Modelling Astrophysical Hydrodynamics

Christoph Kühn

One of the most amazing applications of magneto fluid dynamics are astrophysical approximations. High temperatures are responsible for fusion and ionization processes in space. Furthermore, the motion of charged particles in space is part of its astrophysical description. The motion of charged particles near planets with a magnetic core or inside accretion discs in the environment of a black hole is the result from attaching forces of other particles and is influenced by electric and magnetic fields.

The velocity distribution is comparable with a fluid motion in a way similar to the relation between microscopic molecular flow and the corresponding macroscopic fluid flow. Therefore, characteristic non-dimensional numbers from fluid mechanics -like the Reynolds, Knudsen or Nusselt number- obtain an astrophysical meaning. Through this approach, the motion of charged particles is comparable with the hydrodynamics of electrically charged fluids. As a result, unsteady magnetic fields can be described by compressible magneto-hydrodynamic transport equations.

According to the parallels with fluid mechanics, the consideration of high shear rates (Reynolds number) and dilute particle flow (Knudsen number) leads to a compressible description of a turbulent flow inside an accretion disc. In addition, all turbulent effects influence and at the same time are influenced by the magnetic field near a black hole. Through this approximation, the astrophysical examination of energy fluxes (Nusselt number) can be described by turbulent, compressible and magneto-fluid dynamics.