Viscous potential flow analysis of Kelvin-Helmholtz instability of cylindrical interface

TLDR: In this paper, a linear analysis of Kelvin-Helmholtz instability of cylindrical interface is carried out using viscous potential flow theory, and a dispersion relation has been obtained and stability criteria are given in the terms of relative velocity.

Abstract: A linear analysis of Kelvin-Helmholtz instability of cylindrical interface is carried out using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and tangential stresses are not considered. Both asymmetric and axisymmetric disturbances are considered. A dispersion relation has been obtained and stability criteria are given in the terms of the relative velocity. A comparison between inviscid potential flow and viscous potential flow has been made. It has been observed that Reynolds number and inner fluid fraction both have destabilizing effect on the stability of the system.