Research objectives and content
In spite of the infinite dimensional nature of the partial differential equations appearing in fluid mechanics, many features of turbulence can be described in terms of systems with a finite number of degree of freedom. Examples are the shell models to mimic the Navier-Stokes equation and the understanding of the scaling properties of fully developed turbulence, dynamo cell models for the kinematic dynamo problem at high magnetic Reynolds number. Velocity fields generated by shell models can be used in order to investigate the passive diffusion of two particles in extended systems.
Coupled-map-lattices (CML) can give insights about spatial
correlation functions and the relations between quantities like dimension, correlation lengths and Lyapunov exponents. On the other hand dynamical and spatial behaviors of CML become "critical" when some parameters approach specific values. We propose to study the dependence of the critical properties on the updating rule.
Training content (objective, benefit and expected impact)
The understanding of passive diffusion is of theoretical and practical importance in diverse fields of science and engineering, ranging from mass and heat transport in geophysical flows to chemical engineering and combustion. In particular, the improvement of forecasting methods for the propagation of dust particles in the atmosphere would have a relevant impact in the technologies to prevent and reduce atmospheric pollution. Links with industry / industrial relevance (22)