Analogies of Ocean/Atmosphere Rotating Fluid Dynamics with Gyroscopes: Teaching Opportunities
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Haine-2013-Analogies of ocean_a.pdf
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1.42 MB
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Author(s)
Haine, Thomas W. N.
Cherian, Deepak Abraham
Date Issued
May 2013
Journal
Bulletin of the American Meteorological Society
Publisher
American Meteorological Society
Citation
Haine, Thomas W. N., and Deepak A. Cherian. “Analogies of Ocean/Atmosphere Rotating Fluid Dynamics with Gyroscopes: Teaching Opportunities.” Bulletin of the American Meteorological Society 94, no. 5 (May 2013): 673-684. © 2013 American Meteorological Society
Version
Final published version
Abstract
The dynamics of the rotating shallow-water (RSW) system include geostrophic f low and inertial oscillation. These classes of motion are ubiquitous in the ocean and atmosphere. They are often surprising to people at first because intuition about rotating fluids is uncommon, especially the counterintuitive effects of the Coriolis force. The gyroscope, or toy top, is a simple device whose dynamics are also surprising. It seems to defy gravity by not falling over, as long as it spins fast enough. The links and similarities between rotating rigid bodies, like gyroscopes, and rotating fluids are rarely considered or emphasized. In fact, the dynamics of the RSW system and the gyroscope are related in specific ways and they exhibit analogous motions. As such, gyroscopes provide important pedagogical opportunities for instruction, comparison, contrast, and demonstration. Gyroscopic precession is analogous to geostrophic flow and nutation is analogous to inertial oscillation. The geostrophic adjustment process in rotating fluids can be illustrated using a gyroscope that undergoes transient adjustment to steady precession from rest. The controlling role of the Rossby number on RSW dynamics is reflected in a corresponding nondimensional number for the gyroscope. The gyroscope can thus be used to illustrate RSW dynamics by providing a tangible system that behaves like rotating fluids do, such as the large-scale ocean and atmosphere. These relationships are explored for their potential use in educational settings to highlight the instruction, comparison, contrast, and demonstration of important fluid dynamics principles.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1175/BAMS-D-12-00023.1
