The linear inviscid stability of two families of centrifugally stable rotating flows in a stably stratified fluid of constant Brunt-Väisälä frequency N is analysed by using numerical and asymptotic methods. Both Taylor-Couette and Keplerian angular velocity profiles Ω TC = (1 − µ)/r 2 + µ and Ω K = (1 − λ)/r 2 + λ/r 3/2 are considered between r = 1 (inner boundary) and r = d > 1 (outer boundary, or without boundary if d = ∞). The stability properties are obtained for flow parameters λ and µ ranging from 0 to +∞, and different values of d and N. The effect of the gap size is analysed first. By considering the potential flow (λ = µ = 0), we show how the instability associated with a mechanism of resonance for finite-gap changes into a radiative instability when d → ∞. Numerical results are compared with large axial wavenumber results and a very good agreement is obtained. For infinite gap (d = ∞), we show that the most unstable modes are obtained for large values of the azimuthal wavenumber for all λ and µ. We demonstrate that their properties can be captured by performing a local analysis near the inner cylinder in the limit of both large azimuthal and axial wavenumbers. The effect of the stratification is also analysed. We show that decreasing N is stabilizing. An asymptotic analysis for small N is also performed and shown to capture the properties of the most unstable mode of the potential flow in this limit.

International audienceThe stability of the flow around a rotating cylinder in a fluid linearly stratified along the cylinder axis is studied numerically and experimentally for moderate Reynolds numbers. The flow is assumed potential and axisymmetric with an angular velocity profile Omega = 1/r(2), where r is the radial coordinate. Neglecting density diffusion and non-Boussinesq effects, the properties of the linear normal modes are first provided. A comprehensive stability diagram is then obtained for Froude numbers between 0 and 3 and Reynolds numbers below 1000. The main result is that the potential flow, which is stable for a homogeneous fluid, becomes unstable for Froude number close to one and for Reynolds numbers larger than 360. The numerical results are then compared with experimental results obtained using shadowgraph and synthetic Schlieren techniques. Two symmetrical helical modes are found to be simultaneously unstable. We show that these modes exhibit an internal gravity wave structure extending far from the cylinder in agreement with the theory. Their wavelength and frequency are shown to be in good agreement with the numerical predictions for a large range of Froude and Reynolds numbers. These experimental results are the first indisputable evidence of the radiative instability

In this paper we report measurements of the heat flux in a slightly tilted channel (angle less than 45°), filled with water, that connects two chambers: the hot in the lower part and the cold on the top. We show that different regimes develop depending on the angle and the applied power. We put in evidence a hard turbulent regime, a soft turbulent regime, a laminar regime, and an intermittent one. In the last regime, the flow oscillates between laminar and turbulent, which locks the temperature gradient to a constant value. We characterize those regimes thanks to the measurement of the axial gradient of temperature and to the measurement of the power. We model them giving descriptions in term of Nusselt and Rayleigh numbers. The soft turbulence to hard turbulence transition is interpreted as the birth of the inertial range of developed turbulence. This transition, which appears in several systems, is particularly clear here, thanks to its consequences on heat transport properties.