Laplacian field
From Wikipedia, the free encyclopedia.
A
Laplacian field is a
vector field which is both
irrotational and
incompressible. If the field is denoted as
v, then it is described by the following
differential equations:
-
Since the
curl of
v is zero, it follows that
v can be expressed as the gradient of a
scalar potential (see
irrotational field)
φ :
- .
Then, since the
divergence of
v is also zero, it follows from equation (1) that
-
which is equivalent to
- .
Therefore, the potential of a Laplacian field satisfies
Laplace's equation.
See also: potential flow, harmonic function
