Ellipticity Conditions of the Shallow Water Balance Equations for Atmospheric Data

Abstract

Abstract 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.