Abstract
Turbulence in fluids and plasmas is one of the least understood topics in classical continuum physics. The problem addresses randomly varying flows, where individual realizations are too complicated to be comprehensible, but which can be described and analysed by statistical methods. In spite of significant progress in the studies of neutral flows (in water etc.), there are still several basic problems, which are not fully understood. As far as plasmas are concerned (i.e. gases composed of charged particles) the situation is even more unfavourable. In this case the sensitivity of the gas to electric and magnetic fields adds to the complexity, and progress has only been made by significant simplifications, which are not always justifiable. It is however quite important that we improve our understanding of turbulent plasmas, since most of the matter on astrophysical and heliospheric scales is in the plasma state, and is often found to be strongly turbulent. One of the most important properties of turbulent fluctuations in gases and fluids is their ability to disperse particles at an anomalously large rate. This implies that boundaries in space are maintained only to the extent allowed by turbulent transport. Similarly, it is found that the electrical conductivity of a plasma is often controlled by turbulence. This latter problem is studied even less than turbulent transport, but it is expected to be central for the understanding of the large scale current systems associated with the Earth's magnetosphere. The research group will address selected central questions concerning turbulent transport, with emphasis on applications in nature.
End Report
The main topics of the project were associated with numerical studies of turbulence in fluids and plasmas, by involving analysis of existing data as well as obtaining new theoretical and numerical results. The present summary can most conveniently be separated into two parts:
A. Our studies of turbulence in neutral fluids were carried out with explicit reference to the presumed importance of turbulence for the feeding process of aquatic microorganisms. For these studies we had initially one database at our disposal, where the motions of many small polystyrene particles were followed, where these particles could be used as representing aquatic microorganisms. These results were obtained by experimental studies at the Risø National Laboratory in Denmark. As a consequence of the success of the first investigations, we were approached by colleagues from Italy, giving us access to related simulation results from some of the largest numerical simulations of turbulent flows carried out today. These results were obtained by direct numerical solutions of the NavierStokes equation. The parameter range of these two datasets supplements those from the laboratory, by having a Reynolds number approximately twice as large. Although, of course, also the simulation data have their limitations, we were nonetheless able to provide estimates with unprecedented accuracy of, for instance, the turbulent particle fluxes to a perfectly absorbing spherical surface.
B. Studies of plasma wave phenomena. Most of this activity was based on numerical methods. Two approaches were used: a fluid type code, where a set of model equations (the ideal compressible MHD equations) were solved numerically. One such method of solution (Smooth Particle Hydrodynamics, or simply SPH) was analyzed in detail. Particular attention was given to cases possessing certain symmetries. As an alternative, we have a ParticleInCell (PIC) code, where the motions of a large number (up to 40 million) of interacting simulation particles are followed numerically. Great efforts were made to represent particle collisions, collisions between charged and neutral particle in particular, correctly. For the time being, we are able to handle relatively low energy particles, involving elastic and charge exchange collisions. These effects are particularly important for ionospheric plasmas, and also for industrial applications.
The work at the Centre resulted in a number of publications and contributions at meetings and conferences, addressing the two central subjects for the activity:
A. We studied predatorprey interactions with reference to aquatic microorganisms. Our results, based on analysis of data obtained by laboratory experiments and numerical simulations, presumably represent the first quantitative estimate for testing certain model predictions. Existing models were generalized to become more realistic, and also these cases were amenable for tests by using the existing database. Some of the results may seem counterintuitive, but turn out to have simple physical explanations. We found the approach by comparing numerical simulations and laboratory experiments particularly fruitful in the studies related to the biological food chain. Significant advances were made in the interpretation of the laboratory data as well as the results form the numerical simulations. Based on these studies, we are in a position to include the effects of the self induced motion of microorganisms, and to make studies of systems coming close to realistic conditions in nature.
B. Numerical codes were developed for analyzing the dynamics of plasmas, where collisions between charged particles and neutrals are sufficiently frequent to give significant effects for wave propagation and plasma stability. One example concerns the dynamics of small meteors (often of the size of a grain of sand, or smaller), that evaporates and subsequently becomes ionized by the friction with the Earth’s neutral atmosphere. Significant progress was made on both topics, and we are now in a position to model, with great accuracy, the plasma surroundings of small meteors, and find good agreement with observations.
The general numerical studies addressed also other methods. A novel mainstream approach was tested out, the SmoothParticleHydrodynamics (SPH) model, which has received great attention in recent years. In principle, this type of model can be applied for neutral flows as well as plasmas, but in the plasma case, they are considered most reliable for large scale structures. Several ionospheric problems were analyzed by numerical models, mostly small scale phenomena as those observed by instrumented space crafts in the Earth’s near ionosphere. Significant progress has been made in the development of numerical codes on these topics, with results having value for our continuation of these projects
Fellows

Børve, Steinar

Dyrud, Lars Peterson

Guio, Patrick

Kontar, Eduard P.

Longo, Savino

Mjølhus, Einar Oliver

Rippis, Peter Dimitris

Wernik, Andrzej Wladyslaw