Contents

• Introduzione
• Introduction
• Introduction to turbulence
  • Navier-Stokes equation
    • Reynolds number
    • Energy balance
    • Energy transfer
  • Phenomenology of the turbulent cascade
    • Kolmogorov K41
    • Intermittency
  • Two-dimensional turbulence
    • Vorticity equation in two dimensions
    • Conservation laws
    • Inverse energy cascade
    • Direct enstrophy cascade
    • Coherent vortices
  
  
• Effects of friction in two-dimensional turbulence
  • Origin of the friction term
  • Steepening of the energy spectrum
  • Analogies with the passive scalar problem
  • Passive scalar with finite lifetime
    • Chaotic advection
    • Chaotic advection and linear damping
    • Intermittency
    • Smooth-filamental transition
  • Lagrangian description of the vorticity cascade
    • Fluid trajectories and exit-times
    • Structure functions and scaling exponents
    • From active to passive problem
  • Numerical results
    • Steepening of the vorticity spectrum
    • Intermittency
    • Vorticity vs. passive scalar statistics
    • Scaling exponents and exit-time statistics
  • Summary
  
  
• Polymer solutions: a brief introduction
  • Polymer dynamics in fluids
  • Dumbbell model
    • Coil-Stretch transition
  • Oldroyd-B model
    • Newtonian limit: viscosity renormalization
    • Energy balance
  • Fene-p
  • Drag reduction
  • Elastic turbulence
  
  
• Two-dimensional turbulence of dilute polymer solutions
  • 2D Oldroyd-B model
  • Passive polymers
    • Coiled state
    • Stretched state
  • Active polymers
    • Depletion of kinetic energy
    • Energy balance
    • Statistics of velocity fluctuations
    • Lagrangian chaos reduction
    • Decaying turbulence
    • Inverse energy cascade
  • Summary
  
  
• Conclusions
• Lagrangian code for polymer dynamics
  • Hyperbolic regions
  • Elliptic regions
  • Neutral regions
  
  
• Bibliography
• Acknowledgments
• About this document ...