Nonlinear stability of axisymmetric swirling flow
The stability of inviscid, incompressible axisymmetric swirling flows to disturbances of finite size was studied. The method employed is the energy - Casimir method, which is an algorithm for the construction of a Lyapunov type stability argument for conservative, infinite dimensional dynamical systems. The problem is phrased in terms of the vortex density (azimuthal vorticity divided by radius), swirl function (radius times the azimuthal component of velocity), and an auxiliary variable, the Stokes stream function. The noncanonical Hamiltonian structure is given for the problem, and the resulting Lie - Poisson bracket used to find the required constants of the motion. The stability argument is given for general axisymmetric equilibria, and for the special cases of columnar and non-rotating equilibria. In the first two cases, it is necessary to cut off the wavenumber of the vortex density component of the admissible class of disturbances in order to address indefiniteness to high wavenumber perturbations. Finally, the results of numerical experiments are reported which test the conclusions of the analytical stability criteria. A direct numerical simulation of the evolution equations was performed using conserving upwind differences and the ADI method of time advancement.
- Research Organization:
- Cornell Univ., Ithaca, NY (USA)
- OSTI ID:
- 5293358
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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