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IMA Workshop
Reduced Descriptions of Coupled GFD Systems (Slow Manifolds in the Ocean and Atmosphere)
February 11-15, 2002


Organizers:

Darryl D. Holm
Mathematical Modeling and Analysis Theoretical Division
Los Alamos National Laboratory (LANL)
dholm@lanl.gov   http://cnls.lanl.gov/~dholm/

James C. McWilliams
Department of Atmospheric Sciences
University of California, Los Angeles
jcm@atmos.ucla.edu

 

 

A distinctive difficulty in climate-system modeling, analysis and prediction is the presence of two or more time scales in the problem. The atmosphere and oceans each support slow Rossby and fast inertia-gravity waves, while the characteristic times of atmosphere, oceans, and ice sheets are about a factor of 10 apart. Thus the proper treatment, via slaved-variable and slow-manifold theory of time-scale disparity within each subsystem and between subsystems is of the essence. The workshop topics will include

(i) the connection between the slow manifold, averaged descriptions, the quasi-geostrophic approximation, and intermediate balanced models;

(ii) models of the coupled ocean-atmosphere system; and

(iii) slow-manifold theory. Tools such as asymptotics, averaging, center manifold, inertial manifold, attractors and their approximations are indispensable for dealing with these problems.

Keywords: coupling, ENSO, intermediate models

WORKSHOP SCHEDULE

Monday Tuesday
MONDAY, FEBRUARY 11
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

9:15 am Douglas N. Arnold, Robert Gulliver, and Darryl Holm Welcome and Introduction
9:30 am William K. Dewar
Florida State University
A nonlinear, conceptual mid-latitude climate model
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am James C. McWilliams
IGPP, UCLA

The Theory and Theology of Nonlinear Balance

Slides

12:00 pm
Lunch Break
2:00 pm

Darryl D. Holm
Los Alamos National Laboratory

Lagrangian averages, averaged Lagrangians and dimension reduction in modeling GFD turbulence

Slides

3:00 pm

Second Chances
C. David Levermore, Moderator

3:00 William K. Dewar
3:15 James C. McWilliams
3:30 Darryl D. Holm

3:45 pm Open Discussion
C. David Levermore, Moderator
4:00 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, FEBRUARY 12
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00am Coffee Reception Room EE/CS 3-176
9:30 am Leslie M. Smith
University of Wisconsin

Population of Slow Manifolds in Strongly Stratified, Rotating Flows with Unbalanced Turbulent Forcing

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Beth A. Wingate
Los Alamos National Laboratory
The alpha-model of turbulence for GFD applications
12:00 pm
Lunch Break
2:00 pm Alex Mahalov
Arizona State University

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Slides:   pdf    postscript

3:00 pm

Second Chances
Darryl D. Holm, Moderator

3:00 Leslie Smith
3:15 Beth Wingate
3:30 Alex Mahalov

3:45 pm Open Discussion
Darryl D. Holm, Moderator
WEDNESDAY, FEBRUARY 13
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 am Coffee Reception Room EE/CS 3-176
9:30 am David G. Dritschel
University of St Andrews

An explicit potential-vorticity conserving approach to modelling three-dimensional Boussinesq flows

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Jeroen Molemaker
University of California, Los Angeles
Unbalanced Instabilities of the Balanced Quasi-Manifold (tent.)
12:00 pm
Lunch Break
2:00 pm C.E. Leith
Lawrence Livermore Laboratories
Fast Manifolds
3:00 pm

Second Chances
James McWilliams, Moderator

3:00 David Dritschel
3:15 Jeroen Molemaker
3:30 C.E. Leith

3:45 pm Open Discussion
James McWilliams, Moderator
THURSDAY, FEBRUARY 14
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 am Coffee Reception Room EE/CS 3-176
9:30 am Djoko Wirosoetisno
University of Twente

Nonlinear Averaging in GFD Systems and Higher-Order Balance Dynamics

Slides:   pdf    postscript

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Jacques Vanneste
University of Edinburgh
Dirac-bracket approach to Hamiltonian balanced models
12:00 pm
Lunch Break
2:00 pm Vladimir Tseitline
Universite P. et M. Curie
Frontal geostrophic adjustment, slow manifold and nonlinear wave phenomena in 1d rotating shallow water model
3:00 pm

Second Chances
C.E. Leith, Moderator

3:00 Djoko Wirosoetisno
3:15 Jacques Vanneste
3:30 Vladimir Tseitline

3:45 pm Open Discussion
C.E. Leith, Moderator
6:00 pm Workshop Dinner Caspian Bistro, 2418 University Ave. S.E.
FRIDAY, FEBRUARY 15
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00am Coffee Reception Room EE/CS 3-176
9:30 am C. David Levermore
University of Maryland, College Park

A Shallow Water Model with Eddy Viscosity for Basins with Varying Bottom Topography

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Edriss S. Titi
University of California
Global Well-posedness and Long-Term Dynamics for Certain Geophysical Models
12:00 pm
Lunch Break
2:00 pm George R. Sell
University of Minnesota
The Search for El Nino: An Update
3:00 pm

Second Chances
Vladimir Tseitline, Moderator

3:00 C. David Levermore
3:15 Edriss Titi
3:30 George R. Sell

3:45 pm Open Discussion
Vladimir Tseitline, Moderator
Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)

As of 2/12/2002
Name
Department Affiliation
Douglas N. Arnold   Institute for Mathematics & its Applications
William K. Dewar Oceanography Florida State University
Douglas Dokken Mathematics University of St. Thomas
David G. Dritschel Applied Mathematics The University of St. Andrews
Greg Duane   Institute for Mathematics and its Applications
Robert Gulliver   Institute for Mathematics & its Applications
Darryl D. Holm Mathematical Modeling and Analysis Theoretical Los Alamos National Laboratory
Michael S. Jolly Mathematics Indiana University
Leonid V. Kalachev Mathematical Sciences University of Montana
John Knox Biological and Agricultural Eng. University of Georgia
C.E. Leith   Lawrence Livermore National Laboratory
David Levermore Institute for Physical Sciences & Technology University of Maryland
Peter Lynch Mathematics Met Eireann
Alex Mahalov Mathematics Arizona State University
James C. McWilliams Atmospheric Sciences University of California, Los Angeles
Aurelia Minut   Institute for Mathematics and its Applications
Jeroen Molemaker Institute of Geophysics & Planetary Physics University of California, Los Angeles
John Norbury   University of Oxford
Vakhtgang Poutkaradze   University of New Mexico
Fadil Santosa   Institute for Mathematics & its Applications
Arnd Scheel Mathematics University of Minnesota
Kurt Scholz Mathematics University of St. Thomas
George R. Sell Mathematics University of Minnesota
Michael W. Smiley Mathematics Iowa State University
Leslie Smith Mechanical Engineering University of Wisconsin-Madison
Edriss Titi Mathematics University of California, Irvine
Vladimir Tseitline Laboratoire de Meteorologie Dynamique Universite de P. et M. Curie
Jacques Vanneste Mathematics & Statistics University of Edinburgh
Beth A. Wingate   Los Alamos National Laboratory
Djoko Wirosoetisno Faculty of Applied Mathematics University of Twente
Irad Yavneh Faculty of Computer Science Technion
Toshio Yoshikawa   Institute for Mathematics and its Applications

2001-2002 IMA Thematic Year on Mathematics in the Geosciences

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