Observational and Theoretical Study of Shear Instability in the Airflow near the Ground

John T. Merrill Rosenstiel School of Marine and Atmospheric Science, University of Miami, Coral Gables, Fla. 33124

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Abstract

Results are presented from a combined observational and theoretical study of apparent shear instability in the airflow near the ground in statically stable (inversion) conditions. Meteorological instruments, including an acoustic echo sounder for time-height visualization, a spaced array of microbarographs and a heavily instrumented tower 150 m tall, provided measurements that were analyzed to determine the phase velocity and amplitude of the wavelike fluctuations and the mean profiles of temperature and wind for the shear flow. A linear, inviscid, dynamic stability analysis performed numerically using spline functions fit through the observed profiles shows that the flow is unstable to perturbations with the observed properties, but with growth rates that are small.

A wave critical level is shown to be present at 130 m, as the 8 m s−1 wind velocity there equals the phase velocity determined by cross-correlation analysis of the microbarograph records. Spectral analysis of the wind, temperature and pressure records confirms that the wave signal appears abruptly, showing no period of exponential growth; the time of arrival is the same as the beginning of the wave signal on the sounder record. Outlying microbarographs show pressure signals that are consistent with propagation of the waves at the observed speed. The observed mean Richardson number is 0.15 near the critical level, below the critical value of ¼, and the observed momentum fluxes show a divergence there that is consistent with wave generation as described by linear theory; however, the total flux is small and not all of it is directly wave-associated.

The results of the stability analysis are in good agreement with the observations. A search was made for eigenvalues and eingensolutions of the Taylor-Goldstein equation. The growth rate and phase speed of unstable modes are found for each of several wavelengths, using profiles of the wind and temperature measured during the wave event. The wavelength range and phase speed agree with those measured, as do the height-dependent properties such as the momentum flux profile. (This comparison is based on scaling the calculated modes so that they match the observed 8 dyn cm−2 pressure fluctuation at the ground.) The group velocity of the normal modes matches their phase velocity closely, and the wave-associated effects are confined to a layer very near the critical level. The instability region is bounded by neutral modes, and no unstable modes were found at longer or shorter wavelengths. Linear instability theory adequately accounts for the generation of the observed oscillations.

Abstract

Results are presented from a combined observational and theoretical study of apparent shear instability in the airflow near the ground in statically stable (inversion) conditions. Meteorological instruments, including an acoustic echo sounder for time-height visualization, a spaced array of microbarographs and a heavily instrumented tower 150 m tall, provided measurements that were analyzed to determine the phase velocity and amplitude of the wavelike fluctuations and the mean profiles of temperature and wind for the shear flow. A linear, inviscid, dynamic stability analysis performed numerically using spline functions fit through the observed profiles shows that the flow is unstable to perturbations with the observed properties, but with growth rates that are small.

A wave critical level is shown to be present at 130 m, as the 8 m s−1 wind velocity there equals the phase velocity determined by cross-correlation analysis of the microbarograph records. Spectral analysis of the wind, temperature and pressure records confirms that the wave signal appears abruptly, showing no period of exponential growth; the time of arrival is the same as the beginning of the wave signal on the sounder record. Outlying microbarographs show pressure signals that are consistent with propagation of the waves at the observed speed. The observed mean Richardson number is 0.15 near the critical level, below the critical value of ¼, and the observed momentum fluxes show a divergence there that is consistent with wave generation as described by linear theory; however, the total flux is small and not all of it is directly wave-associated.

The results of the stability analysis are in good agreement with the observations. A search was made for eigenvalues and eingensolutions of the Taylor-Goldstein equation. The growth rate and phase speed of unstable modes are found for each of several wavelengths, using profiles of the wind and temperature measured during the wave event. The wavelength range and phase speed agree with those measured, as do the height-dependent properties such as the momentum flux profile. (This comparison is based on scaling the calculated modes so that they match the observed 8 dyn cm−2 pressure fluctuation at the ground.) The group velocity of the normal modes matches their phase velocity closely, and the wave-associated effects are confined to a layer very near the critical level. The instability region is bounded by neutral modes, and no unstable modes were found at longer or shorter wavelengths. Linear instability theory adequately accounts for the generation of the observed oscillations.

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