Title:

Instability and mixing in a turbulent stratified TaylorCouette flow

In this thesis, we investigate mixing mechanisms in a stably stratified turbulent TaylorCouette flow, which is the flow in the annular region of two coaxial cylinders, both capable of rotating at different speeds independently, in the presence of vertical stable stratification. Oglethorpe (2014) found that, for an initially linearly stratified TaylorCouette (STC) flow with fixed outer cylinder, the flow spontaneously forms wellmixed layers of constant height separated by sharp density gradient interfaces. She also observed a quasiperiodic mixing phenomenon across the interfaces. Through laser induced fluorescence and particle images velocimetery, we discover the structure of this mixing instability. We find that the mixing occurs as a result of a flow phenomenon generated by two inphase boundary trapped waves, with azimuthal wavenumber $m=1$, riding on the interface. We further look into the flux across the interface resulting from this instability. We find that, for high stratification, the molecular diffusion plays a significant part in the overall observed flux across the interface, and the buoyancy flux does not tend to a constant as previously discussed by Oglethorpe (2014). As a result, we find that the entrainment coefficient, $E\sim Ri_B^{3/2}$, where $Ri_B = g'\frac{R_2}{(\Omega R_1)^2}$ with $R_1$ and $R_2$ being the inner and the outer cylinder radii respectively and $\Omega$ being the angular velocity of the inner cylinder, which is consistent with the classical observations of Turner (1968). Overall, we observe that the buoyancy flux monotonically increases as the mixing occurs (i.e. with reducing $Ri_B$) to a maximum where the interface is overturned by the turbulent eddies present in each of the layers. Furthermore, we perform stability analysis of the STC flow using a base flow having a dependence in both the radial $r$ and the axial $z$ directions,using the mean turbulent flow profile varying in $r$ as the base velocity profile and a density profile with a sharp gradient in the $z$ direction as the base density profile. Using our model, we are able to consistently predict the period of the empirically observed instability, which suggests that this instability has its origins in a linear instability. Finally, we look at the implications of rotating the outer cylinder on the observed instability. Through qualitative experiments and stability analysis, we discover that the same instability exists even outside the domain of centrifugal instability prescribed by Rayleigh's criterion (Rayleigh, 1917).
