  Using magnetohydrodynamic simulations of fluctuation dynamos in turbulent
flows with rms Mach numbers $\mathcal{M}_{\rm rms} = 0.2, 1.1$ and $3$, we show
that magnetic pressure forces play a crucial role in dynamo saturation in
supersonic flows. First, as expected when pressure forces oppose compression,
an increase in anticorrelation between density and magnetic field strengths
obtains even in subsonic flows with the anti-correlation arising from the
intense but rarer magnetic structures. In supersonic flows, due to stronger
compressive motions density and magnetic field strength continue to maintain a
positive correlation. However, the degree of positive correlation decreases as
the dynamo saturates. Secondly, we find that the unit vectors of $\nabla\rho$
and $\nabla B^{2}$ are preferentially antiparallel to each other in subsonic
flows. This is indicative of magnetic pressure opposing compression. This
antiparallel alignment persists in transonic and supersonic flows at dynamo
saturation. However, compressive motions also lead to the emergence of a
parallel alignment in these flows. Finally, we consider the work done against
the components of the Lorentz force and the different sources of magnetic
energy growth and dissipation. We show that while in subsonic flows,
suppression of field line stretching is dominant in saturating the dynamo, the
picture is different in supersonic flows. Both field line stretching and
compression initially amplifies the field. However, growing magnetic pressure
opposes further compression of magnetic flux which tends to reduce the
compressive motions. Simultaneously, field line stretching also reduces. But,
suppression of compressive amplification dominates the saturation of the
dynamo.
