Dynamics of stochastic spatial-temporal patterns in transitional turbulence

This dissertation investigates the dynamical pattern formation in transitional turbulence that results from the interplay between nonlinearity and stochasticity. By employing Landau-type minimal models, we elucidate critical interactions on effective degrees of freedom that emerge from the full complexities of the system. We develop a stochastic approach to analyze the spatiotemporal patterns whose complexity has meant that the subcritical transition to turbulence has remained a century-old challenge since Reynolds’s pioneering experiments in 1883. The complex nature of transitional turbulence is explored from multiple angles: (1) We begin by examining the unique features of sub-critical transitional turbulence. This includes an exploration of the diverse patterns that emerge across varying systems, the statistical behaviors near critical points, and the dynamics of energy flow and energy balance in the systems. Particular emphasis is placed on transitional pipe flow. A minimal non-equilibrium stochastic model is introduced in the spirit of Landau theory for equilibrium systems, which highlights energy balancing in pipe flows. The model successfully reproduces the dynamical properties observed in all the four distinct phases arising in the laminar-turbulence transition in pipes. (2) We then navigate the subtle impact of stochasticity in transitional turbulence, elucidating how two distinct stochastic effects shape the dynamics in both low and high Reynolds number regimes. Through the application of stochastic calculus and singular perturbation techniques, we demonstrate the precise dynamics influenced by stochastic effects. (3) Subsequently, we demonstrate the capability of the model to capture the dynamics of not only pipe flow but also quasi-one-dimensional Taylor-Couette flow, because of the different ways that energy flows into and out of the system in the two geometries. The model predicts that the critical behavior of both systems is in the directed percolation universality class. This allows the first direct comparison of their near-critical dynamics, which reveals the origins of distinct patterns in the two systems, even though both are governed by the directed percolation class. In particular, the theory predicts that the width of the critical regime is greater in the Taylor-Couette case than in the pipe case, as is observed experimentally. (4) Finally, we provide an outlook of our work and discuss potential directions for future research.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Wang, Xueying

Contributors dc:contributor

• Goldenfeld, Nigel
• Dahmen, Karin A
• Maslov, Sergei
• Noronha, Jorge L

• Turbulence
• Transition To Turbulence
• Phase Transition
• Ecology
• Stochastic

Statement dc:rights

• Copyright 2024 Xueying Wang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127432

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127432