# Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness

## TL;DR

This study investigates how spanwise-varying roughness on the inner cylinder of Taylor-Couette flow influences turbulence, flow structures, and angular momentum transport through combined experimental and numerical methods.

## Contribution

It introduces a detailed analysis of the effects of roughness spacing and width on flow dynamics and transport properties in turbulent Taylor-Couette flow, combining experimental and DNS approaches.

## Key findings

- Maximum angular momentum transport occurs at an optimal roughness spacing.
- Roughness induces large-scale turbulent vortices and flow re-arrangement.
- Flow structures and transport properties depend on boundary conditions set by roughness.

## Abstract

Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. Experimentally, we explore $\text{Ta}=\mathcal{O}(10^{12})$ and $0.61\leq \tilde s \leq 3.74$. For both approaches the radius ratio is fixed at $\eta=r_i/r_o = 0.716$, with $r_i$ and $r_o$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport as function of $\tilde s$. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.