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Marseille, France

Di Pierro B.,IRPHE UMR 6594 | Abid M.,IRPHE UMR 6594
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

Inviscid swirling flows are modeled, for analytical studies, using axisymmetric azimuthal, V (r), and axial, W (r), velocity profiles (r is the distance from the axis). The asymptotic analysis procedure (large wave numbers, k axial and m azimuthal) developed by Leibovich and Stewartson [J. Fluid Mech. 126, 335 (1983)]10.1017/S0022112083000191, and used by many authors, breaks down if k W′ (r) +m Ω′ (r) 0,r or if k W′ (r) +m Ω′ (r) =0,r, Ω=V/r. This latter case occurs if W is constant with m=0, if Ω is constant with k=0, or if both W and Ω are constant with arbitrary wave-number vector. These particular cases are considered by Leblanc and LeDuc [J. Fluid Mech. 537, 433 (2005)]10.1017/S0022112005005483. Thus, the case where W and Ω both vary and the Leibovich and Stewartson asymptotics breaks down remains. It is addressed in the present paper for weak variations of axial and azimuthal velocities. The asymptotic results are checked using numerically computed growth rates of the linearized Euler equations for a family of variable-density Batchelor-like vortices as base flows. Good agreement is found even for low values of m and k. © 2010 The American Physical Society.

Di Pierro B.,IRPHE UMR 6594 | Abid M.,IRPHE UMR 6594
Journal of Fluid Mechanics | Year: 2012

Linear and nonlinear impulse responses are computed, using three-dimensional numerical simulations, for an incompressible and variable density (inhomogeneous) Batchelor vortex at a moderately high Reynolds number, Re = 667. In the linear framework, the computed wavepacket is decomposed into azimuthal modes whose growth rates are determined along each spatiotemporal ray, in the laboratory frame. It is found that the Batchelor vortex undergoes a convective/absolute transition when the density ratio (inner/ambient), s, is varied solely (there is no need for an external counter flow to trigger this transition like that needed in the constant density case). More precisely, it is shown that the transition occurs for heavy vortices when the density ratio reaches a critical value, sc 1.08. For light vortices (s < 1) no transition was found. It is also shown that the first azimuthal mode that transits have an azimuthal wavenumber m =-2 and the transition occurs for a swirl number (a measure of the azimuthal to axial velocity ratio), q = 0.57. It is followed by m =-1, then by m=-3. When nonlinearities are allowed, it is found that they saturate the amplitude within the linear-response wavepacket, leaving the wavepacket fronts unaffected. The conclusions should thus be the same as those obtained in the linear case: the linear convective/absolute transition should coincide with the nonlinear one for the variable-density Batchelor vortex. © 2012 Cambridge University Press.

Dipierro B.,IRPHE UMR 6594 | Abid M.,IRPHE UMR 6594
European Physical Journal B | Year: 2012

Using linear instability theory and nonlinear dynamics, the Rayleigh-Taylor instability of variable density swirling flows is studied. It is found that the flow topology could be predicted, when the instability sets in, using a function χ dependent on density and axial and azimuthal velocities. It is shown that even when the inner axial-flow is heavier than the outer one (a favorable case for the development of the Rayleigh-Taylor instability thanks to the centrifugal force) the instability is not necessarily Rayleigh-Taylor- dominated. It is also shown that when the Rayleigh-Taylor instability develops, it is helical. © 2012 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

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