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

TL;DR

This study uses direct numerical simulations to investigate how the number and wavelength of Taylor rolls affect flow statistics in turbulent Taylor-Couette flow, revealing that some flow features depend on domain size while others do not.

Contribution

It demonstrates that the number of Taylor rolls and their wavelength influence certain flow statistics, with some being independent of these parameters, advancing understanding of flow structure robustness.

Findings

Torque and mean flow are unaffected by roll wavelength and number.

Velocity fluctuations and spectra depend on the computational box size.

Velocity spectra show a sharp cutoff at wavelengths larger than the roll wavelength.

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 $Re_i=3.4\cdot10^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of $Re_\tau\approx500$, except for the $\Gamma=14$ simulation where $Re_i=1.5\cdot10^4$ and $Re_\tau\approx240$. 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.