Acoustic-vorticity coupling in linear flows using Wentzel-Kramers-Brillouin (WKB) method
Résumé
The evolution of linear acoustic and vorticity perturbations in incompressible linear flow is studied. In the particular case of the plane Couette flow, two major phenomenons occur: acoustic wave generation by vortexes, and acoustic wave transformations. A straight forward order 1 WentzelKramersBrillouin (WKB) method is developed to perform a systematic study of all 2D incompressible linear flows. A small correction based on the conservation of a constant quantity is made to avoid non uniformities. All the considered flows are decomposed as a weighted sum of a hyperbolic flow and a solid rotation flows. Three modes naturally come out of such an approach: two acoustic modes with opposite phase velocities, and one vorticity mode. The acoustic mode acquire a vorticial component and are not curl-free. In the same time the vorticity mode are not divergence-free. The two above mentioned coupling phenomenons are also studied. They are due to Landau-Zenner type non-adiabatic transitions, and are of an order exponentially small with respect to the shear rate of the flow. The efficiency of the couplings depending on the flow class is investigated. The hyperbolic flow provides the most efficient coupling.
Domaines
Acoustique [physics.class-ph]
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