PROGRAM IDEI – CERCETARI EXPLORATORII

Cod Proiect ID_1103 / 2008

Director Proiect: Florin SPINEANU

Investigarea prin metode de teorie de camp

a structurilor si a auto-organizarii in fluide si plasma

PROJECT SUMMARY

Experimental, numerical and theoretical studies have revealed that the two-dimensional fluids and plasmas exhibit an intrinsic evolution to organisation. This is most obvious at relaxation from turbulent states when the system evolves toward a reduced subset of flow patterns, characterized by a regular form of the streamfunction (coherent structures). This problem is common to the ideal incompressible (Euler) fluid, to plasma in strong magnetic field, to non-neutral plasmas, to planetary atmopshere, MHD, etc. The equations governing the asymptotic stationary, highly ordered states, for any of these systems, could not be derived (for the Euler fluid the sinh-Poisson equation has been inferred from numerical studies). Except for a limited success in applying statistical considerations, there is no conceptual basis on which to develop an analytical approach for this problem.

The 2D ideal (Euler) fluid and the 2D magnetized plasma (and planetary atmosphere) are equivalent with discrete systems consisting of sets of point-like vortices interacting in plane by a potential. We found that the continuum limit of these discrete models can be formalized in terms of a Lagrangian density, preserving the structure: matter (point-like vortices), field (from potential) and interaction between them. The result is a classical field theory from which we derive the equations of motion and look for stationary states that correspond to the lowest action. The first applications to practical cases are very encouraging when compared with the experiment.

The development and the applications of field theoretical formulations in order to highlight the intrinsic trend to self-organization in fluids and plasmas is almost without precedent, therefore the Project will treat a really new subject of research. If successful, this will represent a considerable change in our understanding of the fluid physics, in the concepts and terms to formulate new theories on fluids, and in our technical methods. 

PROJECT OBJECTIVES

1. A consistent theory for the formulation of the physics of fluids and plasmas close to the coherent stationary states, in terms of a classical field theory.

2. A set of field theoretical models that is complementary to the present-day approaches: conservation equations, statistical approach, direct numerical simulations.

3. Quantitative characterization of the stationary (vortical) states, for fluids, atmosphere, magnetized plasma, non-neutral plasma. This means velocity and vorticity profiles, spatially symmetric structures of vortices, degree of metastability.

4. A new, original and powerful theoretical basis (together with its analytical instruments, typical for the field theory, which has huge achievements) to construct models to explain processes important for applications:
1. High confinement regime in tokamak: ring type vortical states.
2. density pinch in tokamak. The density and the vorticity are connected via the Ertel theorem and the vorticity appears to evolve toward a filamentay structure, limited however by the tokamak physics.
3. fast processes of mutual influence boundary/centre in tokamak: the field theory shows the existence of dipolar vortices that may provide ballistic (not diffusive) effects.
4. vortex dynamics on an irrotational background flow (in rotating water-tank). We can derive versions of the sinh-Poisson equation, whe we include in the field theory an irrotational background flow.
5. quantitative characterization of the large scale vortices in linear plasma machines.
6. vortex crystals in non-neutral plasmas.

5. Explicit relationships connecting the main quantitative characteristics of the atmospheric vortex (hurricane, typhoon) when stationarity is a good approximation. These are equations between: the radius of maximal extension, the radius of the eye-wall and the maximum azimuthal velocity of the wind. We have already proposed two equations and they appear to work very well for several known tropical cyclones. Much work on data is still necessary.

6. Extension to 2D magnetohydrodynamics.

First Report

Associated international project

Participation to COST Action ES0905

“Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models”

The main objective of the Action is to provide clear theoretical guidance on convection parameterizations for climate and numerical weather prediction models. Both global and regional atmospheric models are concerned. The Action achieves this objective by creating a core theoretical group to address the fundamental issues of convection parameterization. Modellers and theoreticians join together under this framework. The Action proposes a clear pathway for more coherent and effective parameterizations by integrating existing operational schemes and new theoretical ideas. Proposed alternative approaches intend to replace conventional tuning-based approaches. The Action complements extensive inter-comparison based validations performed by operational modellers.The Action responds particularly to urgent needs which have arisen from increasing the resolutions of forecast models. In these new-generation models, not only the traditional approximations break down, but associated physical processes become increasingly complex. Thus, the parameterization must be extensively re-formulated with more sophisticated physics under new constraints. The Action contributes to reduce uncertainties in weather forecasts and climate projection by overcoming the often weak physical basis of the current parameterizations. Particular benefits will be in prediction of highly unusual extreme weather events, such as local heavy precipitation, tropical cyclone trajectories etc. The IPCC will be a particular international agent that will benefit from the present Action.