Differential forms and fluid dynamics
Abstract
A formulation of some fundamental equations of fluid dynamics based on exterior differential forms (Flanders, 1963) is developed analytically. The derivation is outlined, with particular attention to the exterior derivative, the Stokes theorem, the pull-back of differential forms, restriction of a form to a submanifold, the commutation property, the case of an ideal barotropic fluid, the relationship between exterior and Lie derivatives, and the conservation of helicity. The advantages of this formulation over vector fields for curvilinear coordinate systems are pointed out, and its applicability to the dynamics of superfluids or to magnetohydrodynamics is indicated.
- Publication:
-
Archiv of Mechanics, Archiwum Mechaniki Stosowanej
- Pub Date:
- 1991
- Bibcode:
- 1991ArMeS..43..653P
- Keywords:
-
- Computational Fluid Dynamics;
- Differential Calculus;
- Barotropic Flow;
- Manifolds (Mathematics);
- Spherical Coordinates;
- Fluid Mechanics and Heat Transfer