Global Dynamics

Description

Revised version of Notes on Global dynamics by Prof. Antonio Navarra. All rights reserved.

Contents

Table of Contents

Links to the original material

• 1. Introduction
  • 1.1. Coordinate systems
    • 1.1.1. Spherical Coordinates
    • 1.1.2. The Beta-plane
  • 1.2. Advective derivative
  • 1.3. Primitive Equations
  • 1.4. Hydrostatic balance
  • 1.5. Summary of fundamental equations
• 2. Circulation theorems and Ertel’s potential vorticity
• 3. Homogeneous flows
  • 3.1. The shallow equation in spherical coordinates
  • 3.2. The incompressible equations
  • 3.3. The vorticity equation on the (\beta)-plane
  • 3.4. Accelerating the zonal flow
• 4. The Quasi-Geostrophic potential vorticity
  • 4.1. The equations of motion
  • 4.2. The Boussinesq equation for the atmosphere
  • 4.3. Scales of motion
  • 4.4. The Rossby number expansion
  • 4.5. The quasi-geostrophic potential vorticity equation
  • 4.6. Relation with Ertel’s potential vorticity
    • 4.6.1. Gradients along isopycnals
    • 4.6.2. Fluxes of potential vorticity
    • 4.6.3. Meridional fluxes of potential vorticity
• 5. The vorticity equation
  • 5.1. Western intensification
  • 5.2. The eddy equation
  • 5.3. Enstrophy
  • 5.4. Steady flows
• 6. Flows over topography
  • 6.1. Linearized vorticity equation with topography
  • 6.2. Waves forced by topography
    • 6.2.1. Inviscid waves
    • 6.2.2. Dissipation and Ekman pumping
  • 6.3. Multiple equilibria
• 7. Waves and oscillations
  • 7.1. Sound and Gravity Waves
  • 7.2. Barotropic waves
  • 7.3. Baroclinic waves
  • 7.4. Charney-Drazin
• 8. Energetics
  • 8.1. Eddy energy
  • 8.2. Baroclinic Energetics
  • 8.3. Critical Lines
• 9. The General Circulation of the Atmosphere
  • 9.1. Space-time splittings
  • 9.2. Zonal means
  • 9.3. Time means
  • 9.4. Higher order quantities
  • 9.5. The time averaged zonal general circulation
  • 9.6. The horizontal general circulation
    • 9.6.1. The horizontal wind
    • 9.6.2. Mean Sea Level Pressure
    • 9.6.3. The Sea Surface Temperature
    • 9.6.4. The 2 Meter Temperature
  • 9.7. The Kinetic Energy
  • 9.8. The Meridional Momentum Flux
  • 9.9. The Meridional Heat Flux
• 10. The energy balance
  • 10.1. The balance at the top of the atmosphere
  • 10.2. The surface energy balance
  • 10.3. Precipitation
  • 10.4. Clouds
• 11. The General Circulation of the Oceans
  • 11.1. The thermal structure of the Ocean
  • 11.2. The salinity structure of the Ocean
  • 11.3. Ocean Currents
    • 11.3.1. The overall basin circulation
    • 11.3.2. The equatorial circulation
    • 11.3.3. The Gulf Stream
    • 11.3.4. The Kuroshio
    • 11.3.5. The upwelling zones
    • 11.3.6. The Somali Current
• 12. Heat and momentum sources
  • 12.1. The meridional response to forcings
  • 12.2. The Eliassen-Palm flux
  • 12.3. Induced Meridional Circulation
• 13. Theory of the symmetric circulation
  • 13.1. The balanced flow
  • 13.2. Hide’s theorem
• 14. Tropical waves
  • 14.1. The Kelvin wave
  • 14.2. Rossby equatorial waves
  • 14.3. Gravity waves
  • 14.4. The Yanai wave
  • 14.5. Tropical heat sources and forced motions
• 15. Appendix
  • 15.1. Zonal mean of spectral amplitudes
  • 15.2. Differentiation of implicit functions
  • 15.3. Pressure gradient force in terms of potential temperature
• 16. References

• Original notes: here¹.
• $\text{LATEX}$ notes: here
  • source

Resources

• Course web page

Footnotes

1. if prompted for credentials, use the following: {user: cmcc, psw: pD8phJg3e76J} ↩