Instabilities of variable-density swirling flows

Area of Science:

• Fluid Dynamics
• Asymptotic Analysis
• Hydrodynamics

Background:

• Inviscid swirling flows are often modeled using axisymmetric velocity profiles.
• Existing asymptotic analysis methods (Leibovich and Stewartson) have limitations when velocity gradients satisfy specific conditions.

Purpose of the Study:

• To develop an analytical method for modeling inviscid swirling flows where standard asymptotic procedures fail.
• To investigate the behavior of these flows under weak variations in axial and azimuthal velocities.

Main Methods:

• Applied asymptotic analysis for large axial (k) and azimuthal (m) wave numbers.
• Investigated cases where the Leibovich and Stewartson condition kW'(r) + mΩ'(r) = 0 is not met for all r.
• Validated analytical results with numerical computations of linearized Euler equations for variable-density Batchelor-like vortices.

Main Results:

• Developed a successful asymptotic analysis for inviscid swirling flows with varying velocity profiles, overcoming limitations of previous methods.
• Demonstrated good agreement between analytical predictions and numerical results, even for low wave numbers (m and k).

Conclusions:

• The proposed asymptotic analysis provides a robust method for studying complex swirling flows.
• The findings are applicable to a range of fluid dynamics problems involving vortex dynamics and stability.