Secondary eyewalls are rings of strong winds and precipitation that form in many major (Category 3 or higher) tropical cyclones. They often contract, intensify, and replace the primary eyewall of the tropical cyclone in a process known as an eyewall replacement cycle. Eyewall replacement cycles have been linked to a spatial broadening of tropical cyclone winds as well as fluctuations in tropical cyclone intensity, making secondary eyewall formation an important problem for forecasters aiming to refine predictions of both tropical cyclone intensity and damage. In this thesis, we first provide an overview of current work on secondary eyewall formation (Chapter 1) and then examine the relationship between secondary eyewall formation and changes to a tropical cyclone's wind field in two contexts: (1) rapid intensification of the primary eyewall (Chapter 2) and (2) an expansion of the outer wind field (Chapter 3). The second chapter of the thesis demonstrates that in both an idealized hurricane intensity model (the Coupled Hurricane Intensity Prediction System) and best-track data and observations of secondary eyewalls, rapid intensification is often followed by secondary eyewall formation. This is concerning from the point of view of risk estimation because it suggests that, in addition to making tropical cyclones more intense, rapid intensification may also result in spatial broadening of the tropical cyclone winds near the inner core. The third chapter of the thesis describes work using an axisymmetric numerical model (Cloud Model 1) to establish a dynamical relationship between secondary eyewall formation and wind broadening in the outer region of a tropical cyclone. In these simulations, secondary eyewall formation is a means by which the inner region of a tropical cyclone adjusts to growth in the outer wind field. While some past studies have used quasi-steady frameworks for studying secondary eyewall formation, the results from Chapters 2 and 3 of this work emphasize the importance of examining secondary eyewall formation in frameworks in which the tropical cyclone's wind structure is evolving.Ph.D.