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G. Chimonas and D. Fua

Abstract

Small-scale (Kelvin-Helmholtz) shear instabilities usually display very little dispersion. However, investigations by Hazel reveal an anomalous modal structure when the length scales associated with the density and velocity gradients are sufficiently different. We examine this modal splitting, and discover two distinct families of small-scale waves. The mean phase velocities of the two families can be quite different. The result is of considerable interest in studies of nonlinear interactions among small-scale shear instabilities, since it greatly extends the phase speeds allowed to the resulting disturbances.

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D. Fuà and F. Einaudi

Abstract

We are presenting the results of a stability analysis of a background wind shear in the presence of stable stratification and of height dependent coefficients of eddy viscosity and eddy thermal conduction. It is shown that the vertical gradients of the eddy coefficients substantially affect the phase velocities, growth rates and vertical structure of the gravity wave and are responsible for the appearance of some counter-gradient heat fluxes and Reynolds stresses. It is suggested that these gradients may explain the observed counter-gradient fluxes in the stable atmospheric boundary layer.

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D. P. Lalas, F. Einaudi, and D. Fua

Abstract

The simple Kelvin-Helmholtz model for shear zones in the atmosphere is modified, by introducing a solid boundary below to account for the effect of the ground. The new characteristics of neutral and unstable waves that can exist in such configuration are analyzed for various values of wind velocity, depth of the bottom layer, and Brunt-Väisälä frequency. It is shown that the presence of the ground considerably destabilizes waves with long horizontal wavelengths. In particular, long wavelengths are always unstable, so that no neutral stability boundary exists. Furthermore, the solid lower boundary introduces an infinite number of neutral modes, all of which correspond to evanescent waves in the top layer. Finally, the model with the ground is used to calculate the characteristics of the most unstable waves that would be generated for some well-documented observed cases and the calculated values are found to be in reasonable agreement with observations.

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F. Einaudi, J. J. Finnigan, and D. Fuà

Abstract

The analysis of an earlier work on the interaction between an internal gravity wave and the wave-induced turbulence is extended here to the case where the wave is generated by vertical wind shear. The initial system is described by a background wind and a temperature distribution such that the Richardson number is less than ¼. A gravity wave is generated by such a dynamically unstable system and grows exponentially in time. The wave modifies the Richardson number and lowers it, particularly in the neighborhood of the critical level. When the generalized Richardson number falls below an assumed critical level, turbulence is assumed to develop and is described by a “1½th order” scheme. A diffusion coefficient can then be calculated which has a mean and a fluctuating part. It is the latter which turns out to be responsible for the positive feedback between the wave and the wave-induced turbulence resulting in the wave growing at a faster rate than the one predicted by linear theory.

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J. J. Finnigan, F. Einaudi, and D. Fua

Abstract

Observations have been made of a stably-stratified nighttime boundary layer perturbed by Kelvin-Helmholtz internal waves with critical levels around 600 m. Significant turbulence intensities were measured although the time-mean gradient Richardson numbers were large and positive. It is shown by constructing energy budgets of wave and turbulent components separately that there is an essential flow of kinetic energy from wave to turbulence and that the mechanics of this exchange process depend upon the nonlinear character of the wave field.

Turbulent energy budgets were followed through a wave cycle and revealed that turbulence production occurred during only one quarter of a wave period, the rest of the time being taken up by redistribution of turbulent kinetic energy (tke) among the three orthogonal components, relaxation under the effects of density stratification and dissipation. The principal path of energy dissipation is through conversion of vertical component tke to density fluctuations, which are in turn dissipated by molecular conductivity. Direct viscous dissipation of tke is negligible in comparison. This behavior is consistent with the quasi-two-dimensional character imposed on the turbulence by the strong stability and is clearly apparent in the behavior of the velocity and temperature spectra.

