Objective The object of the Project is the investigation of small-scale coherent structures and collapse formation in systems of hydrodynamic type. These systems concern hydrodynamic and magneto-hydrodynamic (MHD) flows, both incompressible and compressible, with and without free surface (or interfaces).The emphasis will be devoted to the problem of collapse that assumes that the dynamics are far from thermodynamic equilibrium, and that nonlinearity cannot be considered as negligible. The proposal combines theoretical and numerical investigations and the results will be related to experimental observations. The proposed project will make possible a continuation and strengthening of the collaboration between the involved groups as well as the establishment of new links. The investigations will offer innovative approaches to the classical problems of hydrodynamics and MHD, such as formation of singularities on the free surface of fluids, breaking of continuously distributed vortex lines for fluids and magnetic lines in MHD, interaction of vortices with wind-water waves, collapse of self-gravitating vortex rings with applications to the extra-galaxy objects. In addition the planned investigations have potential applications in fields as hydrodynamic and MHD turbulence, astrophysics, oceanology and environmental research.The following is a summary of the main results that are expected in the proposed project:- A description of vortex line breaking in 3D integrable hydrodynamics in both nondegenrated and degenerated cases.- A study of thin vortex layers in the framework of quasi-two-dimensional hydrodynamics and their self-similar collapsing asymptotics;- A comprehensive investigation of the magnetic line breaking for incompressible ideal MHD;- An analysis of the local induction approximation for different hydrodynamic models in an external field: compressible hydrodynamics, trapped Bose-condensates; relativistic hydrodynamics;- Derivation of equations for vortex filament motion for different hydrodynamic models with account for inhomogeneity;- Theoretical and numerical study of singularities appearing on the surface of ideal fluid;- Effect of dispersion on reconnection of nearly singular sructures in hydro- and MHD systems;- A study of nonlinear Alfven waves, their instabilities, collapses and turbulence;- Theoretical and numerical study of weak turbulence of Alfven waves in the presence of dissipative effects;- A study of spatio-temporal collapsing distributions for ideal MHD.;- A description of shock front structures of the strong non-central explosion blast wave in medium with bi-power density behaviour;- A study of self-gravitating vortex rings with applications to the extra-galactic objects;- Hamiltonian description of MHD and relativistic hydrodynamics with one- and two-dimensional discontinuities;- The 3D interaction of vortices with a free fluid surface will be described;- Development of numerical codes for vortex interactions;- New numerical methods will be developed as an important part of the project.In particular, unconditionally stable methods of numerical solution of nonlinear evolution equations will be considered. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Topic(s) 1A - Nuclear Physics, Astronomy, Astrophysics OPEN - OPEN Call Call for proposal Data not available Funding Scheme Data not available Coordinator Observatoire de la Cote d'Azur EU contribution No data Address Bd. De l'Observatoire 06304 Nice France See on map Total cost No data Participants (5) Sort alphabetically Sort by EU Contribution Expand all Collapse all Center for Nonlinear Studies of the Landau Institute for Theoretical Physics Russia EU contribution No data Address Kosygina 2 117940 Moscow See on map Total cost No data Institute of Radio Astronomy Ukraine EU contribution No data Address Krasnoznamennaya, 4 61002 Kharkov See on map Total cost No data RISOE NATIONAL LABORATORY Denmark EU contribution No data Address FREDERIKSBORGVEJ 399 4000 ROSKILDE See on map Total cost No data Ruhr Universität Bochum Germany EU contribution No data Address 44780 Bochum See on map Total cost No data Russian Academy of Sciences Russia EU contribution No data Address Kosygina st., 2 117334 Moscow See on map Total cost No data