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D. Jacqmin and R. S. Lindzen

Abstract

We have made high resolution calculations of the wintertime stationary atmospheric response to planetary scale topographic and thermal forcings. A numerical model has been used that solves the spherical primitive equations linearized about observed zonal wind and temperature fields. The model’s lid is placed high enough so that spurious reflections do not affect the results. Considerable attention has been paid to numerical accuracy.

The model’s response to realistic forcing is in general agreement with observational analysis of van Loon et al. We find that in middle latitudes the response to topographic forcing strongly dominates the response to thermal forcing. In the midlatitude troposphere, the topographic response is insensitive to changes in the zonal wind. The interannual variability of the tropospheric waves is due more to the heating response. The 500 mb amplitude of the interannual variability due to the sum of both forcings is, as indicated by our model, and as measured at the Himalayan low, less than 40 meters.

In the stratosphere, both the variance and mean are dominated by the topographic response. The sensitivity of the topographic response is much greater in the stratosphere than in the troposphere. Refractive index theory is found to adequately explain the variability of the response.

In general, sensitivity of the planetary waves to changes in the zonal wind is found to be much smaller than other recent calculations (Lin, Rong-hui and Gambo) have indicated. We believe that the high degree of sensitivity found by other models is spurious and due primarily to insufficient numerical resolution.

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R. S. Lindzen and B. Farrell

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R. S. Lindzen and Brian Farrell

Abstract

The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a β plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem, for the most part, has precluded extracting simple results of some generality. In this note, it is shown that there does exist a very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. Moreover, the result extends to substantially more general profiles than those in the Charney problem.

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R. S. Lindzen and S-S. Hong

Abstract

No abstract is available.

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R. L. Miller and R. S. Lindzen

Abstract

African waves are believed to originate as shear instabilities, although in certain cases rainfall is organized so that latent heating contributes to wave growth. What determines whether the shear instability can organize rainfall is considered here; in particular, why African waves organize rainfall mainly during the late summer, despite the regular occurrence of shear instability and rainfall throughout the season.During GATE, moisture convergence by the waves was also largest toward the late summer. It is assumed that an African wave will organize rainfall if it converges moisture—as measured by the ascent at the top of the moist layer—with sufficient amplitude. The wave amplitude is specified at some level beneath the 600-mb African jet, whose instability is a plausible source of the wave. The ascent is calculated using the quasigeostrophic potential vorticity and thermodynamic equations, and depends on the zonal wind separating the unstable jet from the top of the moist layer.Before turning to the example of the African jet, the more general behavior of the model is considered. In the absence of shear, a wave can arrive at the moist layer with undiminished amplitude. However, the ascent corresponding to this wave is small—less than the estimated ascent for Phase I of GATE when rainfall remained unorganized. For larger values of the shear, this threshold can be exceeded, although the ascent decays beneath the jet. Thus, the question arises whether a wave source can organize rainfall from an arbitrarily large distance above the moist layer. It is suggested that organization can only occur if the unstable jet is within a few kilometers of the moist layer and separated by large shear, although exceptions are noted.The calculation is applied to a wind profile resembling the observed 600-mb African jet. The wave amplitude decays beneath the jet so that the ascent at the top of the moist layer increases as the separation of the jet and moist layer decreases. Evidence is presented that the waves are closer to the moist layer during the late summer, resulting in larger ascent at this time.Large variations in the ascent can also occur even if the separation of the jet and moist layer remains constant. It is shown that the ascent can vary greatly as a result of small changes in the jet that are within its observed summer variability.

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R. S. Lindzen and C-Y. Tsay

Abstract

Stratospheric wind data for the Marshall Islands region during 1 April–1 July, 1958, are analyzed for contributions in the 4–6 day period range. It is shown that, excluding waves with vertical wavelengths <2 km from the data, 4–6 day power in the equatorial stratosphere during this period must be due to some combination of Kelvin, mixed gravity-Rossby, and n=1 Rossby waves with zonal wavenumbers <7–10. It is further shown that a theoretical model wherein each of the above three wave types is associated with a zonal wavenumber of either 3 or 4 is consistent with the data. The resulting observationally calibrated model is used to calculate the acceleration of the mean flow by wave absorption, which is then compared with the observed acceleration. In general, the waves satisfactorily account for accelerations above 23 km. Below 23 km there is a need for an additional source of easterly momentum with a specific vertical distribution which we show could be provided by an n=1 easterly gravity wave whose vertical wavelength, however, would be too short for the wave to be seen in radiosonde data. We also show that if a mean flow together with 4–6 day waves is spectral analyzed, there will be power at periods >4–6 days due to the acceleration of the mean flow by waves, and there may also be power at periods <4–6 days due to the modification of the waves by the changing mean flow. We finally examine what the theory suggests is happening at levels where wave absorption is altering the mean flow, and show, some of the difficulties in relating such behavior to data averaged over a three-month period.

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Mark R. Schoeberl and Richard S. Lindzen

Abstract

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen.

Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

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Richard S. Lindzen and Mark R. Schoeberl

Abstract

The constraints imposed by conservation of potential vorticity and hydrodynamic stability on the amplitude of Rossby waves are investigated.

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K. K. Tung and R. S. Lindzen

Abstract

In Part I a simple theory of resonant Rossby waves in a uniform zonal flow was developed. The present paper extends the previous results to the case of an atmosphere with winds varying with height. The wave responses to a large number of physically possible wind configurations are studied to help determine whether the observed wind fields in the winter atmosphere permit resonance of the large-scale waves and, in cases where resonance is possible, to search for the most favorable conditions for resonance. It is found that an increase in stratospheric jet strength and the descent of the stratospheric jet are both capable of exciting the resonant waves of zonal wavenumbers 1 and 2, with the latter (the descent of the stratospheric jet) being most effective in resonating the large-scale waves. The shorter waves (with zonal wavenumbers 3, 4 and up) are found to be insensitive to changes in wind conditions in the stratosphere as they are mostly trapped in the troposphere. These waves are easier to excite by changes in the wind conditions in the lower atmosphere. This finding may account for the higher frequency of occurrence of tropospheric blocking phenomena caused by the shorter waves (wavenumbers 3, 4 and up). The occurrence of large-scale (wavenumbers 1 and 2) blockings is seen to be relatively rare and is found to be usually accompanied by changes in stratospheric wind conditions.

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R. S. Lindzen and K. K. Tung

Abstract

It is shown that the necessary conditions for the instability of unstratified plane-parallel shear flow, rotating barotropic flows and rotating baroclinic flows are also sufficient conditions for the existence of propagating waves (essentially Rossby waves) and their overreflection (reflection coefficient exceeds 1 in magnitude) from critical levels (where flow speed and phase speed are equal). The identification of the unstable modes with overreflected waves is strongly suggested and allows greater insight into the meaning of various theorems such as Rayleigh’s inflection point theorem.

The present results also suggest an important distinction between instabilities associated with, redistribution such as Bénard convective instability and instabilities, such as those we are concerned with, associated with the self-excitation of waves.

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