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Takeshi Imamura, Takeshi Horinouchi, and Timothy J. Dunkerton

Abstract

A modified, equatorial Kelvin wave solution is obtained in the presence of the zonal-mean meridional circulation. The modified Kelvin wave solution, which is obtained via a perturbation expansion of the linearized, primitive equations on an equatorial β plane, possesses a nonzero meridional wind component. This meridional wind component is absent when the background flow is at rest. The combination of the meridional and zonal winds induces a meridional flux of zonal momentum in the upstream direction of the background north–south flow. This flux is divergent in latitude and produces a nonzero wave-induced force even though the waves are linear, steady, and conservative. It is shown that, although such a force violates the traditional nonacceleration theorem in which the mean meridional circulation is negligible at leading order, the result is in accord with a more general nonacceleration theorem obtained from the exact generalized Lagrangian-mean theory in which the mean meridional circulation is nonzero. The meridional circulation, in effect, attempts to advect wave pseudomomentum off the equator, resulting in a nonzero acceleration in the Eulerian reference frame. The meridional flux of momentum for any equatorially trapped mode is derived from the generalized Lagrangian-mean theory. Those modes with eastward (westward) intrinsic phase velocity transport eastward (westward) zonal momentum in the upstream direction of the background meridional flow in the neighborhood of the equator. It is also shown that the vertical flux of zonal momentum is not constant with altitude in a steady vertical flow since diabatic heating/cooling is needed to sustain the vertical wind. Implications of the results for the terrestrial and Venusian atmospheres are discussed.

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Timothy J. Dunkerton and Richard K. Scott

Abstract

An idealized analytical model of the barotropic potential vorticity (PV) staircase is constructed, constrained by global conservation of absolute angular momentum, perfect homogenization of PV in mixing zones between (prograde) westerly jets, and the requirement of barotropic stability. An imposed functional relationship is also assumed between jet speed and latitudinal separation using a multiple of the “dynamical Rossby wave” Rhines scale inferred from the strength of westerly jets. The relative simplicity of the barotropic system provides a simple relation between absolute angular momentum and PV (or absolute vorticity). A family of solutions comprising an arbitrary number of jets is constructed and is used to illustrate the restriction of jet spacing and strength imposed by the constraints of global conservation of angular momentum and barotropic stability. Asymptotic analysis of the theoretical solution indicates a limiting ratio of jet spacing to the dynamical Rhines scale equal to the square root of 6, meaning that westerly jets are spaced farther apart than predicted by the dynamical Rhines scale. It is inferred that an alternative “geometrical” Rhines scale for jet spacing can be obtained from conservation of absolute angular momentum on the sphere if the strength of zonal jets is known from other considerations. Numerical simulations of the full (nonaxisymmetric) equations reveal a pattern of zonal jet evolution that is consistent with our construction of ideal PV staircases in spherical geometry (which can be considered as limiting cases), as well as with the asymptotic analysis of a geometrical Rhines scale. The evolution of the PV staircase originating from an upscale cascade of energy in the barotropic model is therefore seen to depend on conservation of energy (for the strength of jets) and conservation of absolute angular momentum (for the spacing and number of jets). Further analysis of the numerical results confirms a “Taylor identity” relating the flux of eddy potential vorticity to mean-flow acceleration. Eddy fluxes are responsible for the occasional transitions between mode number as well as for maintaining the sharp westerly jets against small-scale dissipation. Suggestions are made for extending the theoretical model to PV staircases that are asymmetric between hemispheres or with latitudinal variation of amplitude, as modeled in the shallow-water system.

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David C. Fritts and Timothy J. Dunkerton

Abstract

We consider the implications of a nonuniform turbulent diffusion due to the IOM saturation of a gravity wave via convective instabilities. It is found that both wave and turbulence fluxes of heat can be reduced dramatically, depending on the amplitude of the wave motion and the extent to which the turbulent diffusion is localized. These results suggest that previous studies that assumed a uniform turbulent diffusion may have overestimated the beat and constituent fluxes due to gravity wave saturation.

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Timothy J. Dunkerton and Donald P. Delisi

Abstract

Twenty years of radiosonde data have been analyzed in an attempt to develop a latitudinal structure climatology of winds, temperature and geopotential at 30 and 50 mb in the equatorial stratosphere. The fine latitudinal resolution provided by the WMO station network reveals several interesting features in the latitudinal structure of the annual and quasi-biennial cycles which dominate this region. For example, the westerly and easterly acceleration phases of the quasi-biennial oscillation are markedly different. Westerly accelerations appear first at the equator, spreading outward with time to higher latitude and an more intense, on average, than the easterly accelerations. The easterly accelerations are more uniform in latitude, but leer uniform in time, sometimes occurring in two stages.

