The strato-rotational instability of Taylor-Couette and Keplerian flows

The linear inviscid stability of two families of centrifugally stable rotating flows in a stably stratified fluid of constant Brunt-Vaisala frequency N is analysed by using numerical and asymptotic methods. Both Taylor-Couette and Keplerian angular velocity profiles Omega(TC) = (1 - mu)/r(2) + mu and Omega(K) =(1 - lambda)/r(2) + lambda/r(3/2) are considered between r = 1 (inner boundary) and r = d > 1 (outer boundary, or without boundary if d = infinity). The stability properties are obtained for flow parameters lambda and mu ranging from 0 to +infinity, and different values of d and N. The effect of the gap size is analysed first. By considering the potential flow (lambda = mu = 0), we show how the instability associated with a mechanism of resonance for finite-gap changes into a radiative instability when d -> infinity. Numerical results are compared with large axial wavenumber results and a very good agreement is obtained. For infinite gap (d = infinity), we show that the most unstable modes are obtained for large values of the azimuthal wavenumber for all lambda and mu. 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.