Welcome to the GEOS 353, Environmental Fluid Mechanics, webpage for the Fall 2019 semester.
Above: All 11 students in the Fall 2019 GEOS 353 course. Photo by Jaydie Lee.
Course Catalog description: Prerequisites: MA 109 or MA 120, PHYS 202A or PHYS 204A. An introduction to environmental and geophysical fluid mechanics with emphasis on the effects of density stratification and the Earth's rotation. Develop fluency with mathematical symbols and equations used to describe fluid motion including the Navier-Stokes equations.
Fall 2019 Lectures: TR, 12:30 - 1:45 PM. Location: Modoc Hall 123
Office hours: Tuesdays from 2:00 - 2:50 and Thursdays from 9:30 - 12:00 or by appointment.
Tues., Aug. 27: Lecture: review syllabus; fluids vs solids; continuum; Knudsen number; slope, derivative, gradient, partial derivatives.
Thurs., Aug. 29: Lecture: vectors; gradients; unit vectors; partial derivatives.
Tues., Sept. 3: Lecture: partial derivatives; flux-gradient relationships for molecular diffusion of heat, matter, and momentum; Couette flow.
Thurs., Sept. 5: Quiz 1. Lecture: Cauchy stress tensor; body forces versus surface forces
Tues., Sept. 10: Lecture: Newton's second law and derivation of an expression for differential surface forces. Also, mass continuity eqn.
Thurs., Sept. 12: Quiz 2. Lecture: Derive Cauchy's eqn.; introduce Einstein summation notation
Tues., Sept. 17: Lecture: More on index notation; dot product (inner product); full constitutive equation for Newtonian fluid.
Thurs., Sept. 19: Quiz 3. Lecture: Begin with Cauchy's eqn. and derive Euler's eqn.
Tues., Sept. 24: Lecture: Lagrangian versus Eulerian form of the momentum equation. Local time derivative and advection terms.
Thurs., Sept. 26: Quiz 4. Lecture: Review and clarification especially with regard to del operator and dot products.
Tues., Oct. 1: Lecture: path lines, streaklines, streamlines; Kinematics: divergence, vorticity, stretching and shearing deformation.
Thurs., Oct. 3: Quiz 5. Lecture: vorticity; cross-product; then body forces: apparent and true gravity.
Tues., Oct. 8: Lecture: Review of equation of motion with gravity; begin discussion of rotation.
Thurs., Oct. 10: Quiz 6. Lecture: checking units, then use of cross-product to calculate velocity of parcel on a rotating reference frame.
Tues., Oct. 15: Lecture: Inertial and non-inertial reference frames. Derive the Coriolis term in vector form.
Thurs., Oct. 17: Quiz 7. Lecture: Derive Coriolis terms in component form and show how to calculate deflection.
Tues., Oct. 22: Lecture: Levi-Civita symbol; curvature terms; then begin Turbulence: mechanical versus thermal; characteristics of, Reynolds number.
Thurs., Oct. 24: Quiz 8. Lecture: the transition to turbulence; Reynolds decomposition and averaging.
Tues., Oct. 29: Lecture: begin derivation of the Reynolds stress term.
Thurs., Oct. 31: Quiz 9. Lecture: complete derivation of Reynolds stress term, discussion of covariance and correlation.
Tues., Nov. 5: Lecture: Reynolds stress tensor, divergence of Reynolds stress, local first order closure (k-theory), eddy viscosity.
Thurs., Nov. 7: Quiz 10. Lecture: Scale analysis of the equations of motion. Geostrophic flow and hydrostatic balance.
Tues., Nov. 12: Lecture: Momentum equations for Ekman layer and Ekman spiral solution in atmosphere. Rossby number.
Thurs., Nov. 14: Quiz 11. Lecture: Discussion of student term projects then begin stratification and barotropic fluids.
Tues., Nov 19: Lecture: Derive barometric law, hypsometric equation, Poisson's equation, and potential temperature.
Thurs., Nov 21: Lecture: Derive dry adiabatic lapse rate; discussion of atmospheric static stability in terms of potential temperature.
Tues., Nov 26: Thanksgiving break. No classes.
Thurs., Nov. 28: Thanksgiving break. No classes.
Tues., Dec. 3: Lecture: Student presentations on term research: Katherine, Kelsey, Kimberly, Yovanni
Thurs., Dec. 5: Lecture: Student presentations on term research: Andrea, Kelly, Jeremy, Kyra, Eric
Tues., Dec. 10: Lecture: No class.
Thurs., Dec. 12: Lecture: Student presentations on term research: Michal, Hannah. Then, lecture on stratification and the Brunt-Väisälä frequency.
Tues., Dec. 17: Final Exam from 2:00 - 3:50 PM
Dr. Mayor's page