace analysis that estimated the vertical velocity from the vertical displacement of tracer isopleths confirmed that using zonal means at geographical latitudes gives a Lagrangian mean circulation around the Antarctic polar vortex similar to that computed using equivalent latitudes. In the mass-weighted isentropic zonal means, the mean vertical velocity dynamically estimated from the meridional velocity shows strong downward motion outside the Antarctic polar vortex around 45°–55°S in the lower stratosphere, which is consistent with the thermodynamically estimated values from the diabatic heating rate. In comparison, the transformed Eulerian mean analysis tends to overestimate the downward velocity outside the Antarctic polar vortex and underestimate it inside the Antarctic polar vortex. Trace analysis produces a good approximation of the dynamical estimate inside the Antarctic polar vortex, but it does not capture the strong downward velocity outside the vortex because of active horizontal mixing. If eddy mixing effects are included in the mean-meridional transport equation, the trace analysis agrees well with the dynamical estimate. The mean downward motion outside the Antarctic polar vortex causes adiabatic heating and contributes to the formation of the polar night jet stream from the lower to middle stratosphere through the thermal wind balance. Analysis of the mean vertical velocities in reanalysis products (assimilations) is very noisy compared to that from free running models because of dynamical inconsistencies caused by the assimilation process.

## Abstract

The Lagrangian characteristics of vertical motions around the Antarctic polar vortex are investigated using a general circulation model (GCM) and various analysis methods. A trace analysis that estimated the vertical velocity from the vertical displacement of tracer isopleths confirmed that using zonal means at geographical latitudes gives a Lagrangian mean circulation around the Antarctic polar vortex similar to that computed using equivalent latitudes. In the mass-weighted isentropic zonal means, the mean vertical velocity dynamically estimated from the meridional velocity shows strong downward motion outside the Antarctic polar vortex around 45°–55°S in the lower stratosphere, which is consistent with the thermodynamically estimated values from the diabatic heating rate. In comparison, the transformed Eulerian mean analysis tends to overestimate the downward velocity outside the Antarctic polar vortex and underestimate it inside the Antarctic polar vortex. Trace analysis produces a good approximation of the dynamical estimate inside the Antarctic polar vortex, but it does not capture the strong downward velocity outside the vortex because of active horizontal mixing. If eddy mixing effects are included in the mean-meridional transport equation, the trace analysis agrees well with the dynamical estimate. The mean downward motion outside the Antarctic polar vortex causes adiabatic heating and contributes to the formation of the polar night jet stream from the lower to middle stratosphere through the thermal wind balance. Analysis of the mean vertical velocities in reanalysis products (assimilations) is very noisy compared to that from free running models because of dynamical inconsistencies caused by the assimilation process.

## Abstract

The growth rate of baroclinic instability waves is generalized in terms of wave–mean flow interactions, with an emphasis on the influence of the vertical profile of baroclinicity. The wave energy is converted from the zonal mean kinetic energy and the growth rate is proportional to the mean zonal flow difference between the Eliassen–Palm (E-P) flux convergence and divergence areas. Mass-weighted isentropic zonal means facilitate the expression of the lower boundary conditions for the mass streamfunctions and E-P flux.

For Eady waves, intersections of isentropes with lower/upper boundaries induce the E-P flux divergence/convergence. The growth rate is proportional to the mean zonal flow difference between the two boundaries, indicating that baroclinicity at each level contributes evenly to the instability. The reduced zonal mean kinetic energy is compensated by a conversion from the zonal mean available potential energy.

Aquaplanet experiments are carried out to investigate the actual characteristics of baroclinic instability waves. The wave activity is shown to be sensitive to the upper-tropospheric baroclinicity, though it may be most sensitive to baroclinicity near 800 hPa, which is the maximal level of the E-P flux. The local wave energy generation rate suggests that the increased upper-tropospheric zonal flow directly enhances the upper-tropospheric wave energy at the midlatitudes. Note that the actual baroclinic instability waves accompany a considerable amount of the equatorward E-P flux, which causes extinction of wave energy in the subtropical upper troposphere.

## Abstract

The growth rate of baroclinic instability waves is generalized in terms of wave–mean flow interactions, with an emphasis on the influence of the vertical profile of baroclinicity. The wave energy is converted from the zonal mean kinetic energy and the growth rate is proportional to the mean zonal flow difference between the Eliassen–Palm (E-P) flux convergence and divergence areas. Mass-weighted isentropic zonal means facilitate the expression of the lower boundary conditions for the mass streamfunctions and E-P flux.

For Eady waves, intersections of isentropes with lower/upper boundaries induce the E-P flux divergence/convergence. The growth rate is proportional to the mean zonal flow difference between the two boundaries, indicating that baroclinicity at each level contributes evenly to the instability. The reduced zonal mean kinetic energy is compensated by a conversion from the zonal mean available potential energy.

Aquaplanet experiments are carried out to investigate the actual characteristics of baroclinic instability waves. The wave activity is shown to be sensitive to the upper-tropospheric baroclinicity, though it may be most sensitive to baroclinicity near 800 hPa, which is the maximal level of the E-P flux. The local wave energy generation rate suggests that the increased upper-tropospheric zonal flow directly enhances the upper-tropospheric wave energy at the midlatitudes. Note that the actual baroclinic instability waves accompany a considerable amount of the equatorward E-P flux, which causes extinction of wave energy in the subtropical upper troposphere.