Open AccessEllipticity Conditions of the Shallow Water Balance Equations for Atmospheric Data
Author(s) -
Andrei Bourchtein
Publication year - 2006
Publication title -
journal of the atmospheric sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.853
H-Index - 173
eISSN - 1520-0469
pISSN - 0022-4928
DOI - 10.1175/jas3707.1
Subject(s) - primitive equations , shallow water equations , mathematical analysis , stream function , boundary value problem , nonlinear system , vorticity , balance (ability) , forcing (mathematics) , initialization , mathematics , potential vorticity , physics , mechanics , simultaneous equations , computer science , differential equation , vortex , medicine , quantum mechanics , physical medicine and rehabilitation , programming language
Nonlinear normal mode initialization equations, which provide required balance relations for atmospheric data, are considered in the generalized case of shallow water equations in arbitrary orthogonal coordinates. Using the concept of ellipticity in the sense of Douglis–Nirenberg, the conditions of well posedness of boundary value problems for balance equations are derived in the cases of constrained streamfunction, constrained potential vorticity, and constrained pressure fields.