Mechanisms of laminar-turbulent transition in incompressible and compressible separated shear layers
File(s)
Author(s)
Savarino, Flavio
Type
Thesis or dissertation
Abstract
Accurate prediction of laminar–turbulent transition in separated boundary layers requires nonlinear stability frameworks, since linear analyses cannot capture the full transition path. Separation further complicates the problem through strong pressure gradients, non-parallel effects, reversed flow, streamline curvature, and, in supersonic flows, shock-wave interactions.
This thesis develops a unified description of how time- and spanwise-periodic external disturbances trigger transition in separated shear layers, linking incompressible pressure-gradient-induced Laminar Separation Bubble (LSB) and compressible oblique/reflected Shock-Wave/Boundary-Layer Interaction (SWBLI). Two frameworks are used: the Analytical Harmonic Balance Method (AHBM) for the incompressible Navier-Stokes (N-S) equations and the Space-Time Spectral Method (STSM) for the compressible N-S equations. Both are coupled with adjoint-based optimisation to identify ``worst-case'' forcings that maximise mean skin friction, a quantity that systematically rises during transition.
Two canonical convectively unstable flows are examined: an incompressible LSB and a Mach 2.15 oblique/reflected SWBLI. Linear Resolvent Analysis (RA) predicts selective amplification of medium-frequency oblique waves (a Kelvin-Helmholtz (K-H) mode and the 1st Mack mode, respectively). Nonlinear optimisations reveal a consistent route to turbulence: upstream oblique disturbances excite primary shear-layer modes, which quadratically interact to generate streamwise-rotational excitations. This centrifugal/Görtler-type mechanism exploits streamline curvature in the reattachment zone, producing vortices that seed streaks. The incompressible shear layer breaks down via progressive distortion of K-H rollers, whereas the shock-induced layer transitions through a sinuous streak instability, with quadratic interactions dominating. Large-scale lambda-structures develop before breakdown into turbulent spots. Parametric studies confirm that forcing oblique waves alone robustly triggers the turbulent cascade.
This thesis develops a unified description of how time- and spanwise-periodic external disturbances trigger transition in separated shear layers, linking incompressible pressure-gradient-induced Laminar Separation Bubble (LSB) and compressible oblique/reflected Shock-Wave/Boundary-Layer Interaction (SWBLI). Two frameworks are used: the Analytical Harmonic Balance Method (AHBM) for the incompressible Navier-Stokes (N-S) equations and the Space-Time Spectral Method (STSM) for the compressible N-S equations. Both are coupled with adjoint-based optimisation to identify ``worst-case'' forcings that maximise mean skin friction, a quantity that systematically rises during transition.
Two canonical convectively unstable flows are examined: an incompressible LSB and a Mach 2.15 oblique/reflected SWBLI. Linear Resolvent Analysis (RA) predicts selective amplification of medium-frequency oblique waves (a Kelvin-Helmholtz (K-H) mode and the 1st Mack mode, respectively). Nonlinear optimisations reveal a consistent route to turbulence: upstream oblique disturbances excite primary shear-layer modes, which quadratically interact to generate streamwise-rotational excitations. This centrifugal/Görtler-type mechanism exploits streamline curvature in the reattachment zone, producing vortices that seed streaks. The incompressible shear layer breaks down via progressive distortion of K-H rollers, whereas the shock-induced layer transitions through a sinuous streak instability, with quadratic interactions dominating. Large-scale lambda-structures develop before breakdown into turbulent spots. Parametric studies confirm that forcing oblique waves alone robustly triggers the turbulent cascade.
Version
Open Access
Date Issued
2025-10-01
Date Awarded
2026-08-01
Copyright Statement
Attribution-Non Commercial-No Derivatives 4.0 International Licence (CC BY-NC-ND)
Advisor
Rigas, Georgios
Sponsor
United States. Air Force. Office of Scientific Research
European Office of Aerospace Research and Development
Grant Number
FA8655-21-1-7009
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)