title: Instabilities of variable-density swirling flows.
abstract: 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)], and used by many authors, breaks down if kW'(r) + mΩ'(r) ≠ 0, ∀r or if kW'(r) + mΩ'(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)]. 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.
authors.affiliation: IRPHE-UMR 6594, Technopôle de Château-Gombert, 49 rue Joliot Curie, BP 146, 13384 Marseille Cedex 13, France.
authors.forename: Bastien
authors.initials: B
authors.lastname: Di Pierro
authors.forename: Malek
authors.initials: M
authors.lastname: Abid