  Recent Imaging X-ray Polarimetry Explorer (IXPE) observations of blazars tend
to support the shock model for the X-ray emission, but report a low
polarization degree ($\Pi\sim 10\%$) in X-rays compared with the previous
theoretical expectations in the shock model. In order to reconcile the
theoretical expectations with observations, we revisit the polarization of the
shock emission by considering different kind of direction distribution for the
shock-generated magnetic fields (sgMFs). Here, $w'_{\rm
sg}\propto(\sin\theta')^{\zeta_{\rm sg}}$ with $\theta'=0$ along the shock
normal direction is used to describe the direction distribution of the sgMFs in
the shock co-moving frame. It is found that the polarization in the X-ray and
radio emission for a general jet in blazars can be described as $\Pi\sim
44.5[1-\exp(-\zeta_{\rm sg}/2.6)]\%$ and $\Pi\sim 20[1-\exp(-\zeta_{\rm
sg}/2.4)]\%$, respectively. Correspondingly, one can have $\zeta_{\rm sg}\sim
1-1.5$ according to the IXPE observations. Besides the sgMFs, the magnetic
fields generated by the Richmyer-Meshkov instability (rmMFs) is supposed to
present in the jets. The direction of the rmMFs is mainly distributed along the
shock normal in the simulations and thus $w'_{\rm rm}\propto(\cos
\theta')^{\zeta_{\rm rm}}$ is adopted to describe the direction distribution of
rmMFs. We find that the rmMFs is likely to significantly affect the
polarization properties at the low-frequency emission, especially when the
sgMFs decay rapidly. Based on the contemporaneous radio and X-ray observations,
we find the the emission of the electrons in the rmMFs make a significant
contribution in the low-frequency emission and the the ordered background
magnetic fields (obMFs) can be neglected.
