Sphere-Filling Asymptotics of the Barotropic Potential Vorticity Staircase

Sphere-Filling Asymptotics of the Barotropic Potential Vorticity Staircase AbstractFor barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to . This result was obtained previously by the author in the equatorial limit of spherical geometry and by others in periodic beta-plane geometry. An improved asymptotic method has been devised to explain the strength–spacing relationship in sphere-filling solutions. This analysis explains the approximate validity of the equatorial asymptotics and yields new insight on minimum energy states and staircase mode transitions simulated in the presence of random, persistent energy inputs at high horizontal wavenumber. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Atmospheric Sciences American Meteorological Society

Sphere-Filling Asymptotics of the Barotropic Potential Vorticity Staircase

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Publisher
American Meteorological Society
Copyright
Copyright © American Meteorological Society
ISSN
1520-0469
D.O.I.
10.1175/JAS-D-17-0090.1
Publisher site
See Article on Publisher Site

Abstract

AbstractFor barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to . This result was obtained previously by the author in the equatorial limit of spherical geometry and by others in periodic beta-plane geometry. An improved asymptotic method has been devised to explain the strength–spacing relationship in sphere-filling solutions. This analysis explains the approximate validity of the equatorial asymptotics and yields new insight on minimum energy states and staircase mode transitions simulated in the presence of random, persistent energy inputs at high horizontal wavenumber.

Journal

Journal of the Atmospheric SciencesAmerican Meteorological Society

Published: Feb 28, 2018

References

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