Turbulence and nonlinear phenomena in fluid flows



  1. Instabilities and transition to turbulence.
  2. Eulerian and Lagrangian description of fluid flows. The equations of fluid dynamics.
  3. Fully developed turbulence. 2/3 Law and the Law of energy disipation. Kolmogorov's 41 Theory. Two dimensional flows.
  4. Intermittency and Multifractality.
  5. Dispersion in fluid flows. Turbulent and shear dispersion. Relative dispersion.
  6. Chaotic Advection. Hamiltonian Dynamics and KAM tori. Open flows.
  7. Lyapunov Exponents. Finite-time and Finite-size Lyapunov Exponents. Hyperbolic structures and manifolds. Applications to ocean dynamics.
  8. Mixing of the passive scalar.