Synchronization of turbulent channel flow

About the Project

Chaos may seem like complete disorder, but even chaotic systems can sometimes fall into step — a phenomenon called chaos synchronisation. Two systems that start differently can gradually align their behaviour through a small amount of interaction or shared information, much like pendulum clocks on the same wall eventually ticking together.

In turbulent flows, synchronisation is a powerful way to understand and control chaos. By gently coupling a simulation with measurements from the real flow, the simulation can synchronise with reality, effectively reconstructing the entire flow field. This approach is related to data assimilation, allowing for better prediction, control, and optimisation of turbulent systems in engineering, energy, and environmental applications.

The synchronisation of high-Reynolds-number turbulent flows is a forefront question in turbulence research, and our group has recently made novel discoveries on the conditional Lyapunov exponent and vector in synchronised turbulent flows with or without rotation, leading to three papers publishing in Journal of Fluid Mechanics, one of the leading journals in the field.

In this project, the candidate will extend our previous work to channel flows, both with and without wall roughness. The research will focus on, firstly, optimal synchronisation of minimal unit turbulence (MUT), leveraging the simplified dynamics in MUT to explore effective on-off coupling; and secondly, optimising coupling strategies for rough walls, exploiting the characteristics of wall roughness to enhance synchronisation.

The candidate is expected to carry out high-performance numerical simulations using our in-house CFD code, extract physical insights from simplified flow models, and characterise synchronisation thresholds and the robustness of synchronised states using analytical and statistical techniques.

Funding Notes

This project is for self-funded or externally funded students only.

References

1. Synchronisation of rotating turbulent (https://www-cambridge-org.sheffield.idm.oclc.org/core/journals/journal-of-fluid-mechanics/article/conditional-lyapunov-exponents-and-synchronisation-of-rotating-turbulent-flows/2233424EF1B7E8C4B2BACD4C48DABCBF)
2. Spectral dynamics of the conditional Lyapunov vector (https://www-cambridge-org.sheffield.idm.oclc.org/core/journals/journal-of-fluid-mechanics/article/spectral-dynamics-and-spatial-structures-of-the-conditional-lyapunov-vector-in-slave-kolmogorov-flow/513B0E57DC44BC69F05251E33E25C378)
3. The intrinsic relationship between the synchronisation threshold and the Lyapunov vector ( https://www-cambridge-org.sheffield.idm.oclc.org/core/journals/journal-of-fluid-mechanics/article/intrinsic-relationship-between-synchronisation-thresholds-and-lyapunov-vectors-evidence-from-large-eddy-simulations-and-shell-models/B869DB26F3064A63BE571DE4BB5DAA31)