The Role of Nonnormality in Overreflection Theory

Abstract

The role of nonnormality in the overreflection of gravity waves is investigated. In the limit of weak stratification, wave packets having a critical level inside a shear layer of finite depth are reflected with amplified energy. This process, which exhibits the characteristics of stimulated emission, occurs in three stages: first, the incoming wave enters the shear layer and excites nonpropagating perturbations leaning with and against the shear. Subsequently, the energy of perturbations leaning against the shear grows in a manner similar to energy growth of perturbations in constant shear flows, indicating that the Orr mechanism that is slightly modified by stratification underlies the observed growth. Finally, the amplified perturbations excite propagating waves originating from the vicinity of the shear layer boundary. The role of nonnormality in this process is also investigated from the perspective of the associated nonorthogonality of the modes of the dynamical system. It is found that the incident wave packet projects on nonorthogonal analytic modes having the structure of a downward propagating wave in the far field below the shear layer and overreflection expressed by the interaction among these nonorthogonal modes.

Internal gravity-shear waves in the atmospheric boundary layer from acoustic remote sensing data

“…One of the most important problems of dynamic meteorology is the generation, propagation, and decay of internal gravity waves in the atmosphere, because [4][5][6]) or the numeri cal modeling studies of mesoscale and large scale wave processes [7][8][9][10]. Far less attention is paid to observa tions of the waves in the atmosphere, their climatol ogy, and measurements of their parameters.…”

The eddy, wave, and interface structure of turbulent shear layers below/above stably stratified regions

“…However, the effects of shear on the 3‐D turbulence wave structure near the interface have not previously been studied. Many aspects of internal waves driven by shear layers have been numerically simulated or studied by coupling idealized models of two‐dimensional (horizontal and vertical) instability modes in the shear layer with internal gravity waves in the external stratified region [e.g., Sutherland and Peltier , ; Bakas and Farrell , ]. They noted a structural coupling between external waves and the eddy/wave modes in the shear layer leading to Reynolds shear stress of the waves.…”

“…A simplified linearized, inhomogeneous rapid distortion calculation based on Carruthers and Hunt [, hereafter CH] provides a model for the interactions between the turbulent shear layer and the stratified region. (The methodology enables different components to grow/decay at different rates, unlike normal mode analysis; see also Bakas and Farrell []).…”