Lecture Schedule for METR 3113
Atmospheric Dynamics I
Fall 2016

Fiedler Notes: Forces and Motion in the Atmosphere

Week Number and Class Slot Lecture Number Date Class Topic Reading Assignment Useful Links and Images
Week 1, Class 1 1 Monday, August 22 Introduction, Overview, Policies, Problem-Solving Guide Class Web Site: Announcement, Policies, Schedule, Knowledge Expectations, Problem Solving Guide Image of atmospheric scales
Week 1, Class 2 2 Wednesday, August 24 Atmospheric variables. Vectors and scalars. Dimensions and units. Scales of atmospheric processes. Horizontal and vertical scales. Time scales. Holton and Hakim:  Sections 1.1 to 1.3  
Week 1, Class 3 3 Friday, August 26 Example of manipulations with units in a mathematical expression. Dimensional homogeneity. Dimension and units of the gas constant. Holton and Hakim:  Sections 1.1 to 1.3
Fiedler: Sections 1 and 2
 
Week 2, Class 4 4 Monday, August 29 Purpose of a coordinate system on a line, plane, and in space. Cartesian coordinate systems in one, two, and three dimensions. History of the Cartesian system. Orientation of coordinate axes. Coordinate transformations. Intervals, lines, and vectors in Cartesian coordinates. Holton and Hakim: Appendix C.3
Fiedler:  Section 3
 
Week 2, Class 5 5 Wednesday, August 31 Polar coordinate system. Conversion of polar coordinates to 2-D Cartesian coordinates. Cylindrical coordinate system. Spherical coordinate system. Conversion of spherical coordinates to Cartesian and cylindrical coordinates. Holton and Hakim: Appendix C.3
Fiedler:  Sections 3, 9 and 10
Jang et al. Paper
Week 2, Class 6 6 Friday, September 2 Operations with coordinate systems. Cartesian coordinate rotation. Vector in rotated Cartesian plane coordinates. Angle between two straight lines in 2-D Cartesian system and angle between two vectors. Circle in 2-D Cartesian and polar coordinate systems. Holton and Hakim: Sections 1.1 to 1.3
Fiedler:  Sections 3 and 10
 
Week 3, Class 7   Monday, September 5 (Labor Day Holiday - No Class) LABOR DAY HOLIDAY - NO CLASS LABOR DAY HOLIDAY - NO CLASS  
Week 3, Class 8 7 Wednesday, September 7 Representation of wind components in Cartesian coordinate systems rotated around the vertical axis. Rotation of Ekman-model wind-component profiles. Wind hodograph. Holton and Hakim: Section 8.3.4  
Week 3, Class 9 8 Friday, September 9 Ekman-model wind-component profiles and corresponding wind hodograph (Ekman spiral) plotted in differently oriented Cartesian coordinate systems. Evaluation of line-parallel and line-normal wind components. Holton and Hakim:  Section 8.3.4  
Week 4, Class 10 9 Monday, September 12 Scalars and vectors. Notation. Vector addition. Vector subtraction. Unit vector. Scalar (dot) product. Unit vectors in Cartesian coordinates. Vector magnitude. Vector projection on a coordinate axis (vector component). Multiplication of vector by a scalar. Examples of operations with vectors. Holton and Hakim:  Section 1.1
Fiedler:  Section 3
Storm Rotation and Splitting Video
Week 4, Class 11 10 Wednesday, September 14 Vector magnitude and dot product in rotated Cartesian plane coordinates. Transformations of vector projections. Invariance of the magnitude and scalar product to coordinate rotation. Vector (cross) product. Holton and Hakim:  Section 1.1
Fiedler:  Section 3
 
Week 4, Class 12 11 Friday, September 16 Discussion of Solutions from Problem Sets 1 and 2    
Week 5, Class 13 12 Monday, September 19 Vector differentiation with respect to a scalar argument. Directional derivative and gradient of a scalar field. Del (nabla) operator. Definitions and properties of divergence and curl. Holton and Hakim:  Appendix C
Fiedler:  Section 3.5
 
