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Article Dans Une Revue Journal of Fluid Mechanics Année : 2006

Axisymmetric stability of the flow between two exactly counter-rotating disks with large aspect ratio

Résumé

We study the first bifurcation in the axisymmetric flow between two exactly counterrotating disks with very large aspect ratio Γ ≡R/H, where R is the disk radius and 2H is the inter-disk spacing. The scaling law for the critical Reynolds number is found to be Rec ∝ Γ(−1/2), with Re=ΩH2/ν, Ω being the magnitude of the angular velocity and ν the kinematic viscosity. An asymptotic analysis for large Γ is developed, in which curvature is neglected, but the centrifugal acceleration term is retained. The Navier–Stokes equations then reduce to leading order to those in a Cartesian frame, and the axisymmetric base flow to a parallel flow. This allows us locally to use a Fourier decomposition along the radial direction. In this framework, we explain the physical mechanism of the instability invoking the linear azimuthal velocity profile and the effect of centrifugal acceleration.
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Dates et versions

hal-01848280 , version 1 (24-07-2018)

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  • HAL Id : hal-01848280 , version 1

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Laurent Martin-Witkowski, Ivan Delbende, J. S. Walker, Patrick Le Quéré. Axisymmetric stability of the flow between two exactly counter-rotating disks with large aspect ratio. Journal of Fluid Mechanics, 2006, 546, pp.193-202. ⟨hal-01848280⟩
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