| Instructor: Traian Iliescu |
Office: McBryde 456 Phone : (540) 231-8265 Email : iliescu@vt.edu |
Office Hours: 4:00pm - 5:00pm Monday and Wednesday & by e-mail appointment |
Class Meeting Time and Place:
1:25pm - 2:15pm Monday, Wednesday and Friday
McBryde 212
Course Goals and Objectives:
This course is a general introduction to the mathematical modeling
of atmospheric and oceanic flows.
It will focus on both mathematical and computational
topics.
The main goal is to provide a research playground
for students interested in the equations of the atmosphere and ocean.
The objectives are:
(1) to introduce the basic mathematical tools used in the
development of the equations of the atmosphere and ocean;
(2) to introduce the basic computational methods for the numerical
simulation of these geophysical flows; and
(3) to help each student in his/her research.
Besides mathematics graduate students, graduate students in engineering and
computer science are strongly encouraged to take this course.
Course Contents:
This course will introduce students to the approximations and governing
equations that describe the large scale atmospheric and oceanic flows,
which are characterized by the dominant role of planetary rotation and
stratification.
A strong emphasis will be placed on the serendipity between modern applied
mathematics and geophysical flows, where rigorous analysis, as well as
asymptotic, qualitative, and numerical modeling all interact.
Topics will include: vorticity and potential vorticity dynamics, geostrophic
and thermal wind balance, shallow water and quasi-geostrophic flows, gravity
and Rossby waves, flow instabilities, turbulence, and data assimilation.
Applied mathematical techniques, such as perturbation expansions, multiple-scale
analysis, and the WKB approximation, will play a central role in the derivation
and analysis of traditional atmospheric and oceanic flow models.
Prerequisites: Very basic background in partial differential equations and
their approximation by numerical methods.
Students should be able to use a programming language (such as MATLAB, FORTRAN, or C)
to complete their computational assignments.
Textbook:
Additional references:
Evaluation Criteria and Grading:
Missed Work:
If a student fails to hand in an assignment
on time, his/her score is zero unless the reasons for the failure are
serious and beyond the student's control (``subc'').
The instructor reserves the right to verify that the reasons are serious and
beyond the student control.
It is to the student's advantage to inform the instructor of such reasons
before missing the work.
When work is missed for ``subc" reasons, the instructor, after consultation
with the student, will decide how to handle the missed work.
Honor:
Students work on the final project alone.
Homework may be discussed with other students as well as with the instructor.
In writing up an assignment to be handed in, however, the student works alone
(without other students or other students' papers) and certifies that what is
written accurately represents the student's own understanding of the material
expressed in the student's own words.
The honor code applies to all graded work in this course.
The Virginia Tech Honor System will be strictly enforced.
Virginia Tech Honor System Information
Special Needs:
If you need adaptations or special accommodations because of a disability
(learning disability, attention deficit disorder, psychological, physical, etc.),
if you have emergency medical information to share with me, or if you need
special arrangements in case the building must be evacuated, please make
an appointment with me as soon as possible.
Page last updated: Friday October 16, 2009