Week 5, Class 14   Wednesday, September 21 HOUR EXAMINATION #1 HOUR EXAMINATION #1  
Week 5, Class 15 13 Friday, September 23 Examples of vector calculus operations. Invariance of the vector sum magnitude with respect to the basis rotation. Proving selected vector calculus identities. Importance of the order of operands in vector calculations. Example of the gradient calculation. Fun with del operator. Holton and Hakim:  Appendix C
Fiedler:  Section 2.5
 
Week 6, Class 16 14 Monday, September 26 Laplace operator (Laplacian). Divergence theorem of vector calculus. Divergence theorem and continuity equation; mass flux. Holton and Hakim:  Appendix C
Fiedler:  Section 2.5
 
Week 6, Class 17 15 Wednesday, September 28 Position vector and unit vectors in polar coordinates. Relationships between velocity components in Cartesian and polar coordinates. Acceleration in 2-D polar coordinates. Gradient in 2-D polar coordinates. Holton and Hakim:  Appendix C
Fiedler:  Sections 3 and 10
 
Week 6, Class 18 16 Friday, September 30 Summary of differential vector operations in Cartesian coordinates on a plane. Polar-coordinate forms of differential vector operators. Relation between directional differential and gradient in polar coordinates. Holton and Hakim:  Appendix C
Fiedler:  Sections 3 and 10
 
Week 7, Class 19 17 Monday, October 3 Examples of differential vector operations with 2-D velocity fields. Differential vector operations with 2-D velocity fields in polar coordinates. Holton and Hakim:  Appendix C
Fiedler:  Sections 3 and 10
 
Week 7, Class 20 18 Wednesday, October 5 Reference frame. First law of Newton. Inertial motion and inertial frame. Noninertial reference frame. Geocentric reference frame as an example of noninertial frame. Fundamental forces and apparent forces. Body forces and surface forces. Second law of Newton. One-dimensional equation of motion. Pressure gradient force. Gravitational force. Viscous shear (shearing) and normal stresses. Viscous force. Kinematic viscosity. Holton and Hakim: Sections 1.2 and 1.3
Fiedler:  Sections 5 and 6
 
Week 7, Class 21   Friday, October 7 (Fall Holiday - No Class) FALL HOLIDAY - NO CLASS FALL HOLIDAY - NO CLASS  
Week 8, Class 22 19 Monday, October 10 Apparent forces in the geocentric frame. Centripetal acceleration. Centrifugal force. Gravity force. Geopotential. Holton and Hakim:  Section 1.3 Centrifugal force ride

Centripetal Acceleration Ride
Week 8, Class 23 20 Wednesday, October 12 Zonal and radial deflecting forces in geocentric frame. Coriolis force. Coriolis parameter. Vector representation of the Coriolis force. Holton and Hakim:  Section 1.3  
Week 8, Class 24 21 Friday, October 14 Discussion of Solutions from Problem Sets 3 & 4    
Week 9, Class 25 22 Monday, October 17 Examples of motion involving Coriolis force. Missile trajectory. Constant angular momentum (inertial) oscillation. Radius and period of constant angular momentum (inertial) oscillation. Holton and Hakim:  Section 1.3 Idealized Inertial Oscillation

Real Inertial Oscillation
Week 9, Class 26 23 Wednesday, October 19 Structure of the static atmosphere. Equation of state. Hydrostatic equation. Relation to the geopotential change with height. Hypsometric equation. Geopotential height. Vertical coordinates related to the atmospheric pressure. Pressure gradient in the isobaric coordinate system. Generalized vertical coordinate. Holton and Hakim:  Section 1.4  
Week 9, Class 27   Friday, October 21 HOUR EXAMINATION #2 HOUR EXAMINATION #2 Exam 1 and 2 Graphic
Week 10, Class 28 24 Monday, October 24 Lagrangian and Eulerian frames. Characteristics of mass, momentum, and thermodynamic energy changes in the process of motion. Total differentiation of a scalar field. Total differentiation of vector in rotating frame. Holton and Hakim:  Chapter 2 The Substantial Derivative (Hess, 1957)

