What Is the Basic Building Block of a Fluid?

Steven Brunton says the basic building block of a fluid is a velocity field, together with the pressures that force it to move. A fluid moves, and it moves differently in different places and at different times. At every point in space, a velocity vector tells how the fluid is moving. Where the flow is fast in one place and slow in another, a vortex can form. The picture gets richer when velocity changes a lot over space. A tornado is a fluid velocity field that changes very rapidly in both space and time, and the core of a tornado is low pressure, so pressure pushes the velocity field along.

The equations then tell how that velocity changes in time and in space according to the fluid's own momentum. Momentum is what lets a gust of wind carry itself forward. Internal friction and resistance are viscosity. Honey has more internal resistance than water and more than air. Heating, pressure, and gravity are external forces. Each of them can be written as a term in the Navier-Stokes equation.