## Atmospheric Dynamics (UoE 2007)

- Details
- Stephan Matthiesen
- 2007-01-08

This course introduces the fundamentals which govern atmospheric circulation including steady and unsteady flows and wave motions in the tropics and mid-latitudes and their role in transporting heat. Meteorological data will be used to illustrate phenomena such as cyclones, jetstreams and ENSO (El Niño Southern Oscillation).

Upon successful completion of the course it is intended that the student will be able to:

- show how to derive the Navier-Stokes equations expressed in an inertial frame of reference for inviscid motion of a compressible fluid and for the continuity of mass in the fluid starting from Newton's first law of motion and the conservation of mass
- explain how the Navier-Stokes equations are transformed for a frame of reference rotating with the earth
- demonstrate a grasp of the orders of magnitude of forces and accelerations present in synoptic-scale weather patterns and hence of the geostrophic and thermal wind approximations
- use those approximations to obtain estimates of winds in synoptic-scale systems from pressure and temperature gradients
- discuss the concept of "potential temperature" and its relevance to the vertical stability of a compressible atmosphere
- discuss the experimental evidence from "rotating dishpan" experiments that degree of departure from zonal symmetry depends on rotation rate and horizontal meridional temperature gradients
- discuss the typical configuration of meridional circulations in the tropics and their relation to the strength of the sub-tropical jet
- explain the concept of potential vorticity and its usefulness as tool for understanding fluid motion
- discuss the motivation for and limitations of treatment of atmospheric wave motion as a perturbation from a basic flow
- explain those aspects of the observed behaviour of mid-latitude planetary-scale waves which are accounted for by linear theory.

### Organisation

- Course organiser: Stephan Matthiesen
- Lectures: Helen Kettle (Chapter 1-8); Stephan Matthiesen (Chapter 9-16)
- Class times: Tue 11.10-12.00; Fri 11.10-12.00; Semester 2 (8 Jan - 23 Mar 2007)
- University of Edinburgh Course information Atmospheric Dynamics (U01863)

### Recommended Textbooks

There are a number of good textbooks. The following books all cover the contents of the course but differ in depth, style, presentation and price; it is more or less a matter of personal preference and interests which book you find most appealing and useful.

- Andrews, David G. (2000):
*An Introduction to Atmospheric Physics*. Cambridge University Press. 230 pages. £ 31.99. - Concise treatment of the fundamentals. Shorter than the others, it covers the course nicely but does not go much beyond it. Also has chapters on phtochemistry, remote sounding and modelling which are outside this course.
- Wallace, John M.; Hobbs, Peter V. (2006):
*Atmospheric Science: An Introductory Survey*. Academic Press. £ 39.99. - Larger format with nice layout. Less mathematical than the others with many lavishly designed diagrammes and figures supporting the explanations in the text. Covers a wide range of topics in atmospheric science, not only the dynamics.
- Salby, Murry L. (1996):
*Fundamentals of Atmospheric Physics*. Academic Press. 628 pages. £ 36.99. - Extensive and mathematically rigorous account of all relevant aspects of atmospheric physics, not only atmospheric dynamics, but also e.g. radiation, thermodynamics, cloud formation and photochemistry (ozone formation).
- Holton, James R. (2004):
*An Introduction to Dynamic Meteorology*. Elsevier/Academic Press. 536 pages. £ 39.99. - Very extensive and mathematically rigorous treatment of the dynamics. It also includes a CD with Matlab scripts that are used in the exercises to illustrate some of the principles (but note that Matlab, a commercial software package, is required to run them).

## Course Contents

### Chapter 1: Basics — 9 Jan 2007, Helen Kettle

- Topics:
- scales of atmospheric motion; composition of the atmosphere; gas laws; hydrostatic equation; observed distribution of pressure, temperature and density with height
- Suggested Reading:
- Andrews chapters 1, 2.1.-2.3.; Wallace and Hobbs chapters ??; Salby chapters 1.1.-1.2.; Holton chapters 1.1.-1.3., 1.6.
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 22kb)

### Chapter 2: Vertical Distributions — 12 Jan 2007, Helen Kettle

- Topics:
- understanding vertical distributions; potential temperature; static stability; Brunt-Väisälä frequency (buoyancy frequency) and oscillations of a statically stable atmosphere
- Suggested Reading:
- Andrews chapters 2.4.-2.6.; Wallace and Hobbs chapters ??; Salby chapters 1.2., 2.4., 7.1.-7.5.; Holton chapters 1.6., 2.6.-2.7.
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 23kb)

### Chapter 3: Equations of Motion — 16 Jan 2007, Helen Kettle

- Topics:
- material derivative; rotating coordinate system; continuity equation; Navier-Stokes equation
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 21kb)

