Instabilities and Turbulence

Instability, unpredictability and disorder are very often encountered in natural, technological, ecological, economic and social systems with important consequences on forecasting, design and decision making. These concepts have been historically introduced in the study of the laminar- turbulent transition in fluid flows, where they still represent an active field of research. Some questions of interest in this context are: Why `laminar' solutions, having a maximum degree of symmetry, become unstable and are replaced by less symmetric solutions? What are the reasons of unpredictability in non-linear systems? Is there anything predictable in turbulent flows? The scope of this course is to present our current understanding of these issues.

No prerequisites

Evaluation: written exam

• deducing fixed points in dynamical systems
• performing the linear stability analysis in dynamical systems and flows
• understanding nonlinear dynamics and the chaos transition
• fluid flow analysis in stready regimes in the incompressible Navier-Stokes equations framework
• understanding the transition to turbulence
• understanding the statistical description of turbulence
• deducing the challenges of turbulence modelling
• investigating turbulence models, from Reynolds Averaged Navier-Stokes equations (RAND) to Large Eddy Simulations (LES) ones
• understanding the structure of the turbulent boundary layer
• obtaining a general understanding on the modern challenges in turbulence and stability analysis"

Form: written
Date: 18 December 2023
Location/format: online
Transcript available: end of the semester and generally 8 weeks after the exam.

Lectures, Practices