  (abridged) The polarized thermal radiation at far infrared and submillimeter
wavelengths from dust grains in interstellar clouds with irregular magnetic
fields is simulated. We show that the polarization properties of quiescent
clouds and of star-forming regions are consistent with Kolmogorov-like
turbulent magnetic fields that are comparable in magnitude to the uniform
component of the magnetic fields. If the beam size is much smaller than the
correlation length $L_{\rm corr}$ of the fields, the calculated percentage
polarization $p$ decreases to an asymptotic value when the number of
correlation lengths $N_{\rm corr}$ through the cloud exceeds a few tens. For
these values of $N_{\rm corr}$, the dispersion in the position angles
$\sigma_\alpha$ is still appreciable--decreasing to only about $20^{\circ}$.
However, when the finite size of a telescope beam is taken into account, the
asymptotic value of $p$ is reached for fewer correlation lengths (smaller
$N_{\rm corr}$) due to averaging over the beam; $\sigma_\alpha$ becames much
smaller and consistent with the observational data. The smoothing of the
polarization properties due to the combined effect of the thickness of the
cloud and the finite size of the beam can be described by a single variable
which we designate as the generalized number of correlation lengths. In
addition, we study various factors that may contribute to the decrease in the
linear polarization percentage with increasing intensity that is observed at
submillimeter and far infrared wavelengths in many, though not in all, dark
clouds (the "polarization hole" effect).
