MSC 405: Atmospheric Dynamics I

Spring Semester 2003
Tuesdays and Thursdays, 0925-1040
Classroom PHY 110, Coral Gables Campus

Instructor: Dr S.J.Majumdar
Phone: (305) 361 4779
e-mail: smajumdar@rsmas.miami.edu


Aim of Course:
To develop a theoretical understanding of basic atmospheric motions, via physical concepts and conservation laws.


Course Structure:
35% Homeworks
25% Mid-Term Exam
40% Final Exam


Recommended Textbook:
Holton, J.R., An Introduction to Dynamic Meteorology, 3rd Edition. Academic Press, 1992.


Course Outline

1.    Introduction
    1.1 What is "Atmospheric Dynamics"?
    1.2 Variables and Units
    1.3 Scale Analysis
2.    Vectors and Calculus
    2.1 Partial Differentiation (Product Rule, Chain Rule, Total Differential, Advection)
    2.2 Revision of Vectors (Dot Product, Cross Product)
    2.3 Vector Calculus: Gradient, Divergence, Curl
3.    Basic Physical Concepts
    3.1 The Atmosphere (Variables, Coordinate Systems)
    3.2 Fundamental Forces (Pressure Gradient Force, Gravitational Force, Viscous Force)
    3.3 Non-Inertial Reference Frames and "Apparent" Forces (Centrifugal Force, Coriolis Force)
    3.4 Physical Descriptions of Force Balances (Geostrophic Wind, Gradient Wind, Effects of Friction)
    3.5 Structure of the Static Atmosphere (Hydrostatic Equation, Geopotential Height and Thickness, p as a vertical coordinate)
4.    The Basic Conservation Laws
    4.1 Conservation of Momentum: Navier-Stokes Equations
    4.2 Scale Analysis of the Momentum Equations
    4.3 Conservation of Mass: Continuity Equation
    4.4 Conservation of Energy: Thermodynamic Energy Equation
5.    Basic Solutions: Balanced Flow
    5.1 Kinematics
    5.2 Geostrophic Balance
    5.3 Momentum Equations in Natural Coordinates
    5.4 Force Balances in Natural Coordinates (Inertial, Geostrophic, Gradient, Cyclostrophic)
    5.5 Thermal Wind Equation
6.    Circulation and Vorticity
    6.1 Circulation
    6.2 Vorticity


Classes

1. 1/14/03  Introduction, Variables and Units, Scale Analysis
2. 1/16/03 Partial Differentiation
3. 1/21/03 Vector Dot Product, Cross Product
4. 1/23/03 Gradient, Divergence, Curl
5. 1/28/03 (HW1 due) Pressure Gradient Force
6. 1/30/03 Review of HW1, Gravitational Force, Centrifugal Force
7. 2/4/03 Acceleration due to Gravity, Geopotential
8. 2/6/03 Coriolis Force
9. 2/11/03 (HW2 due) Geostrophic and Gradient Wind Balance, Ekman Spiral
10. 2/13/03 Review of HW2, Hydrostatic Balance, Geopotential Height and Thickness
11. 2/18/03 (HW3 due) Pressure as a vertical coordinate, Conservation of Momentum
12. 2/20/03 Review of HW3, Momentum equations completed
13. 2/25/03 (HW4 due) Scale Analysis of Momentum Equations
14. 2/27/03 Review of HW4, Continuity Equation, Revision for Mid-Term
15. 3/4/03 MID-TERM EXAM
16. 3/6/03 Review of Mid-Term, Thermodynamic Energy Equation
SPRING BREAK
17. 3/18/03 Momentum equations in Natural Coordinates, Geostrophic Balance
18. 3/20/03 Inertial Oscillations, Gradient and Cyclostrophic Balance
19. 3/25/03 (HW5 due) Thermal Wind Balance: Physical Description and Example
20. 3/27/03 Review of HW5, Thermal Wind Relation
21. 4/1/03 (HW6 due) Circulation, Kelvin's Circulation Theorem
22. 4/3/03 Review of HW6, Bjerknes Circulation Theorem
23. 4/8/03 OUT OF TOWN?  (Sea Breeze)
24. 4/10/03 OUT OF TOWN? (guest lecturer?)
25. 4/15/03 Vorticity
26. 4/17/03 Vorticity Equation
27. 4/22/03 (HW7 due) Potential Vorticity
28. 4/24/03 Review of HW7, Revision for Final Exam
29. 5/1/03? FINAL EXAM


Homeworks and Exams

Homework 1 (5%).  1/21/03  (due 1/28/03) Variables, Scalings, Vector Calculus
Homework 2 (5%).  2/4/03  (due 2/11/03) Pressure Gradient Force, Centrifugal Force
Homework 3 (5%).  2/11/03  (due 2/18/03) Coriolis Force, Geostrophic and Gradient Winds, Geopotential Height and Thickness

Homework 4 (5%).  2/18/03 (due 2/25/03) Momentum Equations, Geostrophic Balance
Mid-Term (25%).     3/4/03  All of the Above
Homework 5 (5%).  3/18/03 (due 3/25/03) Natural Coordinates, Gradient and Cyclostrophic Balance
Homework 6 (5%).  3/25/03 (due 4/1/03) Thermal Wind
Homework 7 (5%).  4/15/03 (due 4/22/03) Circulation and Vorticity

Final Exam (40%).    5/1/03? Everything.