Time Marching Problems

Abstract

The purpose of this chapter is to present some properties inherent in the governing equations listed in Sect. 1.1. Most problems in the geophysical sciences, including atmospheres, oceans, seas, and lakes, involve solving so-called time marching problems. Typically, the state of the fluid in question is known at one specific time. As postulated by Bjerknes (Meteor Z 21:1–7, 1904) in his comments on weather forecasting (see quote in the preface), the aim is then to predict the state of the fluid at a later time. This is done by solving the governing equations listed in Sect. 1.1. Such problems are known in mathematics as initial value problems.