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 $5cdot 10^6,$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.
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