Analysis, Geometry and Stochastics for Planet Earth

The aim of this LMS Joint Research Group Grant, Scheme 3, Analysis, Geometry and Stochastics for Planet Earth is to investigate current challenges in mechanics, dynamics and earth system which require an intricate integration of techniques from geometry, analysis and stochastic processes.

This is the second meeting in a series of four. The first meeting was held at Imperial college, cf. details on the website of the meeting, mainly dedicated to the relation between statistical, probabilistical methods and dynamical questions.

The forthcoming meeting will concentrate on multi-scale effects and self-organisation phenomena. Mathematical challenges will be highlighted, in particular relations to the associated geometric structure.  Related projections techniques and closure techniques for hydrodynamics models and stochastic GFD-models will be discussed. Closure schemes used in practise containing stochastic terms give insight into sub-scale fluctuations and give effective description of turbulence for 2d to 3d hydrodynamics,  up-scattering and scaling properties. Via self-organisation sub-scale degrees of freedom  may collectively give rise to non-negligible terms on larger scales or create non-linear feedback requiring more elaborate and non-intuitive closure schemes. The self-aggregation of convection and precipitation are such kind of phenomena.

A core question in many applications in geo-fluid dynamics is how to model uncertainty and stability using random perturbations. We want to develop systematic ways to infer appropriate noise terms from the geometric structure and/or fluctuations of microscopic (sub-scale) origin. We now start to understand that the geometry of noise terms can be linked to the structure of the underlying non-equilibrium small-scale systems. Progress in this area will require cross-fertilization across the aforementioned areas. There have been substantial developments in stochastic analysis in the last two decades, but most of these remain of a theoretical nature, with no straightforward application to earth systems yet.

Researchers interested to participate are warmly welcome. Please register above. The conference fee is £ 20 and £ 10 for PostDoc/Phd. Limited support for PhD-students and PostDocs are available, please contact the organisers at t.kuna@reading.ac.uk for details.

Programme:

• 14:00-14:10 Introduction
• 14:10-14:55 Prof Darryl Holm (Imperial College London) : “Stochastic Variational Principles for Geophysical Fluid Dynamics (GFD)”
• 15:00 – 15:45 Caroline Muller (Ecole Polytechnique) : “Spatial organization of clouds in the tropical atmosphere”
• 15:50 -16:05 Coffee Break
• 16:05- 17:00: Discussion Group (Phd-students and PostDoc)

Organizers:

Dan Crisan, Tobias Kuna, Johannes Zimmer

Email the organizers at t.kuna-AT-reading.ac.uk.

Funding

The conference is supported by the London Mathematical Society through a Joint Research Group Scheme 3 grant and by EPSRC Centre of Doctoral Training Mathematics of Planet Earth