The Instability of Long's Stationary Solution and the Evolution toward Severe Downslope Windstorm Flow. Part II: The Application of Finite-Amplitude Local Wave-Activity Flow Diagnostics

Abstract

An analysis of severe downslope windstorm evolution, from flow conditions initially described by Long's stationary solution, is considered through the application of finite-amplitude wave-activity diagnostics. Such quantities satisfy a local conservation law of the form At + ? · F = 0. In particular, an analysis of the pseudoenergy density A and flux F is undertaken since the corresponding conservation law may be employed to describe disturbances to basic states that are nonparallel. In this study, such diagnostics are primarily enlisted to identify and chronicle the life cycle of normal-mode instability in the breakdown of Long's solution. As a result of this investigation, it is concluded that the large-amplitude stationary disturbance, which defined the second stage of windstorm evolution in Part I of this study, was the result of a normal-mode instability of Long's solution. The development of this mode, its breakdown via secondary shear instability, and the subsequent evolution toward the mature windstorm state are further investigated by application of the pseudoenergy diagnostics. The analysis suggests that modes of secondary shear instability cause a local eddy forcing of the temporal-mean flow at the downstream edge of the windstorm disturbance. Such forcing appears to be responsible for the downstream expansion of the windstorm. In addition, the pseudoenergy diagnostics indicate that the mature windstorm state is the result of a dynamic balance between mean-shear forcing and the negative feedback associated with the vigorous production of such modes of shear instability.