That is, the path follows the fluid current described by the fluid's velocity field 'v'.

For the more general cases, independent of whether a velocity field can be used or not, the continuity equation becomes:

Say the aether has velocity field as a function of .

The governing equations are thus transformed, and the solution is a filtered velocity field.

The role of the wavefunction is to generate the velocity field for the particles.

Even with one space dimension and a constant velocity field, the system remains difficult to simulate.

The idea is that a velocity field can also be understood as a first order differential operator acting on functions.

The velocity field may be represented by a function that must satisfy:

Other choices of density and pressure are possible with the same velocity field:

Once the velocity field is solved for, other quantities of interest (such as flow rate or drag force) may be found.