麻省理工學院「開放式課程網頁」 | 地球、大氣與行星科學 | 12.820 Turbulence in Geophysical Systems, Spring 2004

Topics Covered in the Course

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