IMA Workshop: Reduced Descriptions of Coupled GFD Systems (Slow manifolds in the ocean and atmosphere), February 11-15, 2002

Mathematics in Geosciences, September 2001 - June 2002

Winter 2002

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

Schedule	Participants	Registration
Abstracts
Material from Talks

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

NOTE: all talks are 45 minutes, followed by a 15-minute discussion

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

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

Abstracts Material from Talks

2001-2002 IMA Thematic Year on Mathematics in the Geosciences

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Winter 2002 IMA Workshop:

Reduced Descriptions of Coupled GFD Systems (Slow Manifolds in the Ocean and Atmosphere)

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

Winter 2002

IMA Workshop:

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