Geometric and stochastic methods
in geophysical fluid dynamics
January 711, 2008
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 scalesfrom 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 pointwise sense, it may still yield
accurate answers in a time, space, or ensembleaveraged 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 largescale computation.
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.)

9:009:50 
Riwal Plougonven (ENS Paris) 


``On the forcing of inertiagravity waves by
synoptic scale flows'' 

10:0011:00 
Coffee break 

11:0011:30 
Oliver Bühler (Courant Institute) 


``Geometric focusing of internal tides'' 

11:3012:00 
Jacques Vanneste (Edinburgh) 


``Asymptotics of a slow manifold'' 

12:0016:30 
Lunch, informal discussions, collaborations,
tea 

16:3017:00 
Jason Frank (CWI Amsterdam) 


``Statistical mechanics of Arakawa's
Jacobians'' 

17:0017:30 
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 

9:009:20 
Vladimir Molchanov (Jacobs University) 


``On the convergence of a Hamiltonian
particlemesh method'' 

9:209:40 
Bob Peeters (U. Twente) 


``Numerical evaluation of a Hamiltonian
particlemesh method'' 

9:4010:00 
Matthias Sommer (FU Berlin) 


``Numerics of energyvorticitytheory'' 

10:0010:30 
Coffee break 

10:3011:00 
Almut Gassmann (MPI Hamburg) 


``Towards global nonhydrostatic modeling for
climate modeling and NWP in Germany'' 

11:0011:30 
Andy White (U.K. Met Office) 


``Spheroidal coordinate systems for models of the
global atmosphere'' 

11:3012:00 
Jörn Behrens (AWI Bremerhaven) 


``Mass conserving and adaptive semiLagrangian
schemes in spherical geometry'' 

12:0016:30 
Lunch, informal discussions, collaborations,
tea 

16:3017:00 
Colin Cotter (Imperial) 


``"Particlemesh methods for Hamiltonian fluid
dynamics'' 

17:0017:30 
Onno Bokhove (U. Twente) 


``Air parcel and air particles: Hamiltonian
dynamics'' 

9:009:50 
Eric VandenEijnden (Courant Institute) 


``Nonequilibrium statistics of a reduced model for
energy transfer in waves'' 

10:0010:30 
Coffee break 

10:3011:00 
Grigorios Pavliotis (Imperial) 


``Multiscale analysis for the stochastic Burgers
equation.'' 

11:0011:30 
Djoko Wirosoetisno (Durham) 


``Point vortex dynamics on a deformed
sphere'' 

11:3012:00 
David Dritschel (St. Andrews) 


``Cascades and conservation: contradictions in
modelling'' 

12:0015:30 
Lunch, informal discussions,
collaborations 

17:0019:00 
``Space walk'' at EADS facility Bremen 


(leave campus at 15:45, passport/ID required) 

9:009:50 
George Craig (DLR Oberpfaffenhofen) 


``Equilibrium statistics of cumulus convection and
stochastic parameterization'' 

10:0010:30 
Coffee break 

10:3011:00 
Wim Verkley (KNMI) 


``Energy spectra of turbulent flows derived from a
maximum entropy principle'' 

11:0011:30 
Sebastian Reich (Potsdam) 


``On timestaggered semiLagrangian advection
schemes'' 

11:3012:00 
Daan Crommelin (CWI Amsterdam) 


``Subgrid scale parameterization with conditional
Markov chains'' 

12:0016:30 
Lunch, informal discussions, collaborations,
tea 

16:3017:00 
Georg Gottwald (Sydney) 


``Good and bad regularizations induced by
numerical schemes'' 

17:0017:30 
Volker John (Saarbrücken) 


``Variational multiscale methods for turbulent
flow simulations'' 

19:30 
Conference dinner 

9:009:50 
Mike Cullen (U.K. Met Office) 


``Data assimilation for systems with multiple
timescales'' 

10:0010:30 
Coffee break 

10:3011:00 
Illia Horenko (FU Berlin) 


``Extraction of hidden information from
multidimensional data'' 

11:0011:30 
Peter Korn (MPI Hamburg) 


``Data assimilation for the Lagrangian Averaged
NavierStokesalpha equations'' 

11:3012:00 
Ian Roulstone (Surrey) 


``Hamiltonian methods in 4DVAR'' 

12:0016:30 
Lunch, informal discussions, collaborations,
tea 
