Dynamics I

August 21, 2017
M W F 9:00-9:50
METR 3113.001


Evgeni Fedorovich
Professor; Edith Kinney Gaylord Presidential Professor


National Weather Center, Room 1350, 120 David L. Boren Blvd, Norman, OK   View map


Fall 2017

METR 3113 – Atmospheric Dynamics I: Introduction to Atmospheric Kinematics and Dynamics

Fall 2017 Syllabus


Dr. Evgeni Fedorovich

School of Meteorology, University of Oklahoma, National Weather Center, Room 5419; Phone: (405) 325-1197; Email: fedorovich@ou.edu

Teaching assistant

Mr. Tyler Bell

Email: tyler.bell@ou.edu

Class meeting time and place

Mon, Wed, Fri: 9:00 – 9:50am; NWC 1350.

Office hours

By appointment through e-mail (also for office hours with the teaching assistant).


Grade of C or better in METR 2023/2021, MATH 2443 or 2934, PHYS 1215 or 2524.

Required textbook

Holton, J. R., and G. J. Hakim, 2013: An Introduction to Dynamic Meteorology, 5th edition, Academic Press (Elsevier), 532 pp. (4th edition of this textbook may also be used).

Supplementary textbooks/materials

Wallace,    J.    M.,    and   P.    V.   Hobbs,   2006:    Atmospheric    Science:    An    Introductory    Survey.

Elsevier/Academic Press, 483 pp.

Fiedler, B. H., 2015: Forces and Motion in the Atmosphere. Manuscript v1.20, University of Oklahoma, 157 pp.


Course materials will be available at https://canvas.ou.edu/.

Proposed grading

Three intermediate tests (September, October, November): 30% each (with the lowest score dropped). Final exam (December): 40%.

Grade cutoffs. A: ≥85%, B: ≥70%, C: ≥50%, D: ≥20%, F: <20%.

General information

Students will be introduced to the formal mathematical characterization of atmospheric motions, to forces acting in the atmosphere, and to equations of atmospheric kinematics and dynamics. Particular topics include coordinate systems used in meteorology, basics of vector calculus, Newton’s laws of motion, conservation of mass and energy, basic force balances and atmospheric motion types, concepts of equilibrium and stability in the atmospheric context, and equations of motion.




  1. Units and Dimensions
  • Standard techniques to operate with physical
  • Conversions between SI and Imperial units used in atmospheric
  • Concept of dimension; idea of dimensional (scale) analysis and principle of dimensional homogeneity.

II.   Coordinate systems

  • Cartesian
  • Polar


III.   Fundamentals of Vector Calculus

  • Concepts of vector (versus scalar), unit vector, and vector decomposition
  • Properties of the vector dot and cross products, commonly employed vector identities and
  • Rules of vector
  • Properties and applications of Ñ (del, nabla) operator in vector
  • Definitions and properties of divergence, gradient, curl, and Laplacian operations; physical meanings of these
  • Divergence theorem of vector


IV.   Basics of Newtonian Mechanics

  • Notions of inertial and non-inertial reference
  • Three Newton’s laws of
  • Newton’s law of
  • One-dimensional equation of motion in inertial frame with different forcing
  • Notion of angular


V.   Fundamental Atmospheric Forces

  • Gravitational
  • Notion of force per unit
  • Pressure gradient
  • Viscous (friction)
  • Hydrostatic equation; geopotential and geopotential
  • Pressure as vertical


  • Archimedes and buoyancy forces in the atmosphere; notion of the
  • Apparent forces in a non-inertial reference
  • Centrifugal and gravity forces in a rotating reference
  • Coriolis


VI.   Motion in Non-inertial Rotating Frame

  • Lagrangian and Eulerian frames; concept of total
  • Differentiation of a vector in a rotating
  • Equation of motion in a rotating frame: vector form of the
  • Equation of motion in a rotating frame: components in a spherical coordinate
  • Relative importance of individual terms in the equation of
  • Geostrophic approximation and geostrophic
  • Hydrostatic approximation in the equations of


VII.   Mass and Energy Conservation

  • Conservation of mass; Lagrangian and Eulerian derivations of continuity equation; incompressible and anelastic forms of the continuity
  • Adiabatic process; potential
  • Thermodynamic and mechanical energy
  • Scale analysis of mass and energy conservation
  • Mass and energy conservation equations in isobaric


VIII.    Balanced Flow in Natural Coordinates

  • Natural
  • Gradient wind approximation; cases of geostrophic flow, inertial flow, and cyclostrophic
  • Solutions of gradient wind equation for northern and southern
  • Notions of regular vs. anomalous, baric vs. antibaric, and cyclonic vs. anticyclonic gradient


Note: The University of Oklahoma is committed to providing reasonable accommodation for all students with disabilities. Students with disabilities who require accommodations in this course are requested to speak with Dr. Fedorovich as early in the semester as possible. Students with disabilities must be registered with the Office of Disability Services prior to receiving accommodations in this course.