The representation of a fluid through scalar or vector fields means that each
physical quantity under consideration is described as a function of time and
position. But the physics of a system is related to parcels, which move in space.
In particular, we are interested in the change of the properties of a parcel with
time.
In principle we might choose to describe the fluid by means of a set of func-
tions of the various parcels. In other words, we might label each parcel by its
coordinates at a given initial time, and then provide their new coordinates as
time proceeds. Such an approach is indeed possible and is called the Lagrangian
approach, but it is more complicated and less used than the Eulerian approach,
where the various quantities are given as a function of the geometrical points of
space. Hereafter, we will develop only this latter approach, but we must be aware
of the existence of the former because sometimes it is used both in theoretical
studies and in experimental practice.
When a buoy is released in the ocean, the information it furnishes is related to its
position. Since it is swept away by the surrounding water, it will record the properties of
that mass of water, which, to a first approximation, can be thought of as a fluid parcel.
