  We report analysis of sub-Alfv\'enic magnetohydrodynamic (MHD) perturbations
in the low-\b{eta} radial-field solar wind using the Parker Solar Probe
spacecraft data from 31 October to 12 November 2018. We calculate wave vectors
using the singular value decomposition method and separate the MHD
perturbations into three types of linear eigenmodes (Alfv\'en, fast, and slow
modes) to explore the properties of the sub-Alfv\'enic perturbations and the
role of compressible perturbations in solar wind heating. The MHD perturbations
there show a high degree of Alfv\'enicity in the radial-field solar wind, with
the energy fraction of Alfv\'en modes dominating (~45%-83%) over those of fast
modes (~16%-43%) and slow modes (~1%-19%). We present a detailed analysis of a
representative event on 10 November 2018. Observations show that fast modes
dominate magnetic compressibility, whereas slow modes dominate density
compressibility. The energy damping rate of compressible modes is comparable to
the heating rate, suggesting the collisionless damping of compressible modes
could be significant for solar wind heating. These results are valuable for
further studies of the imbalanced turbulence near the Sun and possible heating
effects of compressible modes at MHD scales in low-\b{eta} plasma.
