Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

The stably stratified Taylor-Couette flow is investigated experimentally and numerically through linear stability analysis. In the experiments, the stability threshold and flow regimes have been mapped over the ranges of outer and inner Reynolds numbers: -2000 < Re-o < 2000 and 0 < Re-i < 3000, for the radius ratio r(i)/ro = 0.9 and the Brunt-Vaisala frequency N approximate to 3.2 rad s(-1). The corresponding Froude numbers F-o and F-i are always much smaller than unity. Depending on Re-o (or equivalently on the angular velocity ratio mu = Omega(o)/Omega i), three different regimes have been identified above instability onset: a weakly non-axisymmetric mode with low azimuthal wavenumber m = O(1) is observed for Re-o < 0 (mu < 0), a highly non-axisymmetric mode with m similar to 12 occurs for Re-o > 840 (mu > 0.57) while both modes are present simultaneously in the lower and upper parts of the flow for 0 <= Re-o <= 840 (0 <= mu <= 0.57). The destabilization of these primary modes and the transition to turbulence as Rei increases have been also studied. The linear stability analysis proves that the weakly non-axisymmetric mode is due to the centrifugal instability while the highly non-axisymmetric mode comes from the strato-rotational instability. These two instabilities can be clearly distinguished because of their distinct dominant azimuthal wavenumber and frequency, in agreement with the recent results of Park et al. (J. Fluid Mech., vol. 822, 2017, pp. 80-108). The stability threshold and the characteristics of the primary modes observed in the experiments are in very good agreement with the numerical predictions. Moreover, we show that the centrifugal and strato-rotational instabilities are observed simultaneously for 0 <= Re-o <= 840 in the lower and upper parts of the flow, respectively, because of the variations of the local Reynolds numbers along the vertical due to the salinity gradient.