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An analysis of the vertical structure equation for arbitrary thermal profilesThe vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.
Document ID
19890048686
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Cohn, Stephen E. (New York Univ. New York, NY, United States)
Dee, Dick P. (New York University NY, United States)
Date Acquired
August 14, 2013
Publication Date
January 1, 1989
Publication Information
Publication: Royal Meteorological Society, Quarterly Journal
Volume: 115
ISSN: 0035-9009
Subject Category
METEOROLOGY AND CLIMATOLOGY
Funding Number(s)
CONTRACT_GRANT: FINEP-4-3-86-0778-00
CONTRACT_GRANT: NSF INT-85-14423
CONTRACT_GRANT: CNPQ-1,01,10,014/85
CONTRACT_GRANT: NAG5-341
CONTRACT_GRANT: NAG5-820
CONTRACT_GRANT: NOAA-NA-84AAD00018
Distribution Limits
Public
Copyright
Other