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## Abstract

The wavenumber-frequency spectra of the kinetic energy of the zonal and meridional components of the motion in the mid-troposphere of the Southern Hemisphere show a definite spectral domain of wave activities. This spectral domain is generally oriented from a region of low wavenumbers and low frequencies to a region of high wavenumber and negative frequencies designated for waves moving from west to east. The wavenumber-frequency spectra of the large-scale motion indicate that wave activities in the summer have the same intensity as in the winter in the Southern Hemisphere, whereas in the Northern Hemisphere the wave intensity in summer is about 50% of that in winter.

The frequency spectra of the kinetic energy of the zonal and meridional components of the motion show similar distributions at all latitudes and seasons for the respective components of the motion. In the high-frequency range, the frequency spectra of both the zonal and meridional motion are approximately proportional to the –1 power of the frequency.

The wavenumber spectra of the kinetic energy of the zonal and meridional motion also show a similar distribution at all latitudes and seasons for the respective components of the motion. In the high-wave-number range, the spectra of both the zonal and meridional components of the motion are approximately proportional to the –3 power of the wavenumber, which is characteristic of the wavenumber spectrum for the two-dimensional flow of an incompressible viscous fluid. The fact that the wavenumber and frequency spectra are proportional to different powers of wavenumber and frequency indicates that Taylor's transformation does not apply to the large-scale motion in the atmosphere.

The mean kinetic energy of the zonal motion in the mid-troposphere of the Southern Hemisphere shows a maximum near 40S in winter and 50S in summer, with 75% of the kinetic energy of the zonal motion being associated with the stationary mean zonal motion and 25% with the zonal component of the moving waves.

The mean kinetic energy of the meridional component of the motion shows a maximum at 50S for both the summer and winter seasons. Practically all the kinetic energy of the meridional motion is associated with the moving waves.

## Abstract

The wavenumber-frequency spectra of the kinetic energy of the zonal and meridional components of the motion in the mid-troposphere of the Southern Hemisphere show a definite spectral domain of wave activities. This spectral domain is generally oriented from a region of low wavenumbers and low frequencies to a region of high wavenumber and negative frequencies designated for waves moving from west to east. The wavenumber-frequency spectra of the large-scale motion indicate that wave activities in the summer have the same intensity as in the winter in the Southern Hemisphere, whereas in the Northern Hemisphere the wave intensity in summer is about 50% of that in winter.

The frequency spectra of the kinetic energy of the zonal and meridional components of the motion show similar distributions at all latitudes and seasons for the respective components of the motion. In the high-frequency range, the frequency spectra of both the zonal and meridional motion are approximately proportional to the –1 power of the frequency.

The wavenumber spectra of the kinetic energy of the zonal and meridional motion also show a similar distribution at all latitudes and seasons for the respective components of the motion. In the high-wave-number range, the spectra of both the zonal and meridional components of the motion are approximately proportional to the –3 power of the wavenumber, which is characteristic of the wavenumber spectrum for the two-dimensional flow of an incompressible viscous fluid. The fact that the wavenumber and frequency spectra are proportional to different powers of wavenumber and frequency indicates that Taylor's transformation does not apply to the large-scale motion in the atmosphere.

The mean kinetic energy of the zonal motion in the mid-troposphere of the Southern Hemisphere shows a maximum near 40S in winter and 50S in summer, with 75% of the kinetic energy of the zonal motion being associated with the stationary mean zonal motion and 25% with the zonal component of the moving waves.

The mean kinetic energy of the meridional component of the motion shows a maximum at 50S for both the summer and winter seasons. Practically all the kinetic energy of the meridional motion is associated with the moving waves.

## Abstract

A 26-level primitive equation spherical harmonic spectral model allowing for both wave-wave and wave-zonal flow interactions is developed for the study of stratospheric sudden warmings simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. The fist two cases, designated N1 and L1, involve both wave-wave and wave-zonal flow interactions and only wave-zonal flow interactions, respectively, with wavenumber 1 forcing. The other two cases, N2 and L2, are the same as N1 and L1, respectively, except for wavenumber 2 forcing.

Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere particularly in case N1 as manifested by the split in the initial polar vortex into a quasi-wavenumber 2 pattern. Also in case N1 the weighted geopotential amplitude of wavenumber 2 is as much as 70% that of wavenumber 1. There is a tendency toward an out-of-phase relationship between the weighted geopotential amplitudes of wavenumbers 1 and 2 in the course of time integration. In fact, just prior to the sudden warming, the weighted geopotential amplitude of wavenumber 2 reaches maximum, while that of wavenumber 1 starts to weaken.

In cases N1 and N2 at 60°N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. Eventually two separate easterly layers are merged. The linear cases L1 and L2 exhibit warmings which are both more shallow and more intense at 30 km than the nonlinear cases. Wave-wave interactions present in cases N1 and N2 seem to moderate the restoring forces on the zonal flow contributed by Rayleigh friction and Newtonian cooling/heating included in the model. Comparisons of the present results with those of Matsuno (1971), Holton (1976) and Schoeberl and Strobel (1980) are discussed.

