@article{5826,
  author = {B. N. Kuvshinov and T. J. Schep},
  title = {Geometrical approach to fluid models},
  abstract = {Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). (C) 1997 American Institute of Physics.},
  year = {1997},
  journal = {Physics of Plasmas},
  volume = {4},
  number = {3},
  pages = {537-550},
  month = {Mar},
  isbn = {1070-664X},
  doi = {10.1063/1.872576},
  language = {eng},
}