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| Content Provider | Springer Nature Link |
|---|---|
| Author | Catania, Davide |
| Copyright Year | 2010 |
| Abstract | We consider two magnetohydrodynamic-α (MHDα) models with kinematic viscosity and magnetic diffusivity for an incompressible fluid in a three-dimensional periodic box (torus). More precisely, we consider the Navier–Stokes-α-MHD and the Modified Leray-α-MHD models. Similar models are useful to study the turbulent behavior of fluids in presence of a magnetic field because of the current impossibility to handle non-regularized systems neither analytically nor via numerical simulations. In both cases, the global existence of the solution and of a global attractor can be shown. We provide an upper bound for the Hausdorff and the fractal dimension of the attractor. This bound can be interpreted in terms of degrees of freedom of the long-time dynamics of the involved system and gives information about the numerical stability of the model. We get the same bound that holds for the Simplified Bardina-MHD model, considered in a previous paper (this result provides, in some sense, an intermediate bound between the number of degrees of freedom for the Simplified Bardina model and the Navier–Stokes-α equation in the nonmagnetic case). However, the Navier–Stokes-α-MHD system is preferable since, in the ideal case, it conserves more quadratic invariants derived from the standard MHD model. |
| Ending Page | 115 |
| Page Count | 21 |
| Starting Page | 95 |
| File Format | |
| ISSN | 14226928 |
| e-ISSN | 14226952 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Issue Number | 1 |
| Volume Number | 14 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2011-06-15 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Magnetohydrodynamics global attractor Fluid- and Aerodynamics PDEs in connection with fluid mechanics turbulence models Existence, uniqueness, and regularity theory modified Leray-α model Navier–Stokes-α model regularizing MHD Classical Continuum Physics incompressible fluid Mathematical Methods in Physics MHD-α model simplified Bardina model |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics |
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