MATH 6425 (16971)

MATHEMATICAL MODELING OF ATMOSPHERIC AND OCEANIC FLOWS

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:

  • "Introduction to geophysical fluid dynamics"
  • by Benoit Cushman-Roisin and Jean-Marie Beckers,
    Academic Press, 2010.

    Important note: The PDF files of the textbook are posted here.

    The textbook will be supplemented with class notes posted on scholar.

    Additional references:

  • "An Introduction to Dynamic Meteorology"
  • by James R. Holton,
    Academic Press, fourth edition,
    (2004) hardcover, ISBN: 0123540151.

  • "Introduction to PDEs and Waves for the Atmosphere and Ocean"
  • by Andrew Majda,
    AMS Bookstore,
    (2003).

  • "Atmospheric and Oceanic Fluid Dynamics"
  • by Geoffrey Vallis,
    Cambridge,
    (2006).


    Evaluation Criteria and Grading:

  • Homework (50% of the final grade)

  • Final Project (50% of the final grade)

  • A score of 85% will guarantee an A, 75% a B and 70% a C.

    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.
     
    Comments to: iliescu@vt.edu
    Page last updated: Friday October 16, 2009