  Throughout the passage within the Galactic halo, high-velocity clouds (HVCs)
sweep up ambient magnetic fields and form stretched and draped configurations
of magnetic fields around them. Many earlier numerical studies adopt
spherically symmetric uniform-density clouds as initial conditions for
simplicity. However, observations demonstrate that HVCs are clumpy and
turbulent. In this paper, we perform 3D magnetohydrodynamic simulations to
study the evolution of clouds with initial density distributions described by
power-law spatial power spectra. We systematically study the role of (i) the
initial density structure, (ii) halo magnetic fields, and (iii) radiative
cooling efficiency upon infalling HVCs. We find that (i) the clouds' density
structure regulates mixing and mass growth. Uniform clouds grow from the onset
of the simulations while clumpy clouds initially lose gas and then grow at
later times. Along the same lines, the growth curve of clumpy clouds depends on
the slope of the initial density power spectra. (ii) Magnetic fields suppress
hydrodynamic instabilities and the growth of small-scale structures. As a
result, magnetized clouds develop long filaments extended along the streaming
direction whereas non-magnetized clouds are fragmented into many small clumps.
(iii) Efficient cooling keeps the main cloud body more compact and produces
decelerated dense clumps condensed from the halo gas. This work potentially
helps us understand and predict the observed properties of HVCs such as the
detectability of magnetized clouds, the presence of decelerated HI structures
associated with HVC complexes and small-scale features, and a possible link
between the origin and the fate of HVCs.
