Wave emergence in turbulent Taylor–Couette flow with free-surface
Title: Wave emergence in turbulent Taylor–Couette flow with free-surface
SNIC Project: SNIC 2022/5-297
Project Type: SNIC Medium Compute
Principal Investigator: Cristobal Arratia <cristobal.arratia@su.se>
Affiliation: NORDITA
Duration: 2022-05-30 – 2023-06-01
Classification: 20306


Among the various challenges of the study of turbulent flows, this project is concerned with the emergence of coherent structures at large spatial scales. This phenomenon is in direct contrast with the picture of turbulence as a cascade bringing energy to small scales and restoring (statistically) the imposed symmetries; these coherent structures break symmetry. In particular this project focuses on the case of gravity waves in free-surface Taylor-Couette flow, given by the partially filled gap between two vertical concentric cylinders. This flow was studied experimentally in ML06 (Mujica and Lathrop, J.Fluid Mech. 551:49-62, 2006) and MAFM15 (Martinez-Mercado et al, New J.Phys. 17(1):013039, 2015), who report the appearance of a low frequency, large scale modulation of the free surface (a wave) within the turbulent regime. This wave bifurcates from an axisymmetric turbulent state and exhibits hysteresis, indicating the bifurcation is subcritical. The current work aims to analyze this flow by computing the mean flow and characterizing its stability and amplification properties. This type of analysis has previously been performed for other turbulent flows, and has been fairly successful in explaining some aspects of turbulent spectra and coherent structures through the linear amplification properties of the mean flow. This has also been used in quasi-linear models to explain some of the frequency selection mechanisms and large scale structures. We aim to use these methods to understand the experimentally observed modulations in free-surface Taylor-Couette flows. To the best of our knowledge this would be the first such investigation of mean flow amplification of free-surface flows in a non-parallel setting. The computational project is set up in accordance with the previous experimental work in MAFM15, where the Froude number (relating the driving speed and gravity) has been found to be the primary relevant parameter for the investigations. However, since the triggering of the subcritical instability likely relies on the turbulent fluctuations, the flow must necessarily be turbulent enough to push the flow past the critical amplitude threshold. Therefore we focus our work on two different Reynolds numbers. A lower Reynolds number (Re) of 100, 000 where we expect the flow to exhibit sufficient turbulence activity such that the bifurcation scenario may be qualitatively observed (possibly with forcing and at a different Froude number). In this regime we aim to carry out the mean flow stability and amplification analysis for several Froude number cases, allowing to build an understanding of the mean flow amplification properties and the qualitative dynamics of the flow. Finally a second higher Reynolds number regime of 300, 000 will also be studied, allowing us to compare directly with the experimental flow conditions and obtain quantitative results that may be directly compared with the experiments. This would be much more computationally expensive and in the current project we aim to perform analysis on only two cases within this regime. The computational costs for the different cases have been estimated through tests on Tetralith and are mentioned below.