CHAPTER 4 A closer look at the advection equation

This means that the value of does not change following a particle. We say that is “conserved” following a particle. In fluid dynamics, we consider an infinite collection of fluid particles. According to (4.2), each particle maintains its value of as it moves. If we do a survey of the values of in our fluid system, let advection occur, and conduct a “follow-up” survey, we will find that exactly the same values of are still in the system. The locations of the particles presumably will have changed, but the maximum value of over the population of particles is unchanged by advection, the minimum value is unchanged, the average is unchanged, and in fact all of the statistics of the distribution of over the mass of the fluid are completely unchanged by the advective process. This is an important characteristic of advection.