The Taylor Series
Week 10, Class 29 25 Wednesday, October 26 Total derivative of velocity in rotating frame. Momentum balance equation in rotating frame. Velocity and acceleration in spherical coordinates. Momentum balance in spherical coordinates. Momentum balance equation in component form. Holton and Hakim:  Chapter 2  
Week 10, Class 30 26 Friday, October 28 Discussion of Solutions from Problem Set 5    
Week 11, Class 31 27 Monday, October 31 Scale analysis of the equations of horizontal motion. Geostrophic approximation and geostrophic wind. Scaling the third equation of motion (equation of vertical motion). Geostrophic approximation and geostrophic wind. Approximate forms of horizontal prognostic equations. Rossby number. Hydrostatic approximation. Pressure and density deviations from hydrostatic values. Holton and Hakim:  Section 1.6, Chapter 2  
Week 11, Class 32 28 Wednesday, November 2 Conservation of mass in a moving fluid: Eulerian derivation. Continuity equation and divergence theorem. Lagrangian derivation of the continuity equation. Scale analysis of the continuity equation; anelastic and incompressibility approximations. Boussinesq approximation. Holton and Hakim:  Chapter 2  
Week 11, Class 33 29 Friday, November 4 Energy conservation principle applied to a fluid element. Energy balance equation. Kinetic energy balance. Mechanical energy equation. Thermodynamic energy equation. Holton and Hakim:  Chapter 2  
Week 12, Class 34 30 Monday, November 7 Alternative forms of the first law of thermodynamics (FLT). Adiabatic process. Isentropic motion. Dry adiabatic lapse rate. Thermodynamic energy equation for synoptic-scale processes. Holton and Hakim:  Chapter 2 Skew-T/Log-P Diagram

Skew-T Zoomed In
Week 12, Class 35 31 Wednesday, November 9 Vector form of time-tendency and advection terms in momentum balance equations. Relation between local and total/substantial change of pressure in time. Autoconvection temperature lapse rate. Holton and Hakim:  Chapters 1 and 2  
Week 12, Class 36 32 Friday, November 11 Discussion of Solutions from Problem Set 6    
Week 13, Class 37 33 Monday, November 14 Vertical acceleration of an air parcel. Buoyancy. Buoyancy frequency. Static stability criteria for dry air. Holton and Hakim:  Chapter 2 Buoyancy Review
Ordinary Differential Equation Review 
Week 13, Class 38 34 Wednesday, November 16 Horizontal momentum equations in the isobaric coordinates. Total derivative in the isobaric coordinates. Continuity and thermodynamic energy equations in the isobaric coordinates. Holton and Hakim:  Section 3.1  
Week 13, Class 39   Friday, November 18 HOUR EXAMINATION #3 HOUR EXAMINATION #3  
Week 14, Class 40 35 Monday, November 21 Natural coordinates. Balanced flow. Particular cases of balanced flow. Gradient wind. Relation between gradient and geostrophic winds. Cyclonic and anticyclonic circulations in natural coordinates. Holton and Hakim: Section 3.2  
Week 14, Class 41   Wednesday, November 23, No Classes THANKSGIVING HOLIDAY - NO CLASS THANKSGIVING HOLIDAY - NO CLASS  
Week 14, Class 42   Friday, November 25, No Classes THANKSGIVING HOLIDAY - NO CLASS THANKSGIVING HOLIDAY - NO CLASS  
Week 15, Class 43 36 Monday, November 28 Solutions of the gradient wind equation. Baric and antibaric flows. Regular and anomalous flows. Atmospheric circulations associated with different gradient-wind force balances. Holton and Hakim: Section 3.2 Jet Stream
Jet Stream
Jet Stream
Week 15, Class 44 37 Wednesday, November 30 Gradient wind classification for the Southern Hemisphere. Holton and Hakim:  Section 3.2
Week 15, Class 45 38 Friday, December 2 The thermal wind Holton and Hakim: Section 3.4 Jet Stream
Jet Stream
Jet Stream


Low-Level Jet
Low-Level Jet
Low-Level Jet
Low-Level Jet
Week 16, Class 46 39 Monday, December 5 Problem-Solving Session and Course Evaluation    
Week 16, Class 47 40 Wednesday, December 7 Discussion of Solutions from Problem Set 7    
Week 16, Class 48 41 Friday, December 9 (Last Day of Class) Problem-Solving Session and Final Exam Review    
FINAL EXAM   Thursday, December 15 COMPREHENSIVE FINAL EXAMINATION (8-10 am) COMPREHENSIVE FINAL EXAMINATION (8-10 am)