The quasi-biennial wind and temperature oscillations are symmetric about the equator, while the annual harmonic in zonal wind is antisymmetric about the equator, but is not proportional to the Coriolis parameter. Monthly mean zonal wind and temperature appear to be in thermal wind balance at the equator.

Some brief remarks are also made concerning variability of the quasi-biennial oscillation and the effects of El Chichón.

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David C. Fritts and Timothy J. Dunkerton

Abstract

We present the results of quasi-linear simulations performed to illuminate the effects of saturation and self-acceleration on gravity waves prompting into the middle atmosphere. It is shown for transient, horizontally monochromatic wave packets that self-accelerations due to transient mean wind accelerations can be a significant factor in the evolution. Self-accelerations represent a possibly major change in the phase speed of the wave motion and permit larger vertical wavelengths and vertical group velocities than would otherwise occur. In some instances, permit gravity wave motions to propagate well beyond an initial critical level, a phenomenon we label “critical-level dislocation.” This phenomenon does not occur under the slowly-varying (WKB) and single phase speed assumptions. As such, it may be an intrinsically non-WKB effect.

Saturation was modeled using a relaxational convective adjustment scheme. This was found to limit wave amplitudes without radically affecting the structure of the primary wave, as anticipated in the linear saturation theory. Due to gradual adjustment, however, wave amplitudes and momentum fluxes were larger than predicted by linear theory. Local saturation was also found to reduce but not eliminate the effects of self-acceleration and to permit the excitation of harmonics of the primary wave motion in a coherent manner.

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Donal O'sullivan and Timothy J. Dunkerton

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The excitation and propagation of inertia–gravity waves (IGWs) generated by an unstable baroclinic wave was examined with a high-resolution 3D nonlinear numerical model. IGWs arose spontaneously as the tropospheric jetstream was distorted by baroclinic instability and strong parcel accelerations took place, primarily in the jetstream exit region of the upper troposphere. Subsequent propagation of IGWs occurred in regions of strong windspeed-in the tropospheric and stratospheric jets, and in a cutoff low formed during the baroclinic lifecycle. IGWs on the flanks of these jets were rotated inward by differential advection and subsequently absorbed by the model's hyperdiffusion. Although absorption of IGWs at the sidewalls of the jet is an artifact of the model, IGW propagation was for the most pan confined to regions with an intrinsic period shorter than the local inertial period. Only a few IGWs were able to penetrate the middle stratosphere, due to weak winds or an unfavorable alignment of wavevector with respect to the mean flow.

IGWs are important both as a synoptic signal in the jetstream, which may influence subsequent tropospheric developments, and as a source of isentropic or cross-isentropic mixing in the lower stratosphere. The authors' results demonstrated for the first time numerically a significant isentropic displacement of potential vorticity isopleths due to IGWs above the tropopause. Since conditions for IGW propagation are favorable within a jet, a region of strong isentropic potential vorticity gradient, it is likely that inertia–gravity waves affect the permeability of the lower stratospheric vortex and may in some instances lead to stratosphere–troposphere exchange.

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M-Pascale Lelong and Timothy J. Dunkerton

Abstract

The three-dimensional breakdown of a large-amplitude, convectively stable inertia–gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that inertia–gravity waves in this region of parameter space break down preferentially via shear instability. In low-frequency waves the instability is ubiquitous, occurring simultaneously throughout the wave field, and the spectrum of instability energy is approximately, but not exactly, isotropic in azimuthal orientation. In higher-frequency waves, shear instability develops adjacent to the region of reduced static stability, and displays a preference for intermediate azimuths (e.g., near 45°). Near-inertial waves experience the fastest growing instabilities. The growth rate of shear instability drops off rapidly as the wave frequency is increased and, for all frequencies, increases with increasing wave amplitude. At most frequencies, the onset of modal shear instability occurs at a wave amplitude slightly above the theoretical stability boundary determined from a local Richardson number argument.

