Instability Of Stratified Boundary Layer And Its Coupling With Gravity Waves

A stratified shear flow over topography can support a variety of waves, including gravity waves, mountain lee waves, and instability waves arising from shear instability. Nonlinear solitary waves have also been frequently observed. While each of these waves has its own distinct characteristics, they may be intrinsically coupled through topography. Such wave activities and their mutual interactions play a crucial part in mixing and transport processes in the atmosphere, and hence they are of fundamental importance for a proper understanding and ultimately modelling of many boundary-layer meteorology phenomena.The various wave motions in stratified flows can be understood by investigating the instability characteristics of the stratified shear layer, and the role of stratification and vertical shear acting as a waveguide, within which certain waves are trapped and propagate horizontally. Most previous studies were concerned mainly with inviscid dynamics, and there have been very limited studies of the mutual coupling between different wave motions. In this thesis we consider a viscous instability that is a modified form of the familiar Tollmien-Schlichting (T-S) waves by stable density stratification. As with the standard T-S waves, triple-deck formalism was employed to provide a self-consistent description of the linear and nonlinear instabilities. The effects of stratification on the temporal and spatial linear growth rates are studied. It is shown that at the high-frequency limit, the evolution of the wave is governed by a nonlinear evolution equation, which is an extension of the well-known Benjamin-Ono equation. The equation was solved numerically to obtain solutions corresponding to simple solitary waves.The coupling of this newly identified viscous instability with internal gravity waves is also investigated. It is shown that an oncoming gravity wave interacts with localized mountain lee waves induced by topography to generate a viscous instability wave within the boundary layer. The effectiveness of the coupling can be quantified by a coupling coefficient, which was calculated at different parameters. An interesting by-product is the founding that gravity waves many be over reflected by boundary layer, i.e. the reflected wave may be stronger than the incident wave.The instability and its coupling with gravity waves may be related to intermittency of nocturnal boundary layer, where the stably stratified boundary layer remains laminar, but is sporadically disrupted by insurgence of small-scale turbulence.