All Physics Faculty Publications
Document Type
Article
Journal/Book Title/Conference
Chaos
Author ORCID Identifier
Boyd F. Edwards https://orcid.org/0000-0002-2309-1350
Cade Pankey https://orcid.org/0000-0002-1215-2787
John M. Edwards https://orcid.org/0000-0002-0882-312X
Volume
32
Issue
11
Publisher
AIP Publishing LLC
Publication Date
11-8-2022
Award Number
NSF, Division of Chemistry (CHE) 1808225
Funder
NSF, Division of Chemistry (CHE)
First Page
1
Last Page
20
Abstract
As seen by an observer in the rotating frame, the earth’s small spheroidal deformations neutralize the centrifugal force, leaving only the smaller Coriolis force to govern the “inertial” motion of objects that move on its surface, assumed smooth and frictionless. Previous studies of inertial motion employ weakly spheroidal equations of motion that ignore the influence of the centrifugal force and yet treat the earth as a sphere. The latitude dependence of these equations renders them strongly nonlinear. We derive and justify these equations and use them to identify, classify, name, describe, and illustrate all possible classes of inertial motion, including a new class of motion called circumpolar waves, which encircle both poles during each cycle of the motion. We illustrate these classes using CorioVis, our freely available Coriolis visualization software. We identify a rotational/time-reversal symmetry for motion on the earth’s surface and use this symmetry to develop and validate closed-form small-amplitude approximations for the four main classes and one degenerate class of inertial motion. For these five classes, we supply calculations of experimentally relevant frequencies, zonal drifts, and latitude ranges.
Recommended Citation
Boyd F. Edwards, Cade Pankey, and John M. Edwards. "Inertial motion on the earth’s spheroidal surface", Chaos 32, 113122 (2022). https://doi.org/10.1063/5.0123896
Comments
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 32, 113122 (2022); https://doi.org/10.1063/5.0123896 and may be found at https://aip.scitation.org/doi/full/10.1063/5.0123896.