Other
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsa41a1826w&link_type=abstract
American Geophysical Union, Fall Meeting 2011, abstract #SA41A-1826
Other
[3334] Atmospheric Processes / Middle Atmosphere Dynamics, [3369] Atmospheric Processes / Thermospheric Dynamics, [3384] Atmospheric Processes / Acoustic-Gravity Waves
Scientific paper
The formalism that addresses rigorously the instability of waves on a basic state modulated by a primary wave is Floquet theory. However, the commonly used criteria for shear and convective instabilities were developed for steady horizontally uniform background flows. The prototypical shear instability is the Kelvin-Helmholtz instability. The flow is stable if the local Richardson number Ri =N2/{\vert{&partial; /∂ z}\vert}2 > 1/4 everywhere, where N is the Brunt-Väisälä frequency and u is the horizontal wind. The prototypical convective instability is the Rayleigh-Taylor instability. Ignoring wind effects and dissipation, the flow is unstable if N2 < 0 (i.e., Ri <0) somewhere. These instability structures drift with the wind. In Floquet theory the linear system of equations is transformed so that the basic wave is stationary and the vertical coordinate points along the wavenumber vector of the basic wave. A Floquet system supports instabilities when conventional Richardson number criteria indicate that the system is stable. Indeed, finite amplitude waves are unstable no matter how large the Richardson number might be. An essential instability mechanism in Floquet systems is a resonant interaction between a forced primary oscillation and a free oscillation of the time-averaged system. These are parametric instabilities. They can have a significant influence on shaping the spectrum by transferring energy from one scale to another. Hecht et al. [2005] in a study of small scale instability structures during the Maui MALT campaign noted that there were occurrences of ripple (instability) structure when the conventional criteria indicated stable conditions. We have followed up this work with a detailed survey of the occurrence of ripple structure over Maui during periods that were stable and unstable according to conventional criteria. Values of Ri were calculated from meteor radar and lidar data. We have found frequent occurrence of ripple structure when Ri > 1/4 and find structures for large and small Ri that do not drift with the wind. Also of interest are cases when a velocity match between the drift motion and the horizontal wind occurs far away from where Ri<1/4; this too indicates that the ripple structures are not likely to be the prototypical instabilities. These results are analyzed in terms of Floquet theory. Hecht, J. H., A. Z. Liu, R. L. Walterscheid, and R. J. Rudy (2005), MAUI-MALT observations of the evolution of Kelvin-Helmholtz billows formed near 86 km altitude," J. Geophys. Res., 110
Gelinas Lynette Jean
Hecht James H.
Walterscheid Richard L.
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