Centrifugal instability of Taylor-Couette flow in stratified and diffusive fluids

Abstract

The linear and non-linear dynamics of centrifugal instability in Taylor-Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) on cylindrical Couette flow confirms that the stabilising role of stratification on centrifugal instability is suppressed by strong thermal diffusion (i.e. low Prandtl number $Pr$). For $Pr\ll 1$, it is verified that the instability dependence on thermal diffusion and stratification with the non-dimensional Brunt-Väisälä frequency $N$ can be prescribed by a single rescaled parameter $P_N=N^{2}Pr$. From direct numerical simulation (DNS), various non-linear features such as axisymmetric Taylor vortices at saturation, secondary instability leading to non-axisymmetric patterns or transition to chaotic states are investigated for various values of $Pr\le 1$ and the Reynolds number $R{e}_i$. Two-dimensional bi-global LSA on axisymmetric Taylor vortices, which appear as primary centrifugal instability saturates nonlinearly, is also performed to find the secondary critical Reynolds number $R{e}_{i,2}$ at which the Taylor vortices become unstable by non-axisymmetric perturbation. The bi-global LSA reveals that $R{e}_{i,2}$ increases (i.e. the onset of secondary instability is delayed) in the range $10^{-3}<Pr<1$ at $N=1$ or as $N$ increases at $Pr=0.01$. Secondary instability leading to highly non-axisymmetric or irregular chaotic patterns is further investigated by the 3D DNS. The Nusselt number $Nu$ is also computed from the torque at the inner cylinder for various $Pr$ and $R{e}_i$ at $N=1$ to describe how the angular momentum transfer increases with $R{e}_i$ and how $Nu$ varies differently for saturated and chaotic states.

arXiv commentaccepted manuscript in Journal of Fluid Mecahnics

References in corpus (28)

• Stability and turbulent transport in rotating shear flows: prescription from analysis of cylindrical and plane Couette flows data
• Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flow
• Turbulent transport in radiative zones of stars
• Anisotropic turbulent transport in stably stratified rotating stellar radiation zones
• Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection
• Shear mixing in stellar radiative zones I. Effect of thermal diffusion and chemical stratification
• The dynamics of stratified horizontal shear flows at low Péclet number
• Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
• Horizontal shear instabilities at low Prandtl number
• Horizontal shear instabilities in rotating stellar radiation zones: I. Inflectional and inertial instabilities and the effects of thermal diffusion
• Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration
• Angular momentum transport by the GSF instability: nonlinear simulations at the equator
• nsCouette -- A high-performance code for direct numerical simulations of turbulent Taylor-Couette flow
• On the role of the Prandtl number in convection driven by heat sources and sinks
• Stratorotational instability in MHD Taylor-Couette flows
• Angular momentum transport, layering, and zonal jet formation by the GSF instability: nonlinear simulations at a general latitude
• Connections between centrifugal, stratorotational and radiative instabilities in viscous Taylor-Couette flow
• The stratorotational instability of Taylor-Couette flows of moderate Reynolds numbers
• Experiments and long-term High Performance Computations on amplitude modulations of strato-rotational flows
• Linear and nonlinear properties of the Goldreich-Schubert-Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation
• Critical Balance and Scaling of Strongly Stratified Turbulence at Low Prandtl Number
• Modeling coexisting GSF and shear instabilities in rotating stars
• Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh-Bénard convection
• Stably stratified exact coherent structures in shear flow: the effect of Prandtl number
• Numerical validation of scaling laws for stratified turbulence
• Nonlinear evolution of the centrifugal instability using a semi-linear model
• Anisotropic turbulent transport with horizontal shear in stellar radiative zones
• The tachocline revisited