Vortex evolution
Abstract
Friedmann's equation and the potential vorticity equation are generalized for turbulent motion. The generalized equations incorporate some new phenomena connected with turbulent transport of mass. It is proved that, under certain conditions, the Helmholtz-Kelvin theorem concerning the conservation of the velocity circulation around a closed path is violated and the potential vorticity is not a Lagrangian adiabatic invariant. The effects of this turbulent transport of mass on the creation or dissipation of vorticity discussed here are not equivalent to effects of baroclinicity or viscosity. Some possible implications of the new circulation theorem in geophysical and astrophysical fluid dynamics are discussed.
- Publication:
-
Geophysical and Astrophysical Fluid Dynamics
- Pub Date:
- 1983
- DOI:
- 10.1080/03091928308209066
- Bibcode:
- 1983GApFD..24..213K
- Keywords:
-
- Flow Equations;
- Turbulent Flow;
- Vortices;
- Vorticity Equations;
- Flow Velocity;
- Kelvin-Helmholtz Instability;
- Potential Theory;
- Vorticity Transport Hypothesis