General circulation of the atmosphere

Semester 1 2026



Lectures

Each topic is accompanied by readings from the notes and other resources. There will be a problem set roughly every fortnight.

Topic 1: Overview & tools

Learning outcomes

  1. Define what is meant by the term “general circulation”.
  2. Describe the basic thermal and dynamic structure of the atmosphere and its seasonal variations.
  3. List the equations required to solve for the large-scale atmospheric flow and describe the physical principles they are based upon.
  4. Distinguish the Lagrangian and Eulerian perspectives and mathematically describe the conversion between them.
  5. Explain why additional forces arise in rotating reference frames and describe each of them.
  6. Manipulate the equations when written in spherical coordinates and when using pressure as a vertical coordinate

Background reading

  • Lorenz, E. (1983), A history of prevailing ideas about the general circulation of the atmosphere, Bull. Amer. Met. Soc., 64, 730-769.

Lectures

  • 2nd March: Introduction & overview of the general circulation
  • 5th March: The governing equations
  • 9th March: Effects of rotation, the thermodynamic equation, and pressure coordinates
    • Section 2.1.3-2.1.6 of the class notes
    • Handwritten notes: see previous lecture


Topic 2: Radiative-convective equilibrium & Hide's theorem

Learning outcomes

  1. Describe the concepts of radiative equilibrium, radiative-convective equilibrium (RCE), and convective quasi-equilibrium and explain the differences between them.
  2. Recall Hide’s theorem and the conditions under which it applies
  3. Quantitatively evaluate whether a given RCE state is in violation of Hide’s theorem
  4. Give several independent reasons why the RCE solution is not observed on Earth

Background reading

Lectures




Topic 3: Axisymmetric & non-axisymmetric circulations

Learning outcomes

  1. Describe the theoretical basis for the Held & Hou model of an axisymmetric Hadley Cell, including the application of angular-momentum conservation, the determination of the cell width, and the thermodynamics/energy transport of the cell.
  2. Apply the Held & Hou model to Earth's atmosphere and the atmosphere of hypothetical planets with different roation rates, sizes, etc..
  3. Identify the limitations of an axisymmetric description of the tropical circulation.
  4. Analyse atmospheric circulations using Reynold's decomposition to determing the role played by the mean circulation and transient and stationary eddies.
  5. Describe the problem of state estimation as it applied to the atmosphere, and explain methods to solve it including objective station-based analysis and reanalysis.

Background reading

  • Held & Hou (1980), Nonlinear Axially Symmetric Circulations in a Nearly Inviscid Atmosphere, J. Atmos. Sci, 37, 515–533.

Lectures

  • 23rd March: An axisymmetric Hadley circulaton
  • 26th March: An axisymmetric Hadley circulation II
    • Chapter 4 of the class notes
    • Handwritten notes: see previous lecture
  • 30th March: Decomposing the circulation & state estimation
  • 2nd April: Decomposing the circulation & state estimatiion II
    • Section 2.2 of the class notes
    • Handwritten notes: see previous lecture.


    • Topic 4: The angular momentum budget of the atmosphere

    Learning outcomes

    1. Describe the global angular momentum cycle and explain the role played by eddies and friction within it.
    2. Explain what is meant by the term form drag, and demonstrate how it arises.
    3. Qualitatively determine the structure of the meridional overturning circulation and mean surface winds given the angular momentum transports within the atmosphere using the concept of downward control.
    4. Quantitatively evaluate an atmopsheric budget (e.g., for angular momentum budget) from reanalysis data (Assignment 2)

    Background reading

    Lectures

    • 13th April: The angular momentum budget
    • 16th April: The angular momentum budget II
      • Section 5.1 - 5.3 of the class notes
      • Handwritten notes: see previous lecture.


    Topic 5: Jet formation & maintenance: the barotropic case

    Learning outcomes

    1. Explain the various uses of the terms barotropic and baroclinic.
    2. Describe the effect of localised stiring on the zonal wind distribution in a barotropic fluid.
    3. Demonstrate how the shape of eddies may contribute to fluxes of momentum.
    4. Apply the theory of linear Rossby waves to explain how their propagation leads to preferred regions of eddy momentum flux convergence and divergence.
    5. Use this theory to interpret and analyse phase speed spectra of eddy-momentum fluxes in the atmosphere

    Background reading

    Lectures

    • 20th April: Maintenance of a barotropic jet
    • 23rd April: Momentum transport by Rossby waves
      • Section 6.3-6.4 of the class notes
      • Handwritten notes: see previous lecture
    • 27th April: Rossby-wave propagation
      • Section 6.3-6.4 of the class notes
      • Handwritten notes: see previous lecture


    Topic 6: Quasigeostrophic theory and forcing of the zonal mean

    Learning outcomes

    1. Describe the assumptions leading to the Quasi-geostrophic equations.
    2. Analyse and interpret distrubutons of QGPV and their expression in the wind and temperature field.
    3. Analyse and interpret the transformed Eulerian mean circualtion
    4. Analyse and interpret the Eliassen-Palm flux and its connection to wave propagation.
    5. Synthesise the above concepts into an explanation of jet formation in baroclinic atmospheres.

    Background reading

    • Vallis (2018), Atmospheric and Oceanic Fluid Dynamics, Cambridge University Press, ch 10.1-10.4.

    Lectures