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Noise-induced Tipping in a Simple Model of Tropical Cyclone Formation

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abstract
A presumed impact of global climate change is the increase in frequency and intensity of tropical cyclones. Because of the destruction that can occur when tropical cyclones make landfall, understanding their formation should be of interest to governments, risk analysts, as well as climate scientists. As early as 1986, Kerry Emanuel posed that the dynamics of a tropical cyclone can be modeled as a Carnot engine that transfers thermal energy from the ocean into mechanical energy in the form of cyclonic winds. In 2017, Emanuel modeled tropical cyclone formation by developing a low-dimensional dynamical system which couples tangential wind speed of the eye wall with inner-core moisture. In this thesis we present the existence and stability of fixed points for this dynamical system, using a piecewise approximation to ocean feedback. The fixed points in this system correspond to the dissipation or presence of a cyclone. The model admits a saddle-node bifurcation dependent upon wind shear and thermodynamic parameters. By converting the model into a system of stochastic differential equations with additive Gaussian white noise to simulate small scale thermodynamic disturbances, we can explore the most probable path of transition from a non-cyclone state to a cyclone state. Understanding of the formation and stability might provide insight into the underlying mechanisms that govern the formation of cyclones.
subject
bifurcation analysis
Dynamical Systems
Freidlin-Wentzell
most probable path
noise-induced tipping
tropical cyclone
contributor
Corak, Nicholas (author)
Gemmer, John A (committee chair)
Erhardt, Robert (committee member)
Lowman, Lauren EL (committee member)
date
2020-05-29T08:35:40Z (accessioned)
2020-05-29T08:35:40Z (available)
2020 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/96794 (uri)
language
en (iso)
publisher
Wake Forest University
title
Noise-induced Tipping in a Simple Model of Tropical Cyclone Formation
type
Thesis

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