The  deep-atmosphere Euler equations in a non-approximated shallow-atmosphere-alike form

Juang, Hann-Ming Henry

doi:doi:/10.7289/V5/ON-NCEP-488

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The deep-atmosphere Euler equations in a non-approximated shallow-atmosphere-alike form

2017
By Juang, Hann-Ming Henry
Series: Office note (National Centers for Environmental Prediction (U.S.)) ; 488

[PDF-740.29 KB]

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Personal Author:

Juang, Hann-Ming Henry
Corporate Authors:

National Centers for Environmental Prediction (U.S.)
NOAA Program & Office:

NWS (National Weather Service) ; NCEP (National Centers for Environmental Prediction)

NWS (National Weather Service) ; NCEP (National Centers for Environmental Prediction) Less -
Description:

The deep-atmosphere Euler equation set has been derived into a form similar to the shallow-atmosphere Euler equation set without any approximation, which makes it more convenient to evolve any existing shallow-atmosphere dynamics model to deep-atmosphere dynamics.The deep atmospheric dynamics system is a fully non-approximated Euler equation set, which includes all-dimensional Coriolis force, vertically expanded cells (r=a+z), and geocentric gravitational force with height. The deep-atmosphere Euler equation in spherical height coordinates was transferred into spherical generalized vertical coordinates with pseudo horizontal wind in NCEP Office Note 477 (Juang 2014). The deep-atmosphere continuity equation in generalized vertical coordinates can be easily converted into a shallow-atmosphere-alike form by introducing scaled horizontal winds and scaled height with a hydrostatic relationship in generalized coordinates to represent density. The relationship provides a coordinate pressure change with respect to scaled height for a given density. From this relationship we can use geopotential height to define scaled vertical motion, thus all the three-dimensional winds in deep-atmosphere dynamics can be replaced by scaled winds. Since all winds are using a scaled form, the momentum equations are converted into scaled momentum equations with scaled terms plus some add-on terms. [doi:/10.7289/V5/ON-NCEP-488: http://doi.org/10.7289/V5/ON-NCEP-488]
Content Notes:

Hann-Ming Henry Juang.

"September 18, 2017."

"This is an internal reviewed manuscript, primarily intended for informal exchange of information among the NCEP staff members."

System requirements: Adobe Acrobat Reader.

Includes bibliographical references (page 10).
Keywords:

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Euler Characteristic Mathematical Models Numerical Analysis Numerical Weather Forecasting Weather Forecasting
Series:

Office note (National Centers for Environmental Prediction (U.S.)) ; 488
DOI:

doi:/10.7289/V5/ON-NCEP-488
Document Type:

Office Note
Place as Subject:

United States
Rights Information:

Public Domain
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Library
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urn:sha256:c0e6ffa9bc0e31dbc5dd0b856c21f9b86ae7b2ddb30e35659bc5bdf614c98d68
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https://repository.library.noaa.gov/view/noaa/15764/noaa_15764_DS1.pdf
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The deep-atmosphere Euler equations in a non-approximated shallow-atmosphere-alike form

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