12.803

 

Quasi-balanced Circulations in Oceans and Atmospheres

 

Fall 2008

 

 

I.                   Fundamental Conservation and Balance Principles for Large-scale Flow

 

Hydrostatic balance

Conservation of potential vorticity

The invertibility principle

The shallow water equations

The Rossby number and the quasi-geostrophic equations

Geostrophic adjustment

The superposition principle

Higher-order balance systems

Separation of flow into balanced and unbalanced parts

The “omega equation”

 

 

II.                Generation and Dissipation of Quasi-balanced Eddies

 

 

Rossby waves

Barotropic instability

The Rayleigh and Fjørtoft theorems

The Eady model

The Charney model

The Charney-Stern theorem

Surface friction and Ekman Layers

Western Boundary Currents

Effects of phase change of water

Effects of orography: topographic waves

Observed modes of eddy development

Generation and dissipation of ocean eddies

 

III.                Equilibrated Quasi-Balanced Systems

 

The Eliassen-Palm theorem

Two-dimensional and Quasi-geostrophic turbulence and inverse cascades

The Rhines scale and quasi-balanced jets

Equilibration of baroclinic eddies in the ocean