## Abstract

A 26-level primitive equation spherical harmonic spectral model allowing for both wave-wave and wave-zonal flow interactions is developed for the study of stratospheric sudden warmings simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. The fist two cases, designated N1 and L1, involve both wave-wave and wave-zonal flow interactions and only wave-zonal flow interactions, respectively, with wavenumber 1 forcing. The other two cases, N2 and L2, are the same as N1 and L1, respectively, except for wavenumber 2 forcing.

Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere particularly in case N1 as manifested by the split in the initial polar vortex into a quasi-wavenumber 2 pattern. Also in case N1 the weighted geopotential amplitude of wavenumber 2 is as much as 70% that of wavenumber 1. There is a tendency toward an out-of-phase relationship between the weighted geopotential amplitudes of wavenumbers 1 and 2 in the course of time integration. In fact, just prior to the sudden warming, the weighted geopotential amplitude of wavenumber 2 reaches maximum, while that of wavenumber 1 starts to weaken.

In cases N1 and N2 at 60°N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. Eventually two separate easterly layers are merged. The linear cases L1 and L2 exhibit warmings which are both more shallow and more intense at 30 km than the nonlinear cases. Wave-wave interactions present in cases N1 and N2 seem to moderate the restoring forces on the zonal flow contributed by Rayleigh friction and Newtonian cooling/heating included in the model. Comparisons of the present results with those of Matsuno (1971), Holton (1976) and Schoeberl and Strobel (1980) are discussed.

## Abstract

An analysis of the three-dimensional, large-scale movement of air particles for the winter months with the NCAR general circulation model indicates that the horizontal movement of particles in the upper troposphere is greatly affected by wave motion in mid- and high latitudes, by the field of horizontal convergence and divergence, and by mean meridional circulation in the tropics. The mean center of mass of particles in both hemispheres generally moves toward respective poles and the mean squire of the meridional component of the particle distances generally decreases with increasing time, indicating the effect of horizontal convergence on particle movement near the subtropics. The vertical movement of the particles is affected by upward motion near the thermal equator and downward motion near the subtropical region in the Northern and Southern Hemispheres. The vertical dispersion is most intense in the tropics and decreases toward the poles. There are two maxima of particle accumulation, one occurring near 15°N, the other near 30°S, and a minimum accumulation of particles appears near the thermal equator, indicating the effects of the divergence field and meridional circulation between the thermal equator and the subtropics.

The mean squares of zonal, meridional and vertical components of the distance for dusty” of particles released at the equator and 45°N appear to consist of two components, a monotonicaly increasing component due essentially to the effect of turbulent diffusion, and a periodic component due primarily to the horizontal velocity convergence and divergence of mean motion.

## Abstract

An analysis of the three-dimensional, large-scale movement of air particles for the winter months with the NCAR general circulation model indicates that the horizontal movement of particles in the upper troposphere is greatly affected by wave motion in mid- and high latitudes, by the field of horizontal convergence and divergence, and by mean meridional circulation in the tropics. The mean center of mass of particles in both hemispheres generally moves toward respective poles and the mean squire of the meridional component of the particle distances generally decreases with increasing time, indicating the effect of horizontal convergence on particle movement near the subtropics. The vertical movement of the particles is affected by upward motion near the thermal equator and downward motion near the subtropical region in the Northern and Southern Hemispheres. The vertical dispersion is most intense in the tropics and decreases toward the poles. There are two maxima of particle accumulation, one occurring near 15°N, the other near 30°S, and a minimum accumulation of particles appears near the thermal equator, indicating the effects of the divergence field and meridional circulation between the thermal equator and the subtropics.

The mean squares of zonal, meridional and vertical components of the distance for dusty” of particles released at the equator and 45°N appear to consist of two components, a monotonicaly increasing component due essentially to the effect of turbulent diffusion, and a periodic component due primarily to the horizontal velocity convergence and divergence of mean motion.

## Abstract

The wavenumber-frequency spectra of the meridional transport of angular momentum at 100, 200 and 500 mb, at 20, 40, 60 and 80N, show that there exist definite spectral domains of wave interactions between the zonal and meridional velocities at various latitudes. In the middle latitudes near 40N, the spectral band of the meridional transport of angular momentum is oriented from a region of low wavenumbers and low frequencies to a region of high wavenumbers and negative frequencies designated for eastward-moving waves. In low latitudes, however, the spectral band is confined to a narrow band centered near zero frequency.

