Linear stability analysis of circular jets: integer, fractional, and multiple mode excitation
The linear stability analysis of Huang  has been adapted to ignore the effects of swirl, and to allow calculation of the eigenvalues and eigenfunctions for integer, fractional, and multiple modes of excitation. The investigation was intended to be exploratory; to gain the best possible insights into the flow characteristics from analysis of the linearized Euler equations. All of the azimuthal modes investigated (one-half, one, three-halves, and two) were found to lead to the continuous, helical, vortical structure evolution in the streamwise direction of the jet. The analysis for fractional modes of excitation predicted aphysical behavior near the jet center that has been attributed to a unresolved questions in the mathematical analysis of the problem. Multiple mode excitation at the axisymmetric mode and one or more azimuthal modes were found to result in un-even, periodic, vortex-ring growth in the shear layer. An argument was presented for the axisymmetric mode (m=O) resulting in the highest levels of entrainment for all integer, fractional, and multiple modes of excitation. Finally the importance of the azimuthal component of vorticity in the entrainment process was identified.