Turbulence, the Richardson Number (Ri), and Parametric Instabilities in the Turbo-Pause Region ( 100 km)

Turbulence in the Mesosphere and Lower Thermosphere (MLT) region is responsible for vertical transport of constituents and heat at the turbo-pause. It has been primarily due to convection and dynamic instabilities (i.e. Kelvin-Helmholtz Instabilities, KHI). The Richardson number (Ri) is an index described by the ratio of the Brunt-Väisälä frequency to the square of the wind shear, where convection instabilities in laminar flow occur for Ri<0 and KHI for 0<Ri<1/4. The theory here is a generalization of the Ri<1/4 criterion, based on laminar flow. Waves (Floquet theory) dominate the MLT region, a condition absent in early criteria. Walterscheid et al., (2013) observed turbulence in the 84-92 km in airglows whose attributes were theoretically described as parametric instabilities (0<Ri<1) due to wave-wave coupling or resonance. A recent study of turbulence in the MLT by Philbrick et al. (2021) demonstrated, for 25 nights of lidar observations, the probability of R<1/4 decreased with altitude above 100 km, whereas the probability of turbulence increased with altitude, a result unexplained when published. We present an analysis here which demonstrates the observed distribution of the Ri above 100 km to be consistent with a significant contribution being due to parametric instabilities.

References:

Philbrick, C. P., et al. (2021), A Na density lidar method and measurements of turbulence to 105 km at the Andes Lidar Observatory, J. Atmos. Solar-Terrestrial Phys., 105642, doi:10.1016/j.jastp.2021.105642.

Walterscheid, R., L. et al., (2013) Instability structures during periods of large Richardson number (R>1/4): Evidence of parametric instability, J. Geophys. Res.: Atmos., 118, 6929-6939, doi:10.1002/jgrd.50514