A
vector field u is said to be irrotational if
curl u =
0.
This
condition is
equivalent to saying that the field is
conservative. It is also equivalent to saying that there is a
scalar potential U (
unique up to an additive constant) such that
u =
grad U.
Many fields that we are interested in are irrotational, eg
gravitional fields, and time-independent
electric and
magnetic fields, and corresponding potentials may be used to facilitate the theory. In
fluid dynamics it is easy to show that an irrotational flow in an incompressible
fluid will remain irrotational in the absence of
viscous effects, allowing the introduction of a velocity potential.