Effects of viscosity on inertial waves in swirling jets

Effects of viscosity on wave propagation in swirling jets are examined. The swirling jet is modeled by a top-hat axial velocity profile, with a constant axial vorticity in an unperturbed state. The jet is surrounded by an irrotationally revolving inviscid incompressible fluid (i.e. potential flow). An exact solution of the given linearized problem in the form of a partial inertial wave is presented. The velocity and pressure fields in the core can be expressed through the superposition of partial waves. Normal mode analysis leads to an eigenvalue problem which is reduced to find the roots of the dispersion transcendental equation. We conduct the stability analysis based on this dispersion equation.