Boundary Conditions

Abstract

We have been made aware during the last chapter of the importance of boundary conditions. The laws of motion attributed to Sir Isaac Newton have for 300 years quantified the motion of physical objects. The sea is a fluid which is also governed by these laws of mechanics. The basic equations, outlined in the last chapter are these laws together with the conservation of mass. The mathematical theory that underlies the motion of a frictionless fluid is called potential theory. Although the equations that govern the movement of the sea contain non-linear terms (namely (u.∇)u) if these are small and they usually are then potential theory tells us that the motion is determined by what happens at the boundaries. The way numerical schemes work confirms this (see section 3.3 on tidal modelling for example). Therefore the effects that are literally on the edge of models are in fact central drivers and play a major role in determining the resulting motion of the sea.