12.802: Small-scale ocean dynamics

Fundamental principles of geophysical fluid dynamics will be applied to study oceanic motions on scales from hundreds of kilometers down to centimeters. Topics will include wave motions, instabilities and turbulence.

1. Waves -- using surface gravity waves as an example.
• Basics of waves
• Group velocity
• Surface gravity waves
• Shallow water system
• Ray equations
• Inhomogeneous media
• WKB including mean currents
• Nonlinear waves
• Solitary waves
2. General linearized waves in rotating stratified fluid
• Linear waves in compressible stratified fluids.
• Laplace tidal equations notes - part 1.
• Laplace tidal equations notes - part 2.
• Laplace tidal equations notes - part 3.
• Acoustic waves.
• Slides on acoustic waves.
3. Internal gravity waves
• Internal waves.
• Slides internal waves.
• Slides topographic radiation internal waves.
4. Boundaries, topography, and tides
• Tidal generating potential
• Animation
• Laplace tidal equations (hydrostatic)
• Long waves with rotation and boundaries
• Free and forced modes in a basin
5. Instabilities
• Lecture Rayleigh Benard convective instabilities.
• Lorenz 1963 paper.
• Lecture Kelvin Helmholtz instabilities.
6. Turbulence
• Introduction to turbulent flows.
• Energy budgets of turbulent flows.
• Homogeneous isotropic 3D turbulence.
7. Upwelling and River plumes
• coastal upwelling
• notes on plumes
• lab expt (2X speed)
8. Problem Sets
• Problem set 1.
• Newton's analysis and Chandrasekar's commentary about water waves
• Problem set 2.
• Problem set 3.