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Cosmic rays are transported out of the galaxy by diffusion and advection dueto streaming along magnetic field lines and resonant scattering offself-excited MHD waves. Thus momentum is transferred to the plasma via thefrozen-in waves as a mediator assisting the thermal pressure in driving agalactic wind. The bulk of the Galactic CRs are accelerated by shock wavesgenerated in SNRs, a significant fraction of which occur in OB associations ona timescale of several $10^7$ years. We examine the effect of changing boundaryconditions at the base of the galactic wind due to sequential SN explosions onthe outflow. Thus pressure waves will steepen into shock waves leading to insitu post-acceleration of GCRs. We performed simulations of galactic winds influx tube geometry appropriate for disk galaxies, describing the CRdiffusive-advective transport in a hydrodynamical fashion along with the energyexchange with self-generated MHD waves. Our time-dependent CR hydrodynamicsimulations confirm the existence of time asymptotic outflow solutions (forconstant boundary conditions). It is also found that high-energy particlesescaping 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 inthe lower galactic halo up to energies of $10^{17} - 10^{18}$ eV by multipleshock waves propagating through the halo. The particles can gain energy withinless than $3\,$kpc from the galactic plane corresponding to flow times lessthan $5\cdot 10^6\,$years. The mechanism described here offers a naturalsolution to explain the power-law distribution of CRs between the "knee" andthe "ankle". The mechanism described here offers a natural and elegant solutionto explain the power-law distribution of CRs between the "knee" and the"ankle".

Time-dependent galactic winds I. Structure and evolution of galactic outflows accompanied by cosmic ray acceleration