Nonlinear wave propagation in stratified shear flows

Abstract

It is now generally accepted that solitary waves are a commonly occurring and important dynamical feature in geophysical fluids. Waves of this type transfer mass, momentum and energy, and play a significant role in the generation of turbulence in the atmospheric boundary layer (Christie, 1992; Rottman and Einaudi, 1993). In addition, since solitary waves often have large amplitudes they can provide an important mechanism for the generation of deep convection in a conditionally unstable atmosphere. The ubiquitous nature of these disturbances taken in conjunction with the high degree of nonlinearity of many observed waves compels further research in this area. Much of the theoretical work on solitary waves has been concerned with a treatment within the framework of weakly-nonlinear dispersive wave theory. It has become clear, however, that large discrepancies exist between the predictions of weakly-nonlinear theory and field observations, especially observations of highly nonlinear solitary waves in the atmosphere. This discrepancy has been attributed primarily to attempts to apply weakly-nonlinear theory outside its domain of validity. This thesis, therefore, is concerned with a fully-nonlinear treatment of internal solitary wave motions in continuously-stratified shear flows. The first part of this thesis is concerned with the description of highly nonlinear solitary waves in incompressible fluids and focuses on an exhaustive study of the solutions to the general form of the Dubreil-J acotin-Long equation. By considering a number of realistic ambient density and shear profiles, the treatment presented here considerably extends the work of Davis and Acrivos (1967), Tung et al. (1982) and Turkington et al. (1991). As well as being directly relevant to solitary wave propagation in the atmosphere and oceans, this investigation has yielded fundamental results on solitary waves in strongly non-Boussinesq fluids. In particular, this study has revealed a new class of overhanging internal solitary waves in continuously-stratified fluids, the existence of which is a direct consequence of relaxing the Boussinesq approximation. The second part of this thesis deals with time-evolution studies of boundarylayer atmospheric solitary waves using a variant of the fully-compressible, nonhydrostatic model developed by Klemp, Wilhelmsen and Droegemeier (Klemp and Wilhelmsen (1978), Droegemeier and Wilhelmsen (1987) ). This research shows that atmospheric solitary waves of large amplitude behave like solitons; ie., they emerge from interaction essentially unscathed, subject, however, to a significant phase shift. Furthermore, these high-resolution simulations reveal evidence for an -overturning instability in the interior of large amplitude waves with closed-circulation and provide an unprecedented view of transport processes, especially during interactions. Show more