Radiation and reflection of Rossby waves and their role in two-way interactions of the troposphere and stratosphere
File(s)
Author(s)
Dell, Imogen Mhari
Type
Thesis
Abstract
We investigate linear and nonlinear dynamics of small amplitude neutral or nearly neutral disturbances in a rotating parallel shear flow on the beta-plane. The focus is on radiation and reflection of Rossby waves, which represent the fundamental processes underpinning the two-way coupling between the troposphere and strato- sphere. While the coupling involves baroclinic and barotropic effects, the radiation and reflection of Rossby waves are investigated as a first step in a barotropic setting. Typically for a Rossby wave, a critical level is present where the background (zonal) flow is equal to the phase speed of the Rossby wave. In a thin layer surrounding this level, referred to as the critical layer, viscosity and nonlinear effects play an important role, and these are considered in detail. The reflection of an incident Rossby wave is considered first in the linear regime, for which the critical layer is viscous. We show that in a steady flow, over-reflection takes place for a certain range of the frequencies and wavelengths of the incident waves. For a particular frequency and wavelength, the reflection coefficient becomes infinite, indicating the occurrence of resonant over-reflection. This can be associated with the existence of a neutral radiating mode, which radiates a Rossby wave spontaneously without an incoming wave. For incident waves of a sufficiently large amplitude, or of moderate amplitude but with frequency and wavenumbers reasonably close to those of the radiating mode, nonlinear effects come into play. The reflection is considered in the regime where nonlinearity and viscosity are assumed comparable leading to a viscous strongly nonlinear critical layer. It is found that all harmonics are generated simultaneously and moreover spread out to the entire shear flow so that the reflected wave consists of all harmonics at leading order. Meanwhile, the disturbance in the critical layer exhibits rather complex spatial features. The unbounded response and reflection at the resonant over-reflection cannot of course be accepted as physical and the problem is then regularised by allowing the mean flow to vary slowly with respect to time. We show that a small-amplitude incident wave can excite a much stronger radiating Rossby mode. An evolution equation for the amplitude of the radiating mode is derived, involving a cubic history-dependent nonlinear term, un- like nonlocal nonlinear terms in many other amplitude equations. The evolution equation establishes a definite relation between the incident and reflected waves.
Version
Open Access
Date Issued
2021-11
Date Awarded
2023-02
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Wu, Xuesong
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)