E vs. t Line Plots

The equations used to define these quantities are the following:

Kinetic Energy

T = \frac{1}{2}\rho \left(v_{x}^2 + v_{y}^2 + v_{z}^2\right)

As a mathematical expression in VisIt: .5*rho*(vx^2 + vy^2 + vz^2)

• \rho is the density
• v_{i} are the cartesian components of the 3-dimensional velocity vector

Gravitational Energy

E_{grav} = \frac{1}{2}\phi_{\text{gas}}\rho

As a mathematical expression in VisIt: .5*<Gas Phi>*rho

• \rho is the density
• \phi_{\text{gas}} is the potential due to the gas

Magnetic Energy

E_{mag} = \frac{1}{2}\left(B_{x}^2 + B_{y}^2 + B_{z}^2\right)

As a mathematical expression in VisIt: .5*(Bx^2 + By^2 + Bz^2)

• All B_{i} are the cartesian components of the 3-dimensional magnetic field vector

Beta 10, Shear 0

Beta 10, Shear 15

Beta 10, Shear 30

Beta 10, Shear 60