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G. Mastrantonio, F. Einaudi, D. Fua, and D. P. Lalas

Abstract

The characteristics of internal gravity waves generated by tropospheric jet streams are analyzed and discussed. By solving numerically the equations of motion in the linear, inviscid and Boussinesq limit, it is shown that a modal structure exists. Some of these modes have the ability to propagate vertically away from the jet and are likely to he responsible for some of the observed wave activities in the ionosphere as well as at the ground. For selected values of the minimum Richardson number of the flow, growth rates and horizontal phase velocities are given as functions of the horizontal wavenumber, for jet streams of varying width. Finally, a brief study of the stability of the so-called low-level jet, whose spectrum of generated waves undoubtedly will contribute to the dynamics of the nocturnal boundary layer, is undertaken.

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D. Fua, G. Chimonas, F. Einaudi, and O. Zeman

Abstract

We present the results of an analytical and numerical calculation of the interaction between an internal gravity wave and a wave-induced turbulence. The initial atmospheric state, assumed horizontally homogeneous, is statically and dynamically stable with the background Richardson number Ri0 approaching ¼ over some height regions. An initial non-singular neutral gravity wave propagates through such a system and modifies the Richardson number. The new Richardson number Ri may become smaller than ¼ and turbulence may develop. Using a “1½th order” scheme for the turbulence, we calculate the mean and the fluctuating part of the eddy diffusion coefficient. We show that the fluctuating part of the diffusion coefficient, because of its amplitude and phase, may overcome the damping effect of its mean part and force the original wave to grow in time. As the wave grows, it may further lower the Richardson number, increase the intensity of the turbulence, and further strengthen its interaction with it. At least in its initial stages, wave-induced turbulence appears to be an effective mechanism for transfer of energy from the background state into the wave. By showing that the early stages of the wave-induced turbulence interaction can lead to energy being transferred into the wave, we strengthen the case for gravity waves as important elements in the generation of turbulence in the atmosphere. The values we obtain for the eddy diffusion coefficients suggest that the process is quite capable of producing the empirically observed mixing rates at substantial heights above the ground. While the present calculations cannot describe the long-time limit of the wave-turbulence system, one may suggest that the often observed atmospheric conditions in which turbulence and waves appear to co-exist for several hours may result from a sort of equilibrium between the roles of the mean and the fluctuating parts of the eddy diffusion coefficient in taking away from and feeding energy into the wave.

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F. Einaudi, W. L. Clark, J. L. Green, T. E. VanZandt, and D. Fua

Abstract

In order to gain insight into the complex dynamics of a convective system interacting with a gravity wave train, we have carried out an experiment in northeast Colorado during July and August, 1983, utilizing data from several program areas in NOAA. Pressure data from the PROFS mesonetwork of microbarograph stations were combined with velocity profiles from the Wave Propagation Laboratory UHF wind profiler (ST) radar at Stapleton Airport in Denver and convective cell location data from the NWS Limon weather radar. Several events were clearly visible in the microbarograph data, from which four (called Events A, B, C and D) in late July were selected for further study. These events differed from each other in fundamental ways.

In each event the waves represent oscillations of a substantial depth of the troposphere and seem to appear and disappear together with the convective cells. In Events A and B the waves have a critical level and are probably unstable modes generated by wind shear in the jet stream, from which they extract energy. We suggest that the convective cells cause the selection of some modes over others in a system that is initially dynamically unstable. In Event A the wave appears to be locked together with the convective cells, which move at the same velocity as the phase velocity of the wave. The wave and the cells seem to grow and evolve synergetically. In Event B the wave and convective cells commence at about the same time, but the cell velocities are quite different from the wave phase velocity. The cell velocities vary substantially over the time of the event and appear to be controlled by the local winds.

In the Events C and D, the waves move faster than the maximum wind in the jet and at least twice as fast as the convective cells. It is suggested that these are nonsingular neutral modes whose excitation depends on a number of mechanisms, such as vertical convective motions and acceleration in the jet flow.

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