  The scaling laws for the magnetic compression of a toroidally rotating field
reversed configuration (FRC) have been investigated in this work. The
magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating
FRCs employing the NIMROD code [C. R. Sovinec \textit{et al.}, J. Comput. Phys.
\textbf{195}, 355 (2004)], are compared with the Spencer's one-dimensional (1D)
theory [R. L. Spencer \textit{et al.}, Phys. Fluids \textbf{26}, 1564 (1983)]
for a wide range of initial flow speeds and profiles. The toroidal flow can
influence the scalings directly through the alteration of the compressional
work as also evidenced in the 1D adiabatic model, and indirectly by reshaping
the initial equilibrium. However, in comparison to the static initial FRC
equilibrium cases, the pressure and the radius scalings remain invariant for
the magnetic compression ratio $B_{w2}/B_{w1}$ up to 6 in presence of the
initial equilibrium flow, suggesting a broader applicable regime of the Spencer
scaling law for FRC magnetic compression. The invariant scaling has been proven
a natural consequence of the conservation of angular momentum of both fluid and
magnetic field during the dynamic compression process.
