  We study the tunneling of Bogoliubov excitations through a barrier in a
Bose-Einstein condensate. We extend our previous work [Phys. Rev. A
\textbf{78}, 013628 (2008)] to the case when condensate densities are different
between the left and right of the barrier potential. In the framework of the
Bogoliubov mean-field theory, we calculate the transmission probability and
phase shift, as well as the energy flux and quasiparticle current carried by
Bogoliubov excitations. We find that Bogoliubov phonons twist the condensate
phase due to a back-reaction effect, which induces the Josephson supercurrent.
While the total current given by the sum of quasiparticle current and induced
supercurrent is conserved, the quasiparticle current flowing through the
barrier potential is shown to be remarkably enhanced in the low energy region.
When the condensate densities are different between the left and right of the
barrier, the excess quasiparticle current, as well as the induced supercurrent,
remains finite far away from the barrier. We also consider the tunneling of
excitations and atoms through the boundary between the normal and superfluid
regions. We show that supercurrent can be generated inside the condensate by
injecting free atoms from outside. On the other hand, atoms are emitted when
the
  Bogoliubov phonons propagate toward the phase boundary from the superfluid
region.
