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, ProblemSolving 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 2D 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 2D Cartesian system and angle between two vectors. Circle in 2D 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 Ekmanmodel windcomponent profiles. Wind hodograph.  Holton and Hakim: Section 8.3.4  
Week 3, Class 9  8  Friday, September 9  Ekmanmodel windcomponent profiles and corresponding wind hodograph (Ekman spiral) plotted in differently oriented Cartesian coordinate systems. Evaluation of lineparallel and linenormal 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  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 2D polar coordinates. Gradient in 2D 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. Polarcoordinate 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 2D velocity fields. Differential vector operations with 2D 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. Onedimensional 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 synopticscale processes.  Holton and Hakim: Chapter 2 
SkewT/LogP Diagram SkewT Zoomed In 
Week 12, Class 35  31  Wednesday, November 9  Vector form of timetendency 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 gradientwind 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 LowLevel Jet LowLevel Jet LowLevel Jet LowLevel Jet 
Week 16, Class 46  39  Monday, December 5  ProblemSolving 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)  ProblemSolving Session and Final Exam Review  
FINAL EXAM  Thursday, December 15  COMPREHENSIVE FINAL EXAMINATION (810 am)  COMPREHENSIVE FINAL EXAMINATION (810 am) 