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