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.
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Programme(s)
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Topic(s)
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Funding Scheme
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Coordinator
06304 Nice
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.