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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 and F. Einaudi

Abstract

Sufficient conditions for the stability of a moist atmosphere, with possible condensation occurring, in the presence of a background wind are given. The atmosphere is assumed saturated at all heights, and only frequencies below the audible range are considered. It is shown that the effect of condensation is essentially that of reducing the Brunt-Väisälä frequency and hence of decreasing the stability of the system.

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F. Einaudi and D. P. Lalas

Abstract

In this paper the stability and the propagation characteristics of internal gravity waves that propagate in an atmosphere near saturation and, over some height range, create the appropriate thermodynamic conditions for condensation to occur for a fraction of the wave cycle, are investigated. It is shown that if the atmosphere, over some height range, is close enough to saturation, a linear stability analysis is possible and results in a modified Richardson criterion, based on a new Brunt-Väisälä frequency nav smaller than the corresponding nu with condensation effects neglected. Since nav 2 can become negative, even though the atmosphere is originally statically stable, the ability of gravity waves to trigger convective processes in a moist atmosphere is demonstrated. Finally, a numerical example is presented to illustrate the alterations of the characteristics of propagation.

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F. Einaudi and D. P. Lalas

Abstract

The stability and characteristics of Kelvin-Helmholtz waves in an atmosphere that may be saturated over some of its height are investigated analytically and numerically. It is shown that, if there is a temperature jump at the interface, the Wegener hypothesis, i.e., the assumption that stability boundary curves are loci of neutral waves travelling with phase velocity equal to the mean of the velocities of the regions above and below the discontinuity, is invalid. Instead, the stability boundary corresponds to the singular neutral modes with phase speed equal to the velocity in one or the other layer, depending on the sign of the temperature jump and the presence of saturation. Furthermore, the effect of saturation on the stability is found to be substantial. For the common case of a shallow saturated layer adjacent to the interface, the system is shown to behave essentially as if the temperature jump were smaller by an amount proportional to the mixing ratio and thickness. Finally, the validity of the Boussinesq approximation is examined and is found to be in error by less than 1% for horizontal wavelengths between 10 and 104 m.

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F. Einaudi and D. P. Lalas

Abstract

An improved upper bound is given for the growth rate of an unstable disturbance in a gravitationally stratified compressible shear flow, with heat conduction and viscous effects neglected. It is also shown that such a growth rate depends essentially on the characteristics of the flow in the neighborhood of the critical layer.

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D. P. Lalas and F. Einaudi

Abstract

The stability analysis of a hyperbolic tangent velocity profile in an isothermal atmosphere In the presence of the ground is presented. It is shown that such a system has a number of modes in addition to the one studied by Drazin and that unstable waves can he excited, for finite values of some minimum Richardson number of the flow, even in the limit of horizontal wavelengths going to infinity. Some of the unstable waves belonging to these new modes are able to propagate energy and momentum away from the shear zone and may therefore play an important role in microscale flow dynamics and in coupling of small-scale phenomena to mesoscale flow motions.

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F. Einaudi and J. J. Finnigan

Abstract

New data obtained at the Boulder Atmospheric Observatory (BAO) has been compared with a linear stability analysis of the background atmospheric state as measured by rawinsonde ascents. Good agreement was obtained between measured wave parameters such as wavelength, period, and vector phase velocity, and the eigenvalues of the linear solution, but linear eigenvectors scaled by measured pressure at the base of the BAO tower agreed less well with measurement.

An investigation of the wave kinetic energy budget revealed that buoyant production of wave energy was a significant gain despite the strong stability (Ri ≳ 5). Further analysis of the budgets of wave heat flux and temperature variance revealed the essential role of wave-turbulence interaction in maintaining a large amplitude temperature wave and countergradient wave heat flux. A consideration of the turbulent kinetic energy budget showed many of the same features as the wave budget.

A comparison with earlier near-neutral and stable cases analyzed in comparable detail suggests that countergradient wave heat fluxes maintained by nonlinear wave-turbulence interaction and an essential transfer of kinetic energy from wave to turbulence may be generic features of such situations. A mechanism for maintenance of turbulence by waves in strongly stratified boundary layers is described, which emphasizes that the time-mean Richardson number is an irrelevant parameter at such times. In the analysis of the data, general methods are described for extracting wave signals from nonstationary turbulence records and for assessing the statistical significance of the waveform so derived.

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F. Einaudi and D. P. Lalas

Abstract

The nonlinear equations governing the propagation of acoustic-gravity waves in a moist atmosphere are derived following the theory of mixtures. The water droplets are assumed to be very small compared to the characteristic scales of the system and numerous enough to treat them as a fluid. The atmosphere is assumed saturated at all heights, and the equations are linearized about a background with no shear flow. The WKB solution reveals that the local properties of the atmosphere are considerably affected by the exchange of heat due to condensation or evaporation. In particular, for a given frequency and horizontal wavelength, the vertical wavelength increases compared to the case of a dry atmosphere. The treatment applies to all frequencies less than the audible range.

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D. P. Lalas and F. Einaudi

Abstract

A rigorous stability analysis of a saturated atmosphere is carried out and is compared with the parcel method. It is shown that the stability parameter ω 2 (the Brunt-Väisälä frequency) one obtains by the two methods is identical. It is further shown that the replacement of the dry adiabatic by the wet adiabatic lapse rate in studying the stability of a saturated atmosphere is inadequate in certain circumstances. In particular, for an atmosphere at rest with negative temperature gradients, such a replacement may lead to erroneous prediction of instability. Similarly, for an atmosphere with a background wind, the same replacement will lead to underestimation of stability for sufficiently negative temperature gradients.

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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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