2017 Workshop: "Geometric Methods for Geophysical Fluid Dynamics and Climate Modeling"

The workshop aimed at gathering a community of people working on Geometric Methods for fluids and geophysical flows, with expertise ranging from (but not restricted to) variational methods, the analysis of Hamiltonian PDEs, to the development of numerical methods based on the same principles.

The workshop was held in the period 5-7 June 2017.

The workshop resulted in the special issue "Mathematical Developments in Geophysical Fluid Dynamics: Structure, Vortices, and Waves" of Geophysical and Astrophysical Fluid Dynamics.

Organizers:

Gualtiero Badin (University of Hamburg, Germany)

Joern Behrens (University of Hamburg, Germany)


List of Participants (in alphabetical order) and Talk Titles:

  • Werner Bauer (Imperial College, London, UK): "A structure-preserving split finite element discretization of the split 1D wave equations"

  • Richard Blender (University of Hamburg, Germany): "Hydrodynamic Nambu brackets derived by geometric constraints"

  • Onno Bokhove (University of Leeds, UK): "Variational modelling of fluid-structure interactions: coupling water waves to flexible and rigid moving maritime objects"

  • Giovanni Conti (University of Hamburg, Germany): "Hyperbolic Covariant Coherent Structures in Two-Dimensional Flows"

  • Colin Cotter (Imperial College, London, UK): "A variational formulation of vertical slice models"

  • Thomas Dubos (Ecole Polytechnique, Palaiseau, France): "On the covariant structure of models of geophysical fluid motion"

  • Francois Gay-Balmaz (Ecole Normale SupĂ©rieure de Paris, France): "A variational derivation of the thermodynamics of a moist atmophere with irreversible processes"

  • Eyal Heifetz (Tel Aviv University, Israel): "Canonical Hamiltonian representation of stratified shear flows in terms of pseudo-momentum and pseudo-energy conservations"

  • Dimitris Kaltsas (University of Ioannina, Greece): "Nambu representation of spatially reduced MHD models"

  • Peter Korn (Max Plank Institute for Meteorology, Hamburg, Germany): "How geometry helps to build an ocean circulation model"

  • Philip J. Morrison (University of Texas at Austin, USA): "GEMPIC: An exact Poisson integrator for the full Vlasov-Maxwell System"

  • Andrea Natale (Imperial College, London, UK): "A geometric finite element approach for the incompressible Euler equations"

  • Marcel Oliver (Jacobs University, Bremen, Germany): "Optimal Balance via Adiabatic Invariance of Approximate Slow Manifolds"

  • Jacques Vanneste (University of Edinburgh, UK): "Geometric generalised Lagrangian mean theories"

  • Sergiy Vasylkevych (University of Hamburg, Germany): "Balanced semigeostrophic approximations for the f-plane primitive equations"


A couple of references:

G. Badin and F. Crisciani, 2018: "Variational Formulation of Fluid and Geophysical Fluid Dynamics - Mechanics, Symmetries and Conservation Laws -", Springer, ISBN: 978-3-319-59695-2, DOI: 10.1007/978-3-319-59695-2 (Order it at the Springer's book webpage: here)

G. Badin, M. Oliver and S. Vasylkevych, 2018, "Geometric Lagrangian averaged Euler-Boussinesq and Primitive Equations", Journal of Physics A: Mathematical and Theoretical, 51, 455501, doi:10.1088/1751-8121/aae1cb (PDF version)

G. Badin and A.M. Barry, 2018,"Collapse of generalized Euler and surface quasigeostrophic point vortices", Physical Review E, 98, 023110, DOI: 10.1103/PhysRevE.98.023110 (PDF version)

R. Blender and G. Badin, 2017, "Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations", Fluids, 2, 24, doi:10.3390/fluids2020024 (Open Access) (topical collection: "Geophysical Fluid Dynamics")

R. Blender and G. Badin, 2017, "Viscous Dissipation in 2D Fluid Dynamics as a Symplectic Process and its Metriplectic Representation", European Physical Journal Plus, 132, 137, DOI: 10.1140/epjp/i2017-11440-x (PDF version)

R. Blender and G. Badin, 2015: "Hydrodynamic Nambu mechanics derived by geometric constraints", Journal of Physics A: Mathematical and Theoretical, 48, 105501 (PDF version)

The workshop was sponsored by CliSAP.