Gravity Waves in a Horizontal Shear Flow. Part I: Growth Mechanisms in the Absence of Potential Vorticity Perturbations

Abstract

Abstract Interaction of internal gravity waves with a horizontal shear flow in the absence of potential vorticity perturbations is investigated making use of closed-form solutions. Localized wave packet trajectories are obtained, the energy growth mechanisms occurring are identified, and the potential role of perturbation growth in wave breaking is assessed. Regarding meridional propagation, the wave packet motion is limited by turning levels where the waves are reflected and trapping levels where the waves stagnate. Regarding perturbation energy amplification, two growth mechanisms can be distinguished: growth due to advection of zonal velocity and growth due to downgradient Reynolds stresses. The three-dimensional perturbations producing optimal energy growth reveal that these two mechanisms produce large and robust amplification of zonal velocity and/or density and vertical velocity, potentially leading to shear or convective instability. For large static stability, amplification of density perturbations in conjunction with vertical orientation of the constant phase lines close to the trapping level potentially leads to a convective collapse of the wave packet near the trapping level, in agreement with existing direct numerical simulation studies. For lower static stability and for waves with phase lines oriented horizontally, growth due to advection of zonal velocity dominates, leading to rapid growth of streamwise streaks within the localized wave packet and potentially to shear instability.