Zeitlin, V (Laboratoire de Météorologie Dynamique (LMD-ENS)) Wednesday 11 December 2013, 11:00-12:00

Lucarini, V (Universität Hamburg) Thursday 19 December 2013, 10:00-11:00

I will present an overview how superstatistical techniques (a method from nonequilbrium statistical mechanics) can be successfully used to model the statistical properties of turbulent flows. Examples treated are classical turbulence, quantum turbulence, environmental turbulence (wind gusts) and, if time remains, dark matter turbulence.

It is well known that the Extremal Index (EI) measures the intensity of clustering of extreme events in stationary processes. We sill see that for some certain uniformly expanding systems there exists a dichotomy based on whether the rare events correspond to the entrance in small balls around a periodic point or a non-periodic point. In fact, either there exists EI in (0,1) around (repelling) periodic points or the EI is equal to 1 at every non-periodic point. The main assumption is that the systems have sufficient decay of correlations of observables in some Banach space against all L1-observables. Then we consider random perturbations of uniformly expanding systems, such as piecewise expanding maps of the circle. We will see that, in this context, for additive absolutely continuous noise (w.r.t. Lebesgue), the dichotomy vanishes and the EI is always 1

Bodai, T (University of Hamburg) Wednesday 18 December 2013, 10:00-11:00

Two topics will be covered in this lecture. The shallow water equations will be used as a test bed to introduce the ideas. (i) For forced variational systems such as the potential flow shallow water wave equations, variational and symplectic time integrators will be extended using a new finite element approach. Here, a standard variational finite element discretization will be applied in space. (ii) The shallow water equations formulated in terms of Clebsch variables will be discussed. The advantage of Clebsch variables is that they lead to canonical Hamilton's equations for shallow water dynamics, in the Eulerian framework. A disadvantage is that the the system, is less compactly expressed in comparison to the usual formulation in terms of the velocity and fluid depth. I will make a link between a symmetry in the Hamiltonian and the associated mass weighted potential vorticity conservation law, also within the Eulerian framework. This will be done in two dimensions (2D) and in a quasi-2D symmetric form.

Yano, J-I (Meteo France) Tuesday 10 December 2013, 11:00-12:00

Mantica, G (Center for nonlinear and Complex Systems, Universita' dell'Insubria) Thursday 12 December 2013, 10:00-11:00

I describe a symplectic geometric approach to Monge-Ampère equations, discuss some classical and modern geometric structures related to this class of non-linear equations, their invariants and their role in 3D meteorological models. My talk is based on joint works with B. Banos and I . Roulstone.

The role of contact and symplectic geometry of the semi-geostophic (SG) equations, in describing their Legendrian and Hamiltonian properties, will be reviewed. Using the geometry of 2-forms in 4 dimensions and the geometry of 3-forms in 6 dimensions, we show that the incompressible Euler equations in 2 and 3 dimensions admit geometric structures akin to the those present in the SG equations.

Co-authors: Jonathan Mitchell (UCLA), Sam Potter (Princeton University) The dry primitive equations can, with appropriate forcing and dissipation, provide a reasonable simulation of the large-scale features of the Earth's atmosphere and ocean. In this talk I will describe the behaviour of these PDEs when they are taken out of the terrestrial parameter regime. In n particular, I will describe their behaviour when the thermal Rossby number, Ekman number and a radiative relaxation timescale are varied considerably, moving into a parameter regime more appropriate for Mars or Titan. I will pay particular attention to the formation of zonal jets, and in particular of equatorial superrotation, which is a feature of some other planets. It is well-known that zonal jets robustly arise in rotating atmospheres if there is a wavemaker at a particular latitude. Rossby waves are then generated that propagate away, and eastward momentum converges on the source region producing a zonal jet. The Earth's jet stream is, in part, formed this way. However, on slowly rotating atmospheres it seems unlikely that superrotation is produced by that mechanism. Rather, simulations indicate that, at small thermal Rossby number, a mechanism involving equatorial Kelvin waves is involved.