CLIM 711 Introduction to Dynamic Meteorology

Instructor: Jian Lu

Text

• Holton, J. R., An Introduction to Dynamic Meteorology, 3^rd or 4^th edition.

Supplementary Texts

• Gill, A. E., Atmosphere-Ocean Dynamics, 1982, 666pp./ISBN: 0-12-283522-0

• Marshall, J., and R. A. Plumb, Atmosphere, Ocean, and Climate Dynamics: An introductory Text , 2008, 319pp.

• Wallace, J. M, and P. V. Hobbs, Atmospheric Science: An introductory Survey , 2^nd Edition, 2006, 483pp.

Advanced Text

• Vallis, G. K., Atmospheric and Oceanic Fluid Dynamics, 2006, 745pp.

Prerequisites

• Newtonian physics, vector calculus, partial differential equations

Course work:

• Lectures (20%)
• Weekly problem sets (30%)
• Final exam (30%)
• Project (20%)
  
  

1. Laws of motion (Chap. 1)

• Fundamental forces
• Gravitational, pressure gradient, friction, Coriolis
• Mixing length theory, molecular vs. eddy viscosity
• Structure of the static atmosphere
• Generalized vertical coordinate, pressure vertical coordinate

2. Basic conservation laws (Chap. 2)

• Total differentiation, Eulerian and Lagrangian reference frames
• Total derivative of vector
• Rotating frame
• Conservation of momentum in spherical coordinates
• Conservation of mass
• Conservation of energy
• Potential temperature, adiabatic lapse rate
• Static stability
• Scale analysis
• Hydrostatic balance
• Geostrophic balance
• Primitive equations in z coordinates
• Primitive equations in pressure coordinates
• Geostrophic balance
• Thermal wind
• Barotropic flow

3. Circulation and vorticity (Chap. 4)

• Circulation

• Bjerknes theorem (general case)
• Kelvin theorem (barotropic case)
• Relative circulation
• Conservation of angular momentum and ideal Hadley circulation (*)
• Absolute vorticity, relative vorticity
• Natural coordinates: shear and curvature
• Local Cartesian coordinates
• Conservation of potential vorticity
• Examples
• Barotropic (conservation of absolute vorticity)
• Baroclinic mountain forced
• Absolute vorticity eqn.
• Relative vorticity eqn. (vertical component)
• Scale analysis
• Ertel potential vorticity
• Barotropic vorticity eqn.
• Fourier analysis (Sec. 7.2.1)
• Free Rossby waves in 1D and 2D (Sec. 7.7.1)
• Perturbation solution
• Topographically forced Rossby waves (Sec. 4.5, 7.7.2)

4. Quasi-geostrophic theory

• Derivation of quasi-geostrophic potential vorticity equation (Sec 6.2)
• 2-layer model of barclinic instability (Sec. 8.2)
• Equations of motion in log-pressure coordinates (Sec. 8.4.1)
• Extratropical energy cycle (Sec. 10.4)
• Rossby waves in 3 dimensions (Sec. 10.5.1)

5. Waves (Chap. 7)

• The perturbation method
• Shallow-water gravity waves
• Internal gravity waves
• Inertio-gravity waves
• Adjustment to geostrophic balance

6. Baroclinic Instability (Chap. 8)

• Normal mode baroclinic instability: A two-layer model
• Energetics of baroclinic waves
• Baroclinic instability of a continuously stratified atmosphere
• Growth and propagation of neutral modes

7. Midlatitude circulation (Chap. 12 of Vallis book)

• Surface westerlies and maintenance of a barotropic jet
• Layered models of the midlatitude circulation
• Stratified model and real atmosphere
• Baroclinic eddies and potential vorticity transport

Last modified 15 September 2009