Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested (vortex line foliation) with the topology of cylinders, toroids or a combination of both, we show how a Clebsch representation of the flow velocity can be introduced. This is then used to reduce the number of functions to be varied in the variational principles for such flows. We introduce a three function variational formalism for steady and non-steady barotropic flows.

References

Asher Yahalom and Donald Lynden-Bell "Variational Principles for Topological ‎Barotropic Fluid Dynamics" [“Simplified Variational Principles for Barotropic Fluid ‎Dynamics” Los-Alamos Archives - physics/ 0603162] Geophysical & ‎Astrophysical Fluid Dynamics.‎ DOI: 10.1080/03091929.2014.952725 (2014).