Topics Covered in the Course

• Turbulence: Definition and Statistical Description
  • Definition of Turbulence
  • Important Parameters and Regimes of Turbulence
  • Homogeneous versus Non-homogeneous Turbulence
  • Coherent Structures
  • Probability Theory
  • Central Limit Theorem
  • Reynolds Averaging
  • The Closure Problem
• Energetics of Turbulent Flows
  • Kinetic Energy Budgets
  • Potential Energy Budgets
  • Osborn-Cox
• Isotropic Homogeneous 3D Turbulence
  • Kolmogorov Theory
  • Intermittency and the Beta Model
  • Beyond a Spectral Description: Structure Functions
  • Passive Tracer Spectra
• Isotropic Homogeneous 2D Turbulence
  • Energy and Enstrophy Cascades
  • Freely Decaying and Forced 2D Turbulence
  • The Appearance of Coherent Structures
• Quasi-geostrophic Turbulence
  • Effects of Rotation and Stratification on Turbulent Flows
  • Energy and Enstrophy Cascades in Quasi-geostrophic Turbulence
  • Scaling Theories for Quasi-geostrophic Turbulence
  • Mesoscale Eddies
• Turbulent Convection
  • Horizontal versus Vertical Convection
  • Plumes, The Mixing Agent
  • Convection and Spreading
• Parameterizing Turbulence
  • Mixing Length Theory and Effective Viscosity and Diffusivity
  • Law of the Wall
  • Mixed Layer Models
  • First and Second Order Closure Models
  • Large Eddy Simulations Schemes
  • KPP Models
  • Mean Field Approximations
  • Closure Schemes for Mesoscale Eddies
• Weak Turbulence: Wave Dynamics
  • Internal Waves in the Ocean: The Garrett-Munk Spectrum
  • Internal Waves in the Atmosphere: Wave-mean Flow Interactions
  • Weak Turbulence as a Description of the Nonlinear Waves Interactions
• Weak Turbulence: Coherent Structures in Waves
  • Stokes Waves
  • Korteweg-de Vries Equation and Solitary Waves
  • Non Linear Shroedinger Equation and Envelope Solitons
• Turbulent Dispersion
  • Einstein: Diffusion by Discrete Movements
  • Taylor: Diffusion by Continuous Movements
  • Anomalous Diffusion
  • Levy Flights
• Lagrangian-Stochastic Description of Turbulent Motions
  • Particle Motions
  • Stokes Drift
  • Langevin Model of Diffusion
  • Chapman-Kolmogorov Equation