Interfacial Conditions of a Cylindrical Vortex Sheet.
Abstract
Interfacial conditions for a cylindrical vortex sheet or a cylindrical fluid layer with radius-dependent density, velocity and magnetic fields are derived for isentrioptic compressible swirling flows subjected to arbitrary disturbances. Surface tension in included for possible immiscible fluids. These conditions are valid for both spatially and temporally growing waves and for flow profiles with or without discontinuities. The deformation of the sheet or layer affects the flow in two ways: perturbing the total presure field and disturbing the centrifugal force field created by the azimuthal components of the velocity and the magnetic flux. It is shown, through the derivations of the interfacial conditions, the the Rayleigh-Synge and the Alfven discriminant are in fact a differential representation of the centrifugal force field. Both discriminants play a crucial role in the stability characteristics of hydromagnetic swirling flows. As supported by a previously proposed mechanisms, instabilities of such flows are both of centrifugal and of shear origin, the generalized Michael condition being a criterion for centrifugal stability. Centrifugal forces and velocity gradients affect flow characteristics through their interaction with the Lagrangain displacement. For centrifugally stable profiles, unstable waves with large numbers may be stabilized by centrifugal effects. This suggests a mechanism for the dilemma that the most unstable waves for flows of vortex sheet types correspond to the smallest-scale disturbances that are not observed in experiments. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 08, 1980
- Accession Number
- ADA091234
Entities
People
- Y. T. Fung
Organizations
- United States Naval Research Laboratory