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Turbulence measurements from the flow over two-dimensional fixed dune shapes are presented along with analysis and discussion of the ramifications of the observations for transport of sediment as bed load over bed forms. The spatial structure of the local transport rate determines the shape and stability of bed forms such as ripples and dunes, and the transport of sediment is a highly nonlinear process that is profoundly affected by the statistics of the temporal fluctuations in the near-bed flow field. The measurements presented herein show strong spatial evolution of the joint probability distribution of the streamwise and bednormal fluctuating velocity components. Unlike measurements in uniform boundary layers, these distributions and the higher moments of the velocity do not scale with the local shear velocity, indicating that it is probably inappropriate to use the shear stress to characterize the sediment flux. This conclusion is supported by observations of sediment flux over a dune.