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Lookup NU author(s): Professor Robin Johnson
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2025 The Author(s)The governing equations for a compressible, viscous fluid, written in spherical, rotating coordinates, together with a suitable version of the first law of thermodynamics, are non-dimensionalised to investigate the dynamics of a hurricane. The result is the appearance of three fundamental parameters associated with: the thin-shell approximation, the tracking speed of the hurricane and an inverse Rossby number. The first two parameters give, at leading order, a description of the hurricane which incorporates the essentials of the spherical geometry, together with a slow evolution in time of an otherwise steady motion, respectively. It is then shown that the structure of the hurricane can be extracted by constructing an asymptotic solution based on a large inverse Rossby number, ω. In particular, there are two regions: an inner, small region which includes the core and eyewall (where the flow speeds are high), and an outer region where the speeds are smaller, measured by the scaling 1/ω. This same scaling also measures the size of the inner region. Special solutions are found which confirm the validity of the various asymptotic results, leading to a description of the flow in each region. The emphasis throughout is on the asymptotic structure of the dynamical problem, but the thermodynamics that supports and drives the motion is also described.
Author(s): Constantin A, Johnson RS
Publication type: Article
Publication status: Published
Journal: Journal of Differential Equations
Year: 2025
Pages: epub ahead of print
Online publication date: 26/02/2025
Acceptance date: 21/02/2025
Date deposited: 10/03/2025
ISSN (print): 0022-0396
ISSN (electronic): 1090-2732
Publisher: Elsevier
URL: https://doi.org/10.1016/j.jde.2025.02.064
DOI: 10.1016/j.jde.2025.02.064
Data Access Statement: All data used for the research described in the article can be found in the references [3,27,29, 35,40--42].
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