The effect of roll number on the statistics of turbulent Taylor-Couette flow

Abstract

A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectively. Large axial aspect ratios $\Gamma =7$-$8$ (with $\Gamma =L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with $\Gamma =14$ were used in order to allow the system to select the most unstable wavenumber and to possibly develop multiple states. The radius ratio was taken as $\eta =r_i/r_o=0.909$, the inner cylinder Reynolds number was fixed to $R{e}_i=3.4\cdot 10^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of $R{e}_{\tau }\approx 500$, except for the $\Gamma =14$ simulation where $R{e}_i=1.5\cdot 10^4$ and $R{e}_{\tau }\approx 240$. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls $n_r$ and roll wavelength ${\lambda }_z$ were found for $\Gamma =7$. The effect of ${\lambda }_z$ and $n_r$ on the statistics was quantified. The torque and mean flow statistics were found to be independent of both ${\lambda }_z$ and $n_r$, while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra was found to have a very sharp drop off for wavelengths larger than ${\lambda }_z$, while for the small wavelengths they collapse.

References in corpus (7)

• High Reynolds number Taylor-Couette turbulence
• Multiple states in highly turbulent Taylor-Couette flow
• Exploring the phase diagram of fully turbulent Taylor-Couette flow
• The near-wall region of highly turbulent Taylor-Couette flow
• Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder
• Effect of the number of vortices on the torque scaling in Taylor-Couette flow
• Momentum transport in Taylor-Couette flow with vanishing curvature

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• Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection
• Life stages of wall-bounded decay of Taylor-Couette turbulence
• Transitions of turbulent superstructures in generalized Kolmogorov flow
• Taylor rolls on tour: Slow drift of turbulent large-scale structures in flows with continuous symmetries