The Structure and Energetics of Transient Eddies in a Numerical Simulation of Breaking Mountain Waves

Abstract

Results from a detailed numerical simulation of breaking mountain waves in an unbounded stratified floware analyzed in terms of the transient eddies associated with the breaking event. Upstream of the obstacle, bothhorizontal wind speed and Brunt-Vaisala frequency are assumed to be height independent. The integrationsare initialized with an exact steady state solution in the lowest levels, thus avoiding the difficulty of separatingthe low-level transience due to growing unstable modes rrom that associated with the spinup process. Both the"local convective" and "deep resonant" modes discovered by Laprise and Peltier on the basis of solutions ofthe nonseparable linear stability problem are clearly identified through these diagnostic analyses. The localconvective mode grows from the gravitational potential energy associated with the superadiabatic region (SAR) ofthe mountain wave and is temporally episodic. The deep resonant mode extracts its energy from the reservoirof kinetic energy associated with the highly deformed mean flow set up by the nonlinear mountain wave andthis mode is shown to be responsible for initiating the transition which is accompanied by a rapid accelerationofthe low-level flow in the lee ofthe obstacle. The intense downslope windstorms discovered in previous analysesof the type described here, and shown to accord with natural occurrences of such events, are thereby establishedas deriving from a linear instability of the field of nonlinear internal waves launched by stratified flow over anobstacle.