X-ray shocks and radio relics detected in the cluster outskirts are commonly interpreted as shocks induced by mergers of sub-clumps. We study the properties of merger shocks in merging galaxy clusters, using a set of cosmological simulations for the large-scale structure formation of the universe. As a representative case, we here focus on the simulated clusters that undergo almost head-on collisions with mass ratio $sim2$. Due to the turbulent nature of the intracluster medium, shock surfaces are not smooth, but composed of shocks with different Mach numbers. As the merger shocks expand outward from the core to the outskirts, the average Mach number, $left<M_sright>$, increases in time. We suggest that the shocks propagating along the merger axis could be manifested as X-ray shocks and/or radio relics. The kinetic energy through the shocks, $F_phi$, peaks at $sim1$ Gyr after their initial launching, or at $sim1-2$ Mpc from the core. Because of the Mach number dependent model adopted here for the cosmic ray (CR) acceleration efficiency, their CR-energy-weighted Mach number is higher with $left< M_s right>_{rm CR}sim3-4$, compared to the kinetic-energy-weighted Mach number, $left<M_sright>_{phi}sim2-3$. Most energetic shocks are to be found ahead of the lighter dark matter (DM) clump, while the heavier DM clump is located in the opposite side of clusters. Although our study is limited to the merger case considered, the results such as the means and variations of shock properties and their time evolution could be compared with the observed characteristics of merger shocks, constraining interpretations of relevant observations.
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