Stratified Taylor--Couette (TC) flows have been investigated to understand, among others, the equatorial ocean circulation [1,2,3], mixing by vortices [4,5], and in an astrophysical context the stability of accretion disk due to the so-called strato-rotational instability observed experimentally in [6] and first compared to theory in [7]. Here, a centrifugally unstable flow is generated by a cylinder of radius $R$ that is impulsively set into rotation about its vertical axis with angular speed $\Omega$. The gap width is 3 to 13 times larger than the radius of the inner cylinder, and is filled with a linearly stratified fluid with buoyancy frequency $N$. We are considering the thin vorticity layer at the cylinder boundary of which the dynamics are determined by the Froude number $F=Ω/N$ and the Reynolds number $\mathit{Re}=\Omega R^2/\nu$, with $\nu$ the viscosity. A bifurcation is found at $F=1$, with for $F>1$ centrifugally unstable flow with vortices intruding in the ambient stratification, and for $F<1$, helicoidal inertial waves propagating along the inner cylinder boundary. This bifurcation has also been found in the small gap TC flow in [3,8] though here the waves are unstable and increase in amplitude when the Reynolds number $\mathit{Re}_n=\Omega R^2/(n\nu) >130$, with $n$ the azimuthal wave mode, and dissipate for $\mathit{Re}_n<130$. The origin of the instability is discussed. \\

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\end{itemize}