  We discuss magnetic pressure and density fluctuations in strongly turbulent
isothermal MHD flows in "1+2/3" dimensions. We first consider "simple"
nonlinear MHD waves, which allow us show that the slow and fast modes have
different asymptotic dependences of the magnetic pressure B^2 vs. rho. For the
slow mode, B^2 ~= c_1-c_2 rho, while for the fast mode, B^2 ~= rho^2. We also
perform a perturbative analysis to investigate Alfven wave pressure, recovering
previous results that B^2 ~= rho^gamma_e, with gamma_e ~= 2, 3/2 and 1/2 at
respectively large, moderate and low M_a. This variety of scalings implies that
a single polytropic description of magnetic pressure is not possible in
general, since the relation between B^2 and rho depends on which mode dominates
the density fluctuation production, which in turn depends on the angle between
the magnetic field and the direction of wave propagation, and on the Alfvenic
Mach number M_a. Typically, at small M_a, the slow mode dominates, and B is
ANTIcorrelated with rho. At large M_a, both modes contribute to density
fluctuation production, and the magnetic pressure decorrelates from density,
exhibiting a large scatter, which however decreases towards higher densities.
In this case, the unsystematic behavior of the magnetic pressure causes the
density PDF to generally maintain the lognormal shape corresponding to
non-magnetic isothermal turbulence, except when the slow mode dominates, in
which case the PDF develops an excess at low densities. Our results are
consistent with the low values and apparent lack of correlation between the
magnetic field strength and density in surveys of the lower-density molecular
gas, and also with the recorrelation apparently seen at higher densities, if
M_a is relatively large there.
