Arbitrary Orthogonal Coordinates Research Articles

Ellipticity Conditions of the Shallow Water Balance Equations for Atmospheric Data

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.

Matrix Representations for Vector Differential Operators in General Orthogonal Coordinates

The restrictions in arbitrary orthogonal coordinates to a unified matrix presentation of vector operations using generalized differential matrix operators [Y. Chen et al.: IEEE Trans. on Educ., Vol. 41, (1998), p. 61] are pointed out. The corrected matrix representation for the operations ∇⋅(∇A) and B⋅(∇A) valid in arbitrary orthogonal curvilinear coordinates are obtained and shown to be consistent with the calculation using the dyadic technique. The presentation is accessible to undergraduate students.

Extending the gauss theorem to arbitrary orthogonal coordinates

Extending the gauss theorem to arbitrary orthogonal coordinates