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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

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

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

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

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 and Li Yuan

Abstract

We present a stability analysis of the environment due to a large-amplitude inertio—gravity wave. Our purpose is to examine the conditions under which the Kelvin-Helmholtz (KH) instability may be an effective wave saturation process in the middle atmosphere. The concurrence, range of wavenumber, and growth rate of the KH instability are shown to depend on the IGW frequency and the KH orientation within the wave field because of the influence of wave frequency on the shear and local stratification. Results of the analysis indicate that the KH instability is likely a preferred mode of instability for sufficiently low gravity wave frequencies, but that it cannot occur for high-frequency wave motions in the absence of a mean shear. Inertio—gravity waves are also most unstable to KH instabilities aligned transverse to the direction of large-scale wave propagation.

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David C. Fritts and Li Yuan

Abstract

Observations of the motion field near the summer mesopause using the Poker Flat MST radar in a symmetric six-beam configuration during 8 days of July 1986 were used to examine the mean structure, the wave variances, and the momentum fluxes due to gravity wave and tidal motions. Our results reveal a mean horizontal wind structure generally consistent with previous observations, but with considerable daily variability and large mean shears. Particularly significant is a mean downward (Eulerian) vertical velocity of ∼0.3 m s−1, which implies a significant upward flux of wave energy. Horizontal and vertical velocity variances are found to be ∼1500 and 6 m2 s−2 and to remain nearly constant with height. Momentum flux measurements reveal a largely zonal mean flux of ∼5 to 15 m2 s−2 that achieves a maximum just below the height of wind reversal. Daily mean values, on the other hand, exhibit large variability, with maxima as large as ∼30 to 40 m2 s−2. Hourly momentum flux profiles were found to achieve maximum values of ∼60 m2 s−2 and to exhibit variations that appear to correlate with the background wave environment. These observations imply significantly stronger forcing of the mean flow in this region than has been inferred at lower latitudes.

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David C. Fritts and Zhangai Luo

Abstract

Fourier integral and Green's function techniques are used to examine the gravity wave field and mean state arising from an initially unbalanced Gaussian jet. Approximate solutions specifying no mean motion reveal a wave field that is nearly inertial in character. Horizontal motions are symmetric about the jet axes, while vertical motions and the thermal field are antisymmetric. Full solutions of the initial-value problem yield a wave field that is qualitatively like that obtained in the absence of mean state adjustment and a mean jet structure with a balanced thermal field that conserves potential vorticity and is somewhat more extended vertically than the original unbalanced jet. The mean adjustment occurs within an inertial period and the scales and frequencies of the forced wave motions are controlled by the horizontal and vertical extent of the initial perturbation. We suggest that the excitation of inertio–gravity waves in this manner may explain some observations of such motions in association with jet streams and may contribute to the preponderance of gravity wave energy at near-inertial frequencies in the atmosphere.

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Lawrence Coy and David C. Fritts

Abstract

The effect of a vertically propagating, internal gravity wave on the vertical flux of potential temperature (heat) is considered by averaging the local heat flux vector over a potential temperature surface. This approach gives the wave heat flux a simple physical picture which is not readily apparent from the more common Eulerian formulation. This method also allows the eddy diffusion coefficient to be a function of the phase of the wave. Such a phase dependent eddy diffusion has been previously considered from an Eulerian viewpoint as a model of a convectively unstable gravity wave. Here, the Lagrangian method confirms and corrects the Eulerian results. Earlier work is extended by modeling a constant amplitude “breaking” wave, as well as by considering eddy diffusion coefficients that are asymmetric with respect to the wave breaking region. In all cases studied, 1ocalizing the eddy diffusion to the region of wayebreaking decreases the average heat flux.

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