METEO 521: Dynamic Meteorology

Instructor: Dr. Steven Feldstein

Dynamic Meteorology
Spring 2016

Course Outline

  • T refers to the textbook; N refers to the notes on ANGEL.
  1. Introduction
    Goals and scope of the course
    Observations (N/obs.pdf)
    1. Preliminaries 
      Review equations of motion (read T1.1-1.6)

      The lecture will focus on advection and diffusion (N/diffusivity.pdf) 


Sound waves (T1.8, N/soundwave.pdf)
Compressible and incompressible flow (T1.9)
Incompressibility approximation
Boussinesq approximation (T2.4)

Anelastic approximation (T2.5) 

  1. Effect of rotation and stratification

Equations of motion in rotating, spherical coordinates (read T2.1-2.3)
Hydrostatic balance/approximation (T2.7, N/geo.hydro.pdf)
Geostrophic balance/approximation (T2.8)

Thermal wind balance (T2.8, N/thermalwind.pdf)
Static stability (read T2.9)

Introduction and gravity waves (T2.10.1) 

  1. Gravity waves

Shallow water system as a tool (T3.1)

Reduced gravity equations (T3.2; read T3.3)

Thermal wind balance revisited (T3.4)

Introduction of potential vorticity (PV) (T3.6)

Shallow water waves (T3.7, N/Kelvinwaves.pdf)
Geostrophic adjustment (T3.8, N/adjustment.poincare.pdf) Isentropic coordinates (read T3.9)

  1. Vorticity and Potential Vorticity

Preliminaries (read T4.1-4.4)

Potential vorticity conservation (T4.5, N/vor.pv.pdf)

Potential vorticity and Kelvin’s circulation theorem

General form of PV; application to various fluids and flows (T4.6-4.8) 

  1. Simplified equations for ocean and atmosphere

Quasi-Geostrophic scaling (T5.1)

The shallow water quasi-geostrophic equations (T5.3)

The continuously stratified quasi-geostrophic system (T5.4)

Rossby waves (T5.7, 5.8; read T5.A, N/zonal.prop.pdf and meridional.disp.pdf)
Refractive index 

  1. Instabilities

Synoptic dynamics (extratropical cyclones and fronts)
Synoptic dynamics (tropical cyclones and hurricanes)
Kelvin-Helmholtz instability (read T6.1)

Instability of parallel shear flow (T6.2)
Necessary condition for instability (T6.3)
Baroclinic instability (T6.4, N/instability.pdf)
The Eady problem (T6.5)

The two-layer baroclinic instability (T6.6, 6.7) 

  1. Planetary boundary layer

Planetary boundary layer and its structure
Atmospheric turbulence

Secondary circulations and Ekman pumping 

Course Structure

Examination: There will be two mid-terms and a final exam. Each mid-term will contribute 20%, and the final will contribute 30% to your final grade. The dates for the mid-term exams are near February 23 and April 7.

Problem sets: Problem sets will be given about every two weeks. The problem sets will contribute 20% to your final grade.

Lab project: Hand-on laboratory experiments can help us understand key concepts and theories that are unique to rotating fluids. Laboratory-experiment report and class presentation will contribute 10% to your final grade.

  1. The class will be divided into five groups. Each group will be comprised of 3 (for one experiment 2) students. The experiments will take place in 529 Walker. Practice times are 4:00-5:00pm on the previous Thursday in 529 Walker. The following experiments are to be performed:

Exp 1. Taylor Columns (February 9)

Exp 2. Fronts, geostrophic adjustment (February 16)

Exp 3. General circulation - Hadley Circulation (March 1)
Exp 4. General circulation - Eddies (March 22)

Exp 5. General circulation -Ekman layers (March 29) 

  1. Each group will practice the experiment of its choice prior to the class; perform the 
demonstration in front of the class; and explain what we are supposed to learn from the experiment. Each member of the group must participate in all of these three activities. In addition, each group is required to write a short report (2-3 pages long). This report may include (a) an experimental log which can supplement the log available on the “Weather in a Tank” web page (, (b) a discussion of what has been learned from the experiment, and (c) an observed analog of the experiment (e.g., examples from weather maps, analyses from the literature, etc.). In the report, briefly describe how each member of the group contributed to the report.
  2. Your credit will be given based on (a) clarity of demonstration, (b) clarity of explanations (i.e., what we are trying to learn from the experiment, and how this is related to the class material), and (c) the report.
  3. Time line: Let me know your choice of experiment (first come, first choice) and the members of your group by Jan 19.

Prerequisite: Meteo 520.

Textbook: Atmospheric and Oceanic Fluid Dynamics. Vallis, 2006, Cambridge University Press.


  1. Atmosphere-ocean dynamics. Gill, 1983, Academic Press. Call#: GC190.G54 1982 (reserved)
  2. Geophysical Fluid Dynamics. Pedlosky, 1986. Springer-Verlag. Call#: QC809.F5P43 1987 (reserved)
  3. Introduction to circulating atmospheres, James, Ian N. 1994. Cambridge University Press. Call#: QC880.4.A8J34 1994
  4. Middle Atmospheric Dynamics. Andrews, Holton, and Leovy, 1998. Academic Press. Call#: QC881.2.M53A53 1987
  5. An introduction to fluid dynamics. Batchelor, 1967. Batchelor. Cambridge University Press. Call#: QA911.B33
  6. Fluid Mechanics, 1990. Kundu. Academic Press.
  7. Lectures on geophysical fluid dynamics, 1998. Salmon. Oxford University Press. Call#: QC809.F5S25 1998.
  8. Meteo 521 lecture notes. Peter Bannon.
  9. An Introduction to Dynamic Meteorology. Holton 1992. Academic Press. Call#: QC880.H65 1992
  10. Atmospheric Science: In Introductory Survey. Wallace and Hobbs 1977. Academic Press. Call#: QC861.2.W34

Lectures: T Th 9:45am-11:00am 101 Walker Building

Lecturer: Steven Feldstein 516 Walker Building 865-7042

Office hours: by appointment

Goals and Scope of Meteo 521


  • introduce some of the important concepts in dynamic meteorology
    provide a theoretical basis for understanding weather and climate


This course does not cover the entire spectrum of atmospheric motion; this course focuses on large-scale atmospheric motion for which rotation and stable stratification are central. However, as the concepts to be covered in this course are fundamental to atmospheric motion, the same conceptual approach (e.g., scaling, adjustment, concept of balanced flows) can often be applied to other atmospheric phenomena at smaller scales.

Basic mathematics such as calculus, vector calculus, and partial differential equations will be extensively used.

Academic integrity statement

Students in this class are expected to write up their problem sets individually, to work the exams on their own, and to write their papers in their own words using proper citations. Class members may work on the problem sets in groups, but then each student must write up the answers separately. Students are not to copy problem or exam answers from another person’s paper and present them as their own; students may not plagiarize text from papers or websites written by others. Students who present other people’s work as their own will receive at least a 0 on the assignment and may well receive an F or XF in the course. Please see: Earth and Mineral Sciences Academic Integrity Policy: undergrad students/academics/integrity policy, which this course adopts.

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