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David C. Fritts

Abstract

This paper addresses the efficiency and characteristics of two mechanisms that have been proposed to account for the excitation of radiating gravity waves by Kelvin-Helmholtz (KH) instabilities at a free shear layer in a stratified atmosphere. These mechanisms are the vortex pairing or subharmonic interaction observed to occur at the interface between two homogeneous fluid layers and the KH interaction or “envelope radiation” mechanism found to occur in the presence of propagating unstable modes. Vortex pairing in a stratified environment is found to be highly dependent on the minimum mean Richardson number, being very efficient when the subharmonic is itself a KH mode and relatively unimportant when the subharmonic has propagating character. The envelope radiation mechanism, in contrast, is observed to provide efficient radiating wave excitation in the absence of propagating unstable modes, as anticipated by Fritts. It is suggested that this latter mechanism may lead naturally to the excitation of large-scale gravity waves due to the horizontal inhomogeneity of unstable shear layers and may therefore constitute an important source of atmospheric gravity waves.

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David C. Fritts

Abstract

In this study we examine some of the effects of wave-wave interactions and convective adjustment on the propagation of gravity waves in the middle atmosphere. For both a nearly monochromatic wave and a super-position of waves, nonlinear wave-wave interactions, while reducing primary wave amplitudes somewhat, are found to be unable to prevent the formation of convectively unstable layers. In contrast, convective adjustment of the wave field causes significant amplitude reductions, resulting in amplitudes for a spectrum of wave motions that achieve only a fraction of their monochromatic saturation values. Neither process is found to cause a major disruption of the primary wave field.

Both wave-wave interactions and convective adjustment are found to excite harmonies of the primary wave motions. Excitation by convective adjustment appears to dominate for a monochromatic wave, whereas both processes become important for a spectrum of wave motions. In each case, the characteristics of the excited wave motions (i.e., phase tilt, intrinsic frequency, and direction of propagation) are found to be largely consistent with those of the primary waves.

These results are seen to be in qualitative agreement with atmospheric observations.

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David C. Fritts

Abstract

Previous studies have revealed a number of unstable modes in addition to the Kelvin-Helmholtz instability associated with a velocity shear in the presence of a rigid lower boundary. These additional modes occupy regions in the (α,Ri0) plane which are largely distinct from that occupied by the Kelvin-Helmholtz mode. In this note, we demonstrate that the location of the various unstable modes can be explained in part in terms of the modal structure above and below the velocity shear and the necessary condition for dynamical instability, Ric < 1/4, obtained by Miles (1961). An extension of the stability analysis of Lalas and Einaudi (1976) to a larger shear height reveals that all unstable modes belong to one of two mode families. Finally, we discuss the implication of these results for additional modes or families of modes and the possible roles of various modes in atmospheric dynamics.

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David C. Fritts

Abstract

Unstable Velocity shears are a Common source of vertically propagating gravity waves in the atmosphere. However, the growth rates of unstable modes predicted by linear theory cannot always amount for their observed importance.

We examine in this paper, using a numerical model, the nonlinear excitation and evolution of atmospheric gravity waves. It is found that such waves can reach large amplitudes and induce significant accelerations of the mean velocity profile, resulting in shear stabilization and jet formation. Unstable modes that are vertically propagating above and below the shear layer may, when growing in isolation, achieve a state of quasi-sustained radiation.

The nonlinear excitation of vertically propagating gravity waves via the interaction of two KH modes is found to be very rapid, providing an explanation for their occurrence in the atmosphere.

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David C. Fritts

Abstract

The gravity wave-critical level interaction is found to excite both radiating waves and Kelvin-Helmholtz instabilities through nonlinear interactions near the critical level. Radiating waves are forced directly by perturbations in the harmonies of the incident gravity wave and Kelvin-Helmholtz instabilities, once excited through nonlinear interactions, grow on the unstable velocity shears created by the incident wave. Results are presented which demonstrate that radiating waves can significantly increase the wave-action and momentum flux which is found above a critical level and that Kelvin-Helmholtz instabilities are responsible for stabilizing the induced unstable velocity shears. Finally, the implications of these results for the atmosphere and the oceans are discussed.

