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Fluid Dynamics and the Navier-Stokes Equations

Magnetohydrodynamics (MHD) and the Formation of Jet(s)

Black Hole Schematic Nobody has seen a black hole up till 2014. Nevertheless, schematic diagram such as the one shown in figure 23 invariably presents a system composed with a central object (the black hole), an accretion disk, and a pair of jets moving along twisted magnetic field lines. This picture of the black hole is based theoretically on the combination of three branches of physics - Fluid Dynamics, Electromagnetism, and Gravitation.

The effect of gravity from the black hole is characterized by the escape velocity vesc(r) = (2GM/r)1/2, where M is the mass of the black hole, and r = (R2 + Z2)1/2 provides a link between the spherical and cylindrical coordinates (see upper left corner insert in Figure 23).

With the assumptions of infinite conductivity (for the plasma in the system), isotropic pressure, local charge neutrality, non-relativistic inter-particle speeds), the suite of MHD equations are :

Figure 23 Black Hole Schematic [view large image]

These set of equations can be solved only through numerical computation. In general, the magnetic field has only the z component Bz initially. When the accretion disk is set into rotation, the field lines is wrapped around the rotation axis creating the helical field in the z direction. As ionized matter cannot cross field lines, it is obliged to follow the lines and thus form a collimated jet (Figure 23). The following is a scenario of the numerical computation according to a letter in Nature with the title "A magnetic switch that determines the speed of astrophysical jets".