An analysis of the linear and nonlinear contributions to the meridional transport of angular momentum in various wavenumber-frequency domains indicates that in the mid-troposphere the primary contribution to the nonlinear interactions always involves the interactions of the spectral domain of concern with the mean zonal flow and the stationary planetary waves. It is also found that except in the domain of low-frequency, eastward-moving cyclone waves the following characteristics are in common. 1) the meridional transport of angular momentum is directed toward the north pole; 2) the resultant of the nonlinear interactions due to the longitudinal convergence of the transport provides a poleward flux of angular momentum in the domains of eastward-moving waves, but provides an equatorward transport in the domains of westward-moving waves; 3) the resultant of the nonlinear interactions due to the latitudinal convergence of the transport generally contributes a poleward transport of angular momentum in the domains of westward-moving waves, but contributes an equatorward transport in the domains of eastward-moving waves; 4) the ageostrophic effect always counteracts the nonlinear interactions due to the longitudinal convergence of the transport of angular momentum; and 5) the effects of eddy and molecular stress forces generally work against the ageostrophic effect.

The frequency spectra of the meridional transport of angular momentum indicate that: 1) in the summer most of the transport is accomplished by the moving waves, the eastward-moving waves contributing to most of the poleward transport, and the westward-moving waves to the equatorward transport; 2) in the winter most of the transport is accomplished by the stationary waves, and both the eastward- and westward- moving waves contribute to the poleward transport of angular momentum.

The wavenumber spectra of the transport of angular momentum indicate that in both the summer and winter seasons waves of practically all wavelengths in low and middle latitudes contribute to the poleward transport of angular momentum. In high latitudes, however, only the very long waves contribute to the equatorward transport of angular momentum.

## Abstract

The wavenumber-frequency spectra of the meridional transport of angular momentum at 100, 200 and 500 mb, at 20, 40, 60 and 80N, show that there exist definite spectral domains of wave interactions between the zonal and meridional velocities at various latitudes. In the middle latitudes near 40N, the spectral band of the meridional transport of angular momentum is oriented from a region of low wavenumbers and low frequencies to a region of high wavenumbers and negative frequencies designated for eastward-moving waves. In low latitudes, however, the spectral band is confined to a narrow band centered near zero frequency.

An analysis of the linear and nonlinear contributions to the meridional transport of angular momentum in various wavenumber-frequency domains indicates that in the mid-troposphere the primary contribution to the nonlinear interactions always involves the interactions of the spectral domain of concern with the mean zonal flow and the stationary planetary waves. It is also found that except in the domain of low-frequency, eastward-moving cyclone waves the following characteristics are in common. 1) the meridional transport of angular momentum is directed toward the north pole; 2) the resultant of the nonlinear interactions due to the longitudinal convergence of the transport provides a poleward flux of angular momentum in the domains of eastward-moving waves, but provides an equatorward transport in the domains of westward-moving waves; 3) the resultant of the nonlinear interactions due to the latitudinal convergence of the transport generally contributes a poleward transport of angular momentum in the domains of westward-moving waves, but contributes an equatorward transport in the domains of eastward-moving waves; 4) the ageostrophic effect always counteracts the nonlinear interactions due to the longitudinal convergence of the transport of angular momentum; and 5) the effects of eddy and molecular stress forces generally work against the ageostrophic effect.

The frequency spectra of the meridional transport of angular momentum indicate that: 1) in the summer most of the transport is accomplished by the moving waves, the eastward-moving waves contributing to most of the poleward transport, and the westward-moving waves to the equatorward transport; 2) in the winter most of the transport is accomplished by the stationary waves, and both the eastward- and westward- moving waves contribute to the poleward transport of angular momentum.

The wavenumber spectra of the transport of angular momentum indicate that in both the summer and winter seasons waves of practically all wavelengths in low and middle latitudes contribute to the poleward transport of angular momentum. In high latitudes, however, only the very long waves contribute to the equatorward transport of angular momentum.

## Abstract

A primitive equation spectral model using spherical harmonics is formulated to study dynamic interactions between the troposphere and stratosphere in association with sudden stratospheric warmings. Using sigma coordinates for five tropospheric layers and log-pressure coordinates for 26 stratospheric and mesospheric layers separate model equations for each system are combined to form single matrix governing equations. The gradual introduction of large scale topography to balanced initial states representative of observed mean winter conditions in the Northern Hemisphere is used for the generation of planetary waves during 40-day time integrations. Results of these integrations indicate that stratospheric warnings can be simulated by this orographic forcing and that mean momentum flux divergence due to zonal mean motion appears to be an essential mechanism of these simulated sudden warmings. It was found that the strength of the polar night jet can be, a determining factor whether a warming becomes “major” or “minor.”

## Abstract

A primitive equation spectral model using spherical harmonics is formulated to study dynamic interactions between the troposphere and stratosphere in association with sudden stratospheric warmings. Using sigma coordinates for five tropospheric layers and log-pressure coordinates for 26 stratospheric and mesospheric layers separate model equations for each system are combined to form single matrix governing equations. The gradual introduction of large scale topography to balanced initial states representative of observed mean winter conditions in the Northern Hemisphere is used for the generation of planetary waves during 40-day time integrations. Results of these integrations indicate that stratospheric warnings can be simulated by this orographic forcing and that mean momentum flux divergence due to zonal mean motion appears to be an essential mechanism of these simulated sudden warmings. It was found that the strength of the polar night jet can be, a determining factor whether a warming becomes “major” or “minor.”