Instability and mixing in a turbulent stratified Taylor-Couette Flow

In this thesis, we investigate mixing mechanisms in a stably stratified turbulent Taylor-Couette flow, which is the flow in the annular region of two co-axial 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 Taylor-Couette (STC) flow with fixed outer cylinder, the flow spontaneously forms well-mixed layers of constant height separated by sharp density gradient interfaces. She also observed a quasi-periodic 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 in-phase 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{R₂}{(\Omega R₁)²} with R₁ and R₂ 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).

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2020

Author dc:creator

• Singh, Kanwar Nain

Advisor dc:contributor.advisor

• Caulfield, Colm-cille

• Stratification
• Turbulence
• Mixing
• Instability

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/9bd1e30c-0688-4ffe-9726-278201869c99/download
• https://creativecommons.org/licenses/by-nc-sa/4.0/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.48575

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/301506