### Chapter 4: Tangent Plane Approximation — 19 Jan 2007, Helen Kettle

- Topics:
- tangent plane approximation; approximations for large-scale flow; horizontal forces and acceleration
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 23kb)

### Chapter 5: Synoptic Scale Approximations — 23 Jan 2007, Helen Kettle

- Topics:
- horizontal forces and acceleration; Rossby number; geostrophic wind; ageostrophic wind; steady circular flow, cyclones and anticyclones
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 30kb)

### Tutorial on Chapters 1 to 4 — 26 Jan 2007, Helen Kettle

### Chapter 6: Other Vertical Coordinates — 30 Jan 2007, Helen Kettle

- Topics:
- other vertical coordinates; pressure as vertical coordinate; geopotential; equations of motion in pressure coordinates; geostrophic wind in pressure coordinates
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 23kb)

### Chapter 7: Friction and Eddy viscosity — 2 Feb 2007, Helen Kettle

- Topics:
- molecular viscosity; synoptic-scale and eddy quantities; eddy flux of momentum
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 24kb)

### Chapter 8: Planetary Boundary Layer and Ekman Spiral — 6 Feb 2007, Helen Kettle

- Topics:
- boundary layer; Ekman spiral
- Suggested Reading:
- Course Material:
- Notes (from previous years) - Tutorial questions (PDF 22kb)

### Chapter 9: Equatorial Circulation — 9 Feb 2007, Stephan Matthiesen

- Topics:
- axi-symmetric motion; equinox case; solstice case; asymmetries
- Suggested Reading:
- Course Material:
- Presentation (PDF 341kb) - Notes (from previous years) - Tutorial questions (PDF 16kb)

### Tutorial on Chapters 5 to 8 — 13 Feb 2007, Helen Kettle

### Chapter 10: Vorticity and Divergence — 16 Feb 2007, Stephan Matthiesen

- Topics:
- definition of vorticity; relative vorticity; vorticity in terms of curvature and shear; divergence
- Suggested Reading:
- Course Material:
- Presentation (PDF 272kb) - Notes (from previous years) - Tutorial questions (PDF 23kb)

### Chapter 11: Rates of Change of Vorticity and Divergence — 20 Feb 2007, Stephan Matthiesen

- Topics:
- continuity equation, divergence equation and the relation between divergence and vertical velocity; vorticty equation; divergence and vorticity in pressure coordinates
- Suggested Reading:
- Course Material:
- Presentation (PDF 295kb) - Notes (from previous years) - Tutorial questions (PDF 19kb)

### Chapter 12: Potential Vorticity — 23 Feb 2007, Stephan Matthiesen

- Topics:
- Suggested Reading:
- Course Material:
- Presentation (PDF 1.5Mb) - Notes (from previous years) - Tutorial questions (PDF 26kb)

### Chapter 13: Quasi-Geostrophic Equations — 27 Feb 2007, Stephan Matthiesen

- Topics:
- Suggested Reading:
- Course Material:
- Presentation (PDF 319kb) - Notes (from previous years) - No Tutorial questions

### Tutorial on Chapters 9 to 12 — 2 Mar 2007, Stephan Matthiesen

### Chapter 14: Barotropic Rossby Waves — 6 Mar 2007, Stephan Matthiesen

- Topics:
- Suggested Reading:
- Course Material:
- Presentation (PDF 835kb) - Notes (from previous years) - Tutorial questions (PDF 19kb)

### (no lecture on 9 Mar 2007)

### Chapter 15: Baroclinic Rossby Waves — 13 Mar 2007, Stephan Matthiesen

- Topics:
- Suggested Reading:
- Course Material:
- Presentation (PDF 274) - Notes (from previous years) - Tutorial questions (PDF 24kb)

### Chapter 16: Baroclinic Instability — 16 Mar 2007, Stephan Matthiesen

- Topics:
- Suggested Reading:
- Course Material:
- Presentation (PDF 1.7Mb) - Notes (from previous years) - No Tutorial questions

### Tutorial on Chapters 14 to 15 and (optionally) recap of other tutorial questions — 20 Mar 2007, Stephan Matthiesen

### Chapter 17: Summary and fun topics (optional lecture) — 23 Mar 2007, Stephan Matthiesen

- Topics:
- summary of the course; some interesting bits and bobs in atmospheric dynamics
- Course Material:
- Presentation (PDF 1.2Mb) - No Tutorial questions

### Revision Topics — 17 Apr 2007 (at 11.10), Stephan Matthiesen

- Topics:
- Newton's Laws in spherical coordinates; rotating frame of reference; Rossby number and geostrophy; pressure as vertical coordinate; thermal wind; eddy friction/viscosity; Ekman spiral; tropical circulations; angular momentum and vorticity.
- Suggested Reading:
- as listed in the individual chapters
- Course Material:
- Presentation (PDF 454kb)

- Last Updated: Saturday, 24 November 2018