Observations in rivers or flumes have shown that for low water discharge, sediment transport is a very intermittent process. To understand the physical origins of the solid-discharge fluctuations, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep two-dimensional channel with a mobile bed and steady bead supply at the inlet. Flows were filmed from the side by a high-speed camera. We also revisited Einstein's theory on sediment and derived the statistical properties of the key flow variables. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.