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Timothy J. Dunkerton and Mark P. Baldwin

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Using 25 years of National Meteorological Center (NMC) data for 1964–88 the relation between tropical and extratropical quasi-biennial oscillations (QBOs) was examined for zonally averaged quantities and planetary-wave Eliassen–Palm fluxes in the Northern Hemisphere winter. The extratropical QBO discussed by Holton and Tan existed in both temporal halves of the dataset. Autocorrelation analysis demonstrated that it was an important mode of interannual variability in the extratropical winter stratosphere. Correlation with the tropics was strongest when 40-mb equatorial winds were used to define the tropical QBO. Easterly phase at 40 mb implied a weaker than normal polar night jet and warmer than normal polar temperature and vice versa. An opposite relationship was obtained using 10-mb equatorial winds. The association between tropical and extra-tropical QBOs was observed in about 90% of the winters and was statistically significant.

It is shown that planetary-wave Eliassen–Palm fluxes were generally consistent with the extratropical QBO. These fluxes were more (less) convergent in the midlatitude (subtropical) upper stratosphere in the 40-mb east (= easterly) phase category relative to the west category. The composite difference in flux divergence was a dipole, the location of which coincided with the observed mean zonal wind anomaly. The difference was strongest in early- to midwinter. However, composites of planetary-wave life cycles were similar in the two phase categories, with only slightly more events, slightly larger events, and larger mean flow response in the east category. There was very good correlation between planetary-wave flux convergence and observed mean flow tendencies on a daily basis, but the tendencies were smaller in magnitude.

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Yoshio Kawatani, Kevin Hamilton, Kaoru Sato, Timothy J. Dunkerton, Shingo Watanabe, and Kazuyoshi Kikuchi

Abstract

Observational studies have shown that, on average, the quasi-biennial oscillation (QBO) exhibits a faster phase progression and shorter period during El Niño than during La Niña. Here, the possible mechanism of QBO modulation associated with ENSO is investigated using the MIROC-AGCM with T106 (~1.125°) horizontal resolution. The MIROC-AGCM simulates QBO-like oscillations without any nonorographic gravity wave parameterizations. A 100-yr integration was conducted during which annually repeating sea surface temperatures based on the composite observed El Niño conditions were imposed. A similar 100-yr La Niña integration was also conducted. The MIROC-AGCM simulates realistic differences between El Niño and La Niña, notably shorter QBO periods, a weaker Walker circulation, and more equatorial precipitation during El Niño than during La Niña. Near the equator, vertical wave fluxes of zonal momentum in the uppermost troposphere are larger and the stratospheric QBO forcing due to interaction of the mean flow with resolved gravity waves (particularly for zonal wavenumber ≥43) is much larger during El Niño. The tropical upwelling associated with the Brewer–Dobson circulation is also stronger in the El Niño simulation. The effects of the enhanced tropical upwelling during El Niño are evidently overcome by enhanced wave driving, resulting in the shorter QBO period. The integrations were repeated with another model version (MIROC-ECM with T42 horizontal resolution) that employs a parameterization of nonorographic gravity waves in order to simulate a QBO. In the MIROC-ECM the average QBO periods are nearly identical in the El Niño and La Niña simulations.

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Yoshio Kawatani, Shingo Watanabe, Kaoru Sato, Timothy J. Dunkerton, Saburo Miyahara, and Masaaki Takahashi

Abstract

Three-dimensional wave forcing of simulated quasi-biennial oscillation (QBO) is investigated using a high-resolution atmospheric general circulation model with T213L256 resolution (60-km horizontal and 300-m vertical resolution). In both the eastward and westward wind shear phases of the QBO, nearly all Eliassen–Palm flux (EP flux) divergence due to internal inertia–gravity waves (defined as fluctuations with zonal wavenumber ≥12) results from the divergence of the vertical component of the flux. On the other hand, EP flux divergence due to equatorial trapped waves (EQWs) results from both the meridional and vertical components of the flux in regions of strong vertical wind shear. Longitudinal dependence of wave forcing is also investigated by three-dimensional wave activity flux applicable to gravity waves. Near the top of the Walker circulation, strong eastward (westward) wave forcing occurs in the Eastern (Western) Hemisphere due to internal inertia–gravity waves with small horizontal phase speed. In the eastward wind shear zone associated with the QBO, the eastward wave forcing due to internal inertia–gravity waves in the Eastern Hemisphere is much larger than that in the Western Hemisphere, whereas in the westward wind shear zone, westward wave forcing does not vary much in the zonal direction. Zonal variation of wave forcing in the stratosphere results from (i) zonal variation of wave sources, (ii) the vertically sheared zonal winds associated with the Walker circulation, and (iii) the phase of the QBO.

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