  Cosmic rays are transported out of the galaxy by diffusion and advection due
to streaming along magnetic field lines and resonant scattering off
self-excited MHD waves. Thus momentum is transferred to the plasma via the
frozen-in waves as a mediator assisting the thermal pressure in driving a
galactic wind. The bulk of the Galactic CRs are accelerated by shock waves
generated in SNRs, a significant fraction of which occur in OB associations on
a timescale of several $10^7$ years. We examine the effect of changing boundary
conditions at the base of the galactic wind due to sequential SN explosions on
the outflow. Thus pressure waves will steepen into shock waves leading to in
situ post-acceleration of GCRs. We performed simulations of galactic winds in
flux tube geometry appropriate for disk galaxies, describing the CR
diffusive-advective transport in a hydrodynamical fashion along with the energy
exchange with self-generated MHD waves. Our time-dependent CR hydrodynamic
simulations confirm the existence of time asymptotic outflow solutions (for
constant boundary conditions). It is also found that high-energy particles
escaping from the Galaxy and having a power-law distribution in energy
($\propto E^{-2.7}$) similar to the Milky Way with an upper energy cut-off at
$\sim 10^{15}$ eV are subjected to efficient and rapid post-SNR acceleration in
the lower galactic halo up to energies of $10^{17} - 10^{18}$ eV by multiple
shock waves propagating through the halo. The particles can gain energy within
less than $3\,$kpc from the galactic plane corresponding to flow times less
than $5\cdot 10^6\,$years. The mechanism described here offers a natural
solution to explain the power-law distribution of CRs between the "knee" and
the "ankle". The mechanism described here offers a natural and elegant solution
to explain the power-law distribution of CRs between the "knee" and the
"ankle".
