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The barotropic normal modes in certain shear flows and the traveling waves in the atmosphereIt is shown analytically and numerically that in certain shear flows the linearized nondivergent barotropic vorticity equation has a limited number of neutral normal modes. The latitudinal structures of these shear flows can be expressed as polynomials of the sine of latitude. The first few such shear flows resemble the gross features of the zonal winds in the atmosphere of the earth at different times and altitudes. The spatial structures of the neutral normal modes in these shear flows are spherical harmonics, and, as a consequence, these modes are also the exact solutions of the fully nonlinear equation because the nonlinear interaction term vanishes identically. The spatial structures of the observed 5-, 4-, 2-, and 16-day free traveling waves in the atmosphere are often identified with the spherical harmonics with indices of (m, n) = ( 1, 2), (2, 3), (3, 3), and ( 1, 4), which are known previously as the neutral normal modes of the nondivergent barotropic vorticity equation in a motionless background state. Our results could explain why these free traveling waves can survive the shearing effects of zonal flows that are far different from rest because these spherical harmonics are also normal modes in certain shear flows that resemble the observations of the atmosphere.
Document ID
19930065081
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Chen, Ping
(Washington Univ. Seattle, United States)
Date Acquired
August 16, 2013
Publication Date
July 1, 1993
Publication Information
Publication: Journal of the Atmospheric Sciences
Volume: 50
Issue: 13
ISSN: 0022-4928
Subject Category
Meteorology And Climatology
Accession Number
93A49078
Funding Number(s)
CONTRACT_GRANT: NAS5-26301
Distribution Limits
Public
Copyright
Other

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