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    New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow

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    Author
    Anco, Stephen C.
    Keyword
    Fluid flow
    Conservation law
    Conserved integral
    Constant of motion
    Vorticity
    Helicity
    Enstrophy
    Circulation
    
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    URI
    http://hdl.handle.net/10464/6132
    Abstract
    For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.
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