  We utilize cosmological simulations of 16 galaxy clusters at redshifts
\zeq{0} and \zeq{0.6} to study the effect of inflowing streams on the
properties of the X-ray emitting intracluster medium. We find that the mass
accretion occurs predominantly along streams that originate from the cosmic web
and consist of heated gas. Clusters that are unrelaxed in terms of their X-ray
morphology are characterized by higher mass inflow rates and deeper penetration
of the streams, typically into the inner third of the virial radius. The
penetrating streams generate elevated random motions, bulk flows and cold
fronts. The degree of penetration of the streams may change over time such that
clusters can switch from being unrelaxed to relaxed over a time-scale of
several giga years.
