Geodesic
Modeling of large vortical structures in axisymmetrical jet flows
Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 111-130.

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A numerical study of the origin and development of the instability at the boundary of an axisymmetrical jet flow is carried out. The flow to be studied is represented by infinite uniform along the axis of symmetricity compressible flow with a specific distribution of the streamwise velocity in the radial direction. The method of the linear analysis is applied to investigate stability of disturbances in the form of normal harmonics, which shows the existence of unstable modes. Quantitative characteristics of these modes – the growth rate factor and the phase frequency – are obtained as functions of model parameters that design the regime of the basic jet flow. It is shown that the dominant unstable mode exists, which corresponds to the specific value of the longitudinal wave number. Direct numerical simulation of the nonlinear phase of the axisymmetrical mode development is performed, with the aid of which basic mechanisms of the transition from a simple straight motion in the jet into a complex vortical flow with the formation of large toroidal vortex are explained.
Keywords: gas stream, screech tone, aeroacoustics, the linear stability analysis, numerical modeling of three-dimensional non-stationary currents. 
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I. S. Menshov; A. N. Nenashev. Modeling of large vortical structures in axisymmetrical jet flows. Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 111-130. http://geodesic.mathdoc.fr/item/MM_2011_23_11_a7/

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