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.