This article describes a numerical investigation of the flow in a loop-scavenged two-stroke engine equipped with a head-bowl combustion chamber. The bowl is either placed in the center of the cylinder head or displaced away from the center. Attention is focused on the period of compression and early expansion. Results show that the effects of compression of the tumbling vortex by the piston become prominent after the midcompression stage, resulting in significant cascading of energy from mean flow to turbulence, followed by a fast decay of turbulence. The subsequent emergence of squish and reverse squish helps retard the decay. As a consequence, the cases with head bowls possess higher levels of mean flow and turbulence than those without bowls at top dead center and the later stage. It is also shown in the results that the offset of the head bowl has significant effects on the mean flow and turbulence characteristics, highly dependent on the offset direction.