When I see a plot of a velocity vector field that describes a fluid flow, are the terms "flow field", vector field, velocity field, "velocity profile", and "flow profile" all used interchangeably?
There seem to be differences depending on whether it is a flow over time, $t$, or whether it's a snapshot of the flow, with no dependence on time.
I put quotations on the terms that I am not sure of but hear frequently in a seminar, so I just want to be sure.
Thanks,
Not all of them are equivalent.
"flow field" and "velocity field" are the representation of the "vector field" of velocities. Which means, the representation of velocity field lines through the fluid.
On the other hand, the "velocity profile" or "flow profile" is a diagram that plots the speed of the fluid against a the distance. This is usual in certain delimited channel, like a pipe, a tube, or a canal.
In sum, the first one represents the arrows of the vector field along the fluid. The second one represents the scalar magnitude of velocity in a cross section of the fluid. Some pictures might help:
1.- Velocity field lines: http://fcm.ens.uabc.mx/~chelo/analisis%20vectorial/nucleos/capitulo2/leccion2_4/mates/ecdif/l2-4b_files/image018.jpg
2.- Velocity profile (arrows are helping, but the function that joins their tips is what matters) http://www.bvsde.paho.org/arquitectura/clase23/barce5.gif