CISM-ECCOMAS International Summer School on "Coherent Structures in Unsteady Flows: Mathematical and Computational Methods"

Invited Lecturers

Marc Avila (University of Bremen, ZARM, Germany)

6 lectures on: Exact coherent states (ECS), hydrodynamic stability theory with the example of Taylor— Couette flow, relative equilibria and relative periodic orbits; direct numerical simulation of the Navier—Stokes equations, direct computation of ECS with Newton—Krylov methods, high-performance codes (including hands-on work); connection between ECS and LCS, examples.


Francisco Beron-Vera (University of Miami, Department of Atmospheric Sciences, Miami, FL, USA)

6 lectures on: Energy dissipation routes in the ocean, local and nonlocal mixing and its consequences for deterministic prediction, occurrence of Lagrangian coherence, inertial coherent structures and their detection; transport by coherent vortices in the ocean; extraction of persistent transport patterns from large oceanic data sets; finite-size effects; applications (trash in the ocean, oil spill evolution prediction).


George Haller (ETH Zürich, Institute for Mechanical Systems, Zürich, Switzerland)

6 lectures on: Eulerian and Lagrangian views on coherence, basic considerations (finite time-horizon, frame-indifference), classic coherence criteria in fluids and their shortcomings, LCS detection from finite-time Lyapunov exponents, objective variational methods for LCS and OECS (advective, diffusive and stochastic techniques), rotational coherence, relation to transport barriers.


Oliver Junge (Zentrum Mathematik - M3, Technical University of Munich, Germany)

6 lectures on: Probabilistic theory of advective coherent sets in unsteady flows, transfer operators/generators and their discretization, macroscopic dynamics via spectral decompositions, almost invariant and coherent sets, spectral methods for coherent set detection, dynamic isoperimetry and geometric heat flow, numerical methods and examples.


Rich Kerswell (Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK)

6 lectures on: Exact coherent states (ECS) in wall-bounded shear flows, self-sustaining process of turbulence, techniques to compute ECS, branch continuation, stability, bifurcations; role of ECS in turbulent flow, how to find them and assess them; linear and nonlinear optimization, variational calculus, transient growth, connection to ECS.


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