“Flood time will repay you just to sit and watch. The river seems to be holding itself up before you like a page open to be read. There is no knowing how the currents move. They shift, and boil, and eddy. They are swifter in some places than in others. To think of a “place” on a flowing surface soon baffles your mind, for the places are ever changing and moving. The current, in all its various motions and speeds, flows along, and that flowing may be stirred again at the surface by the wind in all its various motions. Who can think of it?” - Wendell Berry in “Jayber Crow”
The study of motion can be divided into two parts. Kinematics concerns the description of motion, while dynamics inquires into its causes. In elementary mechanics we are concerned with the motion of solid bodies, e.g., orbiting planets, billiard balls and the apple that supposedly fell on Newton’s head. In these cases the motion is simple to describe, so we don’t pay much attention to kinematics. In contrast, fluid motion can be extremely complicated. The task of describing such motion, a precondition to understanding its causes, is not trivial and is the subject of this chapter.
- 5.1: Lagrangian and Eulerian descriptions
- We can observe a flow in two ways, first by focusing on the motion of a specific fluid parcel (see section 1.2), second by stepping back and looking at the pattern as a whole. These are called the Lagrangian and Eulerian descriptions of flow, respectively. Here we will seek to understand the distinction more fully, to become fluent with both points of view, and to translate between them.
- 5.2: The Streamfunction
- Many flows are approximately two-dimensional. For example, the thickness of the Earth’s atmosphere relative to the planet is comparable to the skin on an apple. Large-scale atmospheric flows are therefore nearly two-dimensional.