| This thesis describes an analytical study of vortex Rossby waves in tropical cyclones. Observational analyses of hurricanes in the tropical atmosphere indicate the existence of spiral rainbands which propagate outwards from the eye and affect the structure and intensity of the hurricane. These disturbances may be described as vortex Rossby waves.;The results are used to explain some features of the tropical cyclone's development, namely, the change of angular wind in the critical layer, the secondary eyewall formation and the eyewall dynamics.;The aim of this research is to study the propagation of vortex Rossby waves in tropical cyclones and wave-mean-flow interactions near the critical radius where the mean flow angular velocity matches the phase speed of the waves. Depending on the wave magnitude, the problem can be linear or nonlinear. Analytical techniques including Laplace transforms, multiple scaling and asymptotic expansions are used to obtain approximate solutions of the governing linear and nonlinear equations. In this study we carry out asymptotic analyses to examine the evolution of the interactions near the critical radius in some two-dimensional configurations on an f-plane and a β-plane. |
