The strato-rotational instability

The linear stability of a Taylor Couette Flow, linearly stratified in the direction of the cylinders axis with a constant Brunt-V\"ais\"al\"a frequency $N$, is analysed by asymptotical, numerical and experimental methods. The marginal stability curve in the parameter plane $(\eta=R_i/R_o; \mu=\Omega_o/\Omega_i)$, where $R_i$ and $\Omega_i$ (resp. $R_o$ and $\Omega_o$) are the radius and angular velocity of the inner (resp. outer) cylinder, is obtained for various Froude number $F=\Omega_i/N$ and Reynolds number $Re= \Omega_i r_i^2/\nu$. A particular attention is paid to the infinite gap limit ($\eta=0$) for which an inviscid estimate for the critical $\mu$ for instability is derived theoretically. The instability mechanism is discussed using an asymptotical description for large axial perturbation wavenumbers. The numerical and theoretical results are compared to new experimental data obtained for large gaps.