SMuK 2021 – scientific programme

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EP: Fachverband Extraterrestrische Physik

EP 9: Astrophysics I

EP 9.4: Talk

Friday, September 3, 2021, 12:00–12:15, H5

Modern methods to solve nonlinear fluid equations -- chances, issues and consequences for astrophysical fluid flows — •Dieter Nickeler — Astronomical Institute, Czech Academy of Sciences, Ondrejov, Czech Republic

During the last decades several methods to solve nonlinear equations of hydrodynamics and magneto-hydrodynamics exactly have been developed. The idea is to construct a broad range of solution classes, to get insight into physical and topological properties of the usual physical fluid theories. We discuss the mapping theories such as non-canonical and algebraic transformations, based on the existence of at least one first integral of the corresponding vector field. These mappings enable us to construct fields of higher complexity out of much more simple solutions, e.g. nonlinear fields out of potential fields. In 2D the calculation of potential magnetic fields/flows is facilitated by solving the 2D Laplace equation via conformal mapping theory. In 3D, the Whittaker method is a generalization of conformal mappings, by applying complex analysis to solve the Laplace equation in 3D. Taking advantage of these general solutions, by determining a first integral of the corresponding vector field, the above mentioned transformations are used to construct nonlinear solutions. Due to the nonlinear transformations and the special choice of linear equilibria they are based on, specific topological characteristics, e.g. separatrices (astropauses) and physical effects, e.g. current sheets or vortex sheets, possibly triggering dissipation or magnetic reconnection, are calculated.