Clebsch representation

In physics and mathematics, the Clebsch representation of an arbitrary three-dimensional vector field ${\boldsymbol {v}}({\boldsymbol {x}})$ is:

{\boldsymbol {v}}={\boldsymbol {\nabla }}\varphi +\psi \,{\boldsymbol {\nabla }}\chi ,

where the scalar fields $\varphi ({\boldsymbol {x}})$ $,\psi ({\boldsymbol {x}})$ and $\chi ({\boldsymbol {x}})$ are known as Clebsch potentials or Monge potentials, named after Alfred Clebsch (1833–1872) and Gaspard Monge (1746–1818), and ${\boldsymbol {\nabla }}$ is the gradient operator.

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