TABLE OF CONTENTS In this section we derive the basic conservation equations for the flow within the surface layer. While it is clear that conservation equations for mass and linear momentum are required the number of transport equations for the turbulent properties (e.g. turbulent kinetic energy, Reynolds' stresses, etc.,) depends on the chosen level of closure. We derive the primary mass and momentum conservation equations together with a transport equation for the turbulent kinetic energy k.
There are several approaches for deriving equations for the motion of a mixture. The simplest is the phenomenological approach in which conservation laws are written for each of the two phases separately with additional terms in each to model the interaction of the two phases. The main disadvantage of this intuitive approach is that it usually involves the ad-hoc introduction of the additional terms for the phase interaction. A more reliable method is the averaging method in which equations for the macroscopic behaviour of the flow are obtained by averaging equations which are valid at microscopic level. In this class two different approaches coexist. One is based on the assumption that each phase involved in the mixture can be described as a continuum governed by conservation laws which are expressed in differential form. These equations are obtained by conditioning the conservation equations for a single phase flow (e.g. Dopazo 1977 and Drew 1983). We do not believe the main assumption of dealing with each phase as a continuum (and...
