12.820 / 12.822 Turbulence in the Ocean and Atmosphere, Spring 2005
Syllabus
- Turbulence: governing equations and different regimes
- Definition of turbulence
- Important parameters and regimes of turbulence
- Homogeneous versus non-homogeneous turbulence
- Coherent structures
- A statistical description of turbulence
- 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
- Turbulent convection
- Rayleigh-Benard convection
- Mean field approximation
- Plumes, the mixing agent
- Convection and spreading
- Microscale turbulence in the ocean and atmosphere
- Shear turbulence in the ocean
- Double diffusion in the ocean
- Moist convection in the atmosphere
- Wave turbulence and nonlinear waves
- Wave dispersion
- Wave-wave interactions
- Korteweg - de Vries equation and solitary waves
- Non Linear Schroedinger equation and envelope solitons
- Parameterizing turbulence
- Tracer turbulence
- Mixing length theory and effective viscosity and diffusivity
- First and second order closure models
- Mean field approximation
- Planetary boundary layers
- Law of the wall
- Boundary layer models
- Closure schemes for atmospheric planetary boundary layers
- Closure schemes for oceanic planetary boundary layers
- 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
- Planetary scale turbulence
- Mesoscale eddies in non-quasi-geostrophic flows
- The Transformed Eulerian Mean
- Closure schemes for mesoscale eddies