CLIM 711 Introduction to Dynamic Meteorology

Instructor: E. K. Schneider

Text

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

Prerequisites

• Newtonian physics, vector calculus, partial differential equations

Course work:

• Lectures
• Reading of appropriate sections in text
• Weekly problem sets
• Midterm and final exams
  
  

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. Boundary layer and turbulence (Chap. 5)

• Reynolds averaging
• Boussinesq equations
• Bulk formulae
• Vertically integrated boundary layer
• Ekman layer

o Ekman pumping

o Secondary circulations and spin down

o Parameterization of surface boundary layer in barotropic vorticity equation

o Topographically forced Rossby waves with friction

· Group velocity and dispersion (Sec 7.2.2)

5. 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)

6. Waves (Chap. 7)

• Acoustic waves
• Shallow-water gravity waves
• Internal gravity waves
• Inertio-gravity waves
• Adjustment to geostrophic balance

Last modified 15 December 2005