NUMERICAL MODELING TECHNIQUE FOR THE HYDRODYNAMIC STABILITY OF SWIRLING FLOWS
NUMERICAL MODELING TECHNIQUE FOR THE HYDRODYNAMIC STABILITY OF SWIRLING FLOWS
DOI:
https://doi.org/10.22337/2587-9618-2026-22-3-135-143Keywords:
hydrodynamic stability, small-disturbance method, swirling flow, viscous mode, growth rate coefficientsAbstract
A numerical technique is proposed for investigating the hydrodynamic stability of axisymmetric swirling flows of an incompressible viscous fluid within the linear stability theory framework. The associated eigenvalue problem is governed by a system of sixth-order ordinary differential equations. Asymptotic expansions are constructed at both artificial and irregular singular points to facilitate the solution. The system is integrated numerically using a high-order accurate scheme, and the Gram–Schmidt or thonormalization procedure is employed to suppress the rapid growth of particular solutions, thereby ensuring their linear independence. A computational package based on the developed methodology has been implemented and applied to the stability analysis of the Batchelor vortex. Validation tests are conducted to compare the obtained results against available reference data. The existence of a viscous instability mode is established, for which the maximum growth rate is found to decrease monotonically with increasing Reynolds number.
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