2008/07/04 by Christiane Normand, Normand, Christiane
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Aeolian processes and effects #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0807.0702
18 pages, no figure
openalex publication_date 2008/07/04 · arxiv created 2008/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An analytical approach is carried out that provides an inviscid stability criterion for the strato-rotational instability (in short SRI) occurring in a Taylor-Couette system. The control parameters of the problem are the rotation ratio μ and the radius ratio η. The study is motivated by recent experimental \citelegal and numerical \citerudi, rudi2 results reporting the existence of unstable modes beyond the Rayleigh line for centrifugal instability (μ=η2). The modified Rayleigh criterion for stably stratified flows provides the instability condition, μ<1, while in experiments unstable modes were never found beyond the line μ=η. Taking into account finite gap effects, we consider non axisymmetric perturbations with azimuthal wavenumber l in the limit l Fr<<1, where Fr is the Froude number. We derive a necessary condition for instability : μ< μ^* where μ^*, a function of η, takes the asymptotic values, μ^* → 1 in the narrow gap limit, and μ^* → 2η2(1+η) in the wide gap limit, in agreement with recent numerical findings. A stronger condition, μ0.38, in agreement with experimental results obtained for η=0.8. Whatever the gap size, instability is predicted for values of μ larger than the critical one, μc=η2, corresponding to centrifugal instability.