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David C. Fritts

Abstract

A nonlinear numerical model of the gravity wave-critical level interaction is developed in this paper. This model is used to examine and compare the effects of viscosity, time-dependence and nonlinear interactions on the development of the critical level interaction. It is found, in agreement with earlier studies, that viscosity and heat conduction strongly stabilize the interaction very near the critical level. Time-dependence and nonlinear interactions are found to be strongly stabilizing only for very transient or low viscosity flows, respectively. These two effects are very important, however, in the development of Kelvin-Helmholtz instabilities within unstable velocity shears. Once excited, these instabilities grow on the excess energy available in the unstable shears. When large unstable velocity shears are produced, the Kelvin-Helmholtz instabilities grow until they dominate the critical level interaction. It is argued that the break-down of these Kelvin-Helmholtz billows produced by the critical level interaction can explain some of the thin turbulent layers observed in the atmosphere and the oceans.

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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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Timothy J. Dunkerton
and
David C. Fritts

Abstract

Numerical simulations of vertically-propagating gravity waves interacting with critical layers are presented. For nearly monochromatic wave events, the wave amplitude behavior and mean zonal acceleration agree substantially with the predictions of the semi-analytic models of Grimshaw in 1975, Dunkerton in 1981–82 and Coy in 1983. A mean zonal wind “shock,” or steep sheer zone, forms at the base of a convectively unstable critical layer in these cases.

Because the semi-analytic model is based on the WKB approximation, the gravity wave, mean-flow interaction proceeds somewhat differently when this approximation is not accurate. For highly transient wave packets containing a broad frequency spectrum, momentum deposition and convective instability occurs over a much broader range of heights than predicted by the semi-analytic model. For nearly monochromatic waves, on the other hand, partial reflection from the internal mean flow shock is observed.

The inviscid gravity wave critical layer is inherently turbulent since overturning rapidly develops in the potential temperature field. Negative local Richardson numbers (Ri) are contemporaneous with the development of the internal shock in the monochromatic wave events, are coincident with Lagrangian zonal perturbation velocities exceeding the intrinsic phase speed, and occur very soon after the appearance of regions with Ri<¼. To account for convective wavebreaking a simple, local turbulence parameterization is advanced, which is not based upon turbulent eddy diffusion. Instead, the total wave plus mean flow profile, when required is frictionally relaxed to a convectively neutral equilibrium which conserves potential temperature and total vorticity, analogous to the familiar “convective adjustment” procedure in general circulation models. Despite being a local adjustment within the wave, this turbulence parameterization seems to confirm the amplitude-limiting effects predicted by Lindzen's global amplitude balance model in the relatively simple case studies presented here.

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Gregory D. Nastrom
and
David C. Fritts

Abstract

Aircraft measurements of winds and temperatures collected during the GASP program are used to study the effects of topography as a source of mesoscale variability. Variances of fluctuations at the mesoscale over rough terrain are enhanced up to nearly two orders of magnitude compared to nonsource regions in some cases and are frequently enhanced by an order of magnitude. The implications of these episodic enhancements of variances for the vertical transports of energy and momentum are considered in the framework of gravity wave theory. The observed flight data are used to estimate the momentum flux uw on several flight segments. Results show that the flux is generally negative with mean value −0.26 m2 s−2 and with magnitudes ranging up to −1.5 m2 s−2. Spectral analysis shows that the largest contributions to the net flux come from horizontal scales of ∼25 < λ x <60 km. Finally, the observed momentum fluxes are used to infer the anisotropy factor of gravity waves over rough terrain, which is found to be about 0.45.

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David C. Fritts
and
Gregory D. Nastrom

Abstract

We present studies of four cases of mesoscale variance enhancements of horizontal velocity and temperature due to frontal activity, nonfrontal convection, and wind shear. These data were obtained aboard commercial aircraft during the Global Atmospheric Sampling Program (GASP) in 1978 and 1979 and from the corresponding meteorological analyses and satellite imagery. Additional GASP data were used to permit a statistical assessment of the importance of various sources of enhanced variances. Our results, and those in a companion paper addressing the variance enhancements associated with topography, represent refinements of previous source analyses using the GASP dataset. Significant findings include mean variance enhancements of velocity and temperature due to convection and jet-stream flow ranging from ∼2 to 8 for 64-km and 256-km data segments, and enhancements for individual segments as high as ∼20 to 100. The mean 64-km variance enhancement for all variables and source types, relative to a quiescent background, was estimated to be 6.1. These results suggest a major role for localized sources in energizing the mesoscale motion spectrum at horizontal scales < ∼100 km, and correspondingly greater influences for such motions at greater heights.

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