The spatial heterogeneity of fully turbulent, near-bed flows above gravel river beds is examined using a realistic replica of a natural gravel patch in a large flume. Three-dimensional velocity time series were obtained at four heights (0.008--0.1 m) above the local bed in each of 99 closely spaced verticals for three flows of increasing intensity. The spatial heterogeneity of time-averaged velocities and root-mean-square velocity fluctuations increases under stronger flows and closer to the bed. However, streamwise velocity becomes spatially homogeneous at a distance from the bed of between 2--4 times the median bed elevation. Heterogeneity in the direction of the velocity vector is independent of mean flow velocity, but in all cases it decreases approximately linearly with distance above the surface. Skewness of the instantaneous velocity distributions suggests that slowly moving fluid emanating from the near-bed region impinges upon higher levels with greater frequency and greater spatial coverage as the average flow velocity increases. Spatial heterogeneity in turbulent kinetic energy increases with flow velocity and maxima occurr at positions that intercept layers of intense vortex shedding in the lee of obstacle crests. The spatial organization of the flow properties is nonrandom and consistent across the three flows. Simple regression models are developed to provide a basis for investigating the heterogeneity of near-bed flow at the patch scale (~2 m2) in gravel bed rivers.