Instability structures during periods of large Richardson number (Ri ¼): Evidence of parametric instability

The commonly used criteria for shear and convective instabilities were developed for steady horizontally uniform background fl ows. However, the formalism that rigorously addresses the instability of waves on a basic state modulated by a primary wave is Floquet theory in which the basic state includes a wave. A Floquet system supports parametric instabilities when conventional Richardson number ( Ri ) criteria indicate that the system is stable. In a study of small-scale instability structures during the Maui MALT campaign, Hecht et al. (2005) 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 both stable and unstable according to conventional criteria. Values of Ri were calculated from lidar data. We have found frequent occurrence of ripple structure when Ri > 1 = 4 . We have focused on a period when there are clear indications of waves and ripple structure exhibiting two-dimensional instability structure when Ri ~ 1 or greater. These results are analyzed in terms of Floquet theory and interpreted as parametric instabilities occurring for

modest primary wave amplitudes.