Torque transport mean velocity profiles and turbulent statistics of a wide gap Taylor Couette flow

Abstract

Wall-bounded turbulent flows that possess finite curvature of the mean flow streamlines are known to be starkly different from their plane counterparts. One of the primary distinguishing features of such flows is the existence of a distinct mechanism of instability (centrifugal instability) that is altogether absent in planar flows. This fact is seen to have deep consequences with regards to flow dynamics and coherent structures and begs further inquiry into the underlying physics. With this as the primary motivation, we have chosen a wide-gap Taylor-Couette (TC) configuration with rotating inner cylinder and a fixed outer cylinder as a model problem to isolate and study the effects of flow curvature. Direct numerical simulation (DNS) of the incompressible Navier-Stokes equations in cylindrical polar co-ordinates has been employed for obtaining high-resolution spatio-temporal data of the flow field. The radius ratio and the aspect ratio chosen for the simulations are $0.1$ and $5.5$ respectively. Accurate representation of the flow field in such a large domain demands significant resolution in space and time which directly translates into large memory requirements and runtime of the DNS code. As an attempt to alleviate these issues, the first part of the study deals with the implementation of an efficient multi-core algorithm using an influence matrix based domain decomposition technique. Using this efficient code, we proceed to study the centrifugal instability that occurs around an impulsively rotated cylinder in otherwise quiescent fluid. We find that the critical wavelength and the critical boundary layer thickness (i.e. $\lambda_{c}$ and $\delta_{c}$) at the onset of the instability scale with Reynolds number as $Re^{-2/3}_{a}$. A critical Taylor number defined as $Ta = Re^{2}_{a}(g/a)^{3}$ ($g$ is the gap-width and $a$ is the radius of the inner cylinder) with $g$ being replaced using either $\lambda_{c}$ or $\delta_{c}$ is found to achieve a constant value at large Reynolds numbers...