Linear Hydrodynamic and Hydromagnetic Stability of the Dissipative, Two-Fluid Cylindrical Couette Problem

摘要

The linear hydrodynamic and hydromagnetic stability of two incompressible, immiscible, dissipative fluids occupying separate annular regions of a cylindrical Couette apparatus is considered. The equations and boundary conditions governing this problem with arbitrary jumps in fluid properties and an applied axial magnetic field but without surface tension were derived; and computer programs written to solve them. Results are presented on the effect of density and viscosity jumps, varying gap widths, and differing fluid-fluid interfacial positions on the hydrodynamic stability of this problem. Evaluation of the linear hydromagnetic stability problem was postponed, as has the consideration of unstably stratified fluids. Two separate modes (multiple eigenvalues) were discovered for all cases in which two fluids, differing in any property, are present. A rationale is presented for this phenomenon as well as for most of the other observed results. While most of the observed results are attributed to manifestations of the Taylor Cylindrical Couette instability phenomenon, evidence is presented for the existence of additional 'hidden' eigenvalues attributable to the classical Kelvin-Helmholtz and/or Yih viscosity jump instabilities. (Author)