Transmission and Reflection of Three-Dimensional Anelastic Internal Gravity Wave Packets in Nonuniform Retrograde Shear Flow

Internal gravity wave packets (IGWPs) propagate horizontally and vertically within stably stratified fluids. Linear theory predicts that a small amplitude IGWP propagating upward against a retrograde background shear flow will be Doppler-shifted until its Doppler-shifted frequency equals the background buoyancy frequency. The `reflection level' (RL) at which this occurs is the height at which the incident IGWP reflects, resulting in a downward-propagating IGWP. Anelastic amplitude growth allows IGWPs to evolve nonlinearly: wave-wave interactions induce an order amplitude-squared mean flow that locally accelerates the ambient fluid. Simulated Boussinesq 3-D IGWPs (Gervais et al, PRFluids, under review) were shown to transmit partially above the RL, provided the magnitude of the shear associated with their induced mean flow was locally greater than that of the background shear. We study the anelastic evolution of an initially small amplitude 3-D IGWP initialized with its predicted induced mean flow superimposed as it propagates into a nonuniform retrograde shear flow. Simulations are initialized with a range of amplitudes and vertical wavenumbers. We quantify wave transmission using the ratio of upward-propagating pseudomomentum above the RL to the total (conserved) pseudomomentum.