Instabilities of variable-density swirling flows
| Autor: | Malek Abid, Bastien Di Pierro |
|---|---|
| Přispěvatelé: | Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Asymptotic analysis
Mathematical analysis Rotational symmetry Geometry 01 natural sciences 010305 fluids & plasmas Euler equations Vortex [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] Physics::Fluid Dynamics Base (group theory) symbols.namesake Inviscid flow 0103 physical sciences symbols Wavenumber [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] 010306 general physics Constant (mathematics) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2010, pp.046312. ⟨10.1103/PhysRevE.82.046312⟩ Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2010, pp.046312. ⟨10.1103/PhysRevE.82.046312⟩ |
| ISSN: | 1539-3755 1550-2376 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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