Eulerian

In a standard Eulerian description, we use space-time coordinates. We now want to find ,, ... In Cartesian coordinates, that would be finding u(x,y,z,t), v(x,y,z,t), w(x,y,z,t), p(x,y,z,t), ...

Example:

2D ideal stagnation point flow

Particle paths: Lines traced by the fluid particles. Particle paths can be found from solving:

Streamlines: Lines that are everywhere in the direction of the velocity field. Streamlines can be found from solving:

Various numerical and experimental methods produce streamlines naturally.

Streaklines: Lines of smoke coming out of smoke generators. Streaklines can be found by integrating the path lines for all the smoke particles coming out the generator.

Steady Flow:

For steady flow, pathlines, streamlines, and streaklines are all the same.