Nonlinear Stability Analysis and Transition in Wall-bounded Flows in the Frequency Domain

Abstract

Transition to turbulence in wall-bounded flows is driven by the nonlinear interaction of multiple instability mechanisms, especially in separated and high-speed flows. This seminar presents a frequency-domain framework based on the Harmonic-Balanced Navier–Stokes (HBNS) equations and space–time spectral methods (STSM) for predicting finite-amplitude disturbance evolution without the full cost of direct numerical simulations.

By retaining a small number of harmonics in space and time and their nonlinear triadic interactions, the method captures mean-flow deformation, energy transfer between modes, and the development of transition mechanisms within a stability-analysis framework. Coupled with adjoint-based optimisation, it identifies worst-case external disturbances and nonlinear routes to transition. The approach formally extends linear frequency domain methods, including global stability and resolvent analysis, to the nonlinear regime, enabling the prediction of transition mechanisms beyond the infinitesimal-amplitude limit.

Applications include incompressible laminar separation bubbles, compressible boundary layers, and oblique shock-wave/boundary-layer interactions. The results reveal how Kelvin–Helmholtz, Mack-mode, centrifugal/Görtler-type instabilities, streamwise vortices, and streaks interact to drive breakdown. The seminar will also discuss extensions of the methods for super resolving experimental measurements using physics informed neural networks constrained by the HBNS equations.

Overall, the work provides a unified nonlinear input/output perspective on transition in wall-bounded flows and offers a tractable route for analysing and controlling separated and high-speed aerodynamic flows.

Relevant publications

[1] F. Savarino, D. Sipp, and G. Rigas. Optimal transitional mechanisms of incompressible separated shear layers subject to external disturbances. Journal of Fluid Mechanics, 1016:A43, 2025.

[2] A. Poulain, C. Content, A. Schioppa, P. Nibourel, G. Rigas, and D. Sipp. Adjoint-based optimisation of time- and span-periodic flow fields with space-time spectral method: Application to non-linear instabilities in compressible boundary layer flows. Computers & Fluids, 282:106386, 2024.

[3] F. Savarino, A. Poulain, D. Sipp, and G. Rigas. Optimal transitional mechanisms in oblique shock-wave/boundary-layer interaction using non-linear input/output analysis. AIAA SciTech Forum, Orlando, FL, USA, 2024.

Speaker

Prof. Georgios Rigas is an Associate Professor in Fluid Mechanics at Imperial College London. He received his PhD from Imperial in 2015 and held postdoctoral positions at Caltech and the University of Cambridge before returning to Imperial in 2019. His research focuses on the intersection of fluid mechanics and artificial intelligence, developing algorithms for real-time aerodynamic prediction and control demonstrated in wind-tunnel environments. He leads the UKRI AI for Net Zero Hub at Imperial (https://aifornetzero.co.uk/) and contributes to the Department for Energy Security and Net Zero's ADViCE initiative. He serves as a Board Member for Physical Review Fluids and as Associate Editor in Theoretical and Computational Fluid Mechanics.