Nonlocal theory of area-varying waves on axisymmetric vortex tubes
Area and axial flow variations on rectilinear vortex tubes are considered. The state of the flow is characterized by two dependent variables, a core area, and an azimuthal circulation per unit length, which vary in time and in distance along the length of the tube. Nonlinear integrodifferential equations of motion for these variables are derived by taking certain integrals of the vorticity transport equation. The equations are argued to be valid for moderately short waves (on the order of a few core radii) as well as for long waves. Applications to vortex breakdown and other wave phenomena are considered.
Copyright © 1994 American Institute of Physics. Received 20 April 1993; accepted 30 August 1993. The work was supported by the Applied Hydrodynamics Research Program of the Office of Naval Research under Grant No. N00014-92-J-1189.