Ellipticity of normal mode initialization equations

Abstract

Criterions of ellipticity of nonlinear normal mode initialization systems with various closure conditions are obtained for different atmospheric models. These present the necessary conditions of well-posedness of correspondent differential boundary value problems. It is demonstrated that initialization with fixed geopotential and initialization of internal baroclinic modes are ill-posed problems. In these cases a divergence of iterative process of numerical solution of initialization equations is a practical consequence of ill-posedness of differential problems.