Geometric and stochastic methods
in geophysical fluid dynamics

January 7-11, 2008

Organizing committee

Marcel Oliver (Jacobs University), local organizer
Onno Bokhove (Twente)
Oliver Bühler (Courant)
Jason Frank (CWI)
Sebastian Reich (Potsdam)
Jacques Vanneste (Edinburgh)


Flows in the atmosphere and ocean evolve on a vast range of spatial and temporal scales--from planetary scales and decadal patterns down to the Kolmogorov dissipation length scale, for atmospheric flows at the order of one meter, with important Physics such as rain drop formation at even much smaller scales. Thus, any practical simulation in the forseeable future will be underresolved in the textbook sense of numerical methods.

At the resolvable scales, geophysical flows are inviscid to a high degree of accuracy. Meteorologists have recognized for a long time that, for this reason, intrinsically conservative schemes often outperform nonconservative ones. More recent developments in Hamiltonian perturbation theory as well as advances in the preservation of Hamiltonian structure by numerical schemes have brought about an abundance of models that not only conserve mass but approximately conserve energy and potential vorticity invariants over very long times.

Preserving Hamiltonian structure, however, is only half of the story. In real flows, energy cascades to small scales where it is eventually dissipated, so the picture must be supplemented by parameterizations of the subscale energy dissipation and of any other physics that may take place at subgrid scales. These subgrid closures must, in particular, maintain correct energy fluxes in the resolved part of the spectrum.

Probability plays a crucial role in analyzing, interpreting, and, increasingly, also constructing subgrid closures. While a computation may cease to make point-wise sense, it may still yield accurate answers in a time, space, or ensemble-averaged sense. The importance of Hamiltonian structure for maintaining such averages on the large scales is better understood in the context of molecular dynamics, much less so in fluid dynamics. A promising second line of research is concerned with stochastic subgrid closures.

The goals of this workshop are twofold. First, to synthesize ideas from geometric mechanics and probability in a rational and, whenever possible, rigorous mathematical framework. Second, to enhance the dialog between theoreticians and practitioners from major operational centers to maintain relevance of theoretical research and to facilitate the uptake of theoretical advances in practical large-scale computation.

Tentative Schedule

All talks are in the IRC Seminar room. (In the Jacobs University Campus Center; enter through library entrance, then through first floor main reading room and east wing quiet study area.)

Monday, January 7: Waves in atmosphere and ocean

 9:00-9:50 Riwal Plougonven (ENS Paris)
   ``On the forcing of inertia-gravity waves by synoptic scale flows''
 10:00-11:00     Coffee break
 11:00-11:30 Oliver Bühler (Courant Institute)
   ``Geometric focusing of internal tides''
 11:30-12:00 Jacques Vanneste (Edinburgh)
   ``Asymptotics of a slow manifold''
 12:00-16:30 Lunch, informal discussions, collaborations, tea
 16:30-17:00 Jason Frank (CWI Amsterdam)
   ``Statistical mechanics of Arakawa's Jacobians''
 17:00-17:30 Vladimir Zeitlin (ENS Paris)
   ``Parametric excitation and nonlinear dynamics of trapped waves in the ocean: coastal, topographic and equatorial waveguides''
 18:00 Welcome Reception at the Jacobs University Club

Tuesday, January 8: Conservative numerical schemes

 9:00-9:20 Vladimir Molchanov (Jacobs University)
   ``On the convergence of a Hamiltonian particle-mesh method''
 9:20-9:40 Bob Peeters (U. Twente)
  ``Numerical evaluation of a Hamiltonian particle-mesh method''
 9:40-10:00 Matthias Sommer (FU Berlin)
   ``Numerics of energy-vorticity-theory''
 10:00-10:30     Coffee break
 10:30-11:00 Almut Gassmann (MPI Hamburg)
   ``Towards global nonhydrostatic modeling for climate modeling and NWP in Germany''
 11:00-11:30 Andy White (U.K. Met Office)
   ``Spheroidal coordinate systems for models of the global atmosphere''
 11:30-12:00 Jörn Behrens (AWI Bremerhaven)
   ``Mass conserving and adaptive semi-Lagrangian schemes in spherical geometry''
 12:00-16:30 Lunch, informal discussions, collaborations, tea
 16:30-17:00 Colin Cotter (Imperial)
   ``"Particle-mesh methods for Hamiltonian fluid dynamics''
 17:00-17:30 Onno Bokhove (U. Twente)
   ``Air parcel and air particles: Hamiltonian dynamics''

Wednesday, January 9: Asymptotic methods and simplified models

 9:00-9:50 Eric Vanden-Eijnden (Courant Institute)
   ``Nonequilibrium statistics of a reduced model for energy transfer in waves''
 10:00-10:30     Coffee break
 10:30-11:00 Grigorios Pavliotis (Imperial)
   ``Multiscale analysis for the stochastic Burgers equation.''
 11:00-11:30 Djoko Wirosoetisno (Durham)
   ``Point vortex dynamics on a deformed sphere''
 11:30-12:00 David Dritschel (St. Andrews)
   ``Cascades and conservation: contradictions in modelling''
 12:00-15:30 Lunch, informal discussions, collaborations
 17:00-19:00 ``Space walk'' at EADS facility Bremen
   (leave campus at 15:45, passport/ID required)

Thursday, January 10: Subscale processes

 9:00-9:50 George Craig (DLR Oberpfaffenhofen)
   ``Equilibrium statistics of cumulus convection and stochastic parameterization''
 10:00-10:30     Coffee break
 10:30-11:00 Wim Verkley (KNMI)
   ``Energy spectra of turbulent flows derived from a maximum entropy principle''
 11:00-11:30 Sebastian Reich (Potsdam)
   ``On time-staggered semi-Lagrangian advection schemes''
 11:30-12:00 Daan Crommelin (CWI Amsterdam)
   ``Subgrid scale parameterization with conditional Markov chains''
 12:00-16:30 Lunch, informal discussions, collaborations, tea
 16:30-17:00 Georg Gottwald (Sydney)
   ``Good and bad regularizations induced by numerical schemes''
 17:00-17:30 Volker John (Saarbrücken)
   ``Variational multiscale methods for turbulent flow simulations''
 19:30 Conference dinner

Friday, January 11: Data assimilation and inverse modeling

 9:00-9:50 Mike Cullen (U.K. Met Office)
   ``Data assimilation for systems with multiple timescales''
 10:00-10:30     Coffee break
 10:30-11:00 Illia Horenko (FU Berlin)
   ``Extraction of hidden information from multidimensional data''
 11:00-11:30 Peter Korn (MPI Hamburg)
   ``Data assimilation for the Lagrangian Averaged Navier-Stokes-alpha equations''
 11:30-12:00 Ian Roulstone (Surrey)
   ``Hamiltonian methods in 4DVAR''
 12:00-16:30 Lunch, informal discussions, collaborations, tea

This conference is supported by

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