Different bed surface and flow resistance characteristics for gravel and sand bed

Abstract:

Bed forms affect both bed load transport and flow resistance strongly and change their shapes and sizes depending on underlying grain size distribution and shear stress. A series of flume experiments were conducted at the Saint Anthony Falls Laboratory to study the effect of bed form dynamics on flow turbulence and sediment transport with both gravel and sand as bed material and different flow conditions. From the experimental data, the spectrum of bed elevation time series, the PDFs of bed elevation increments and the flow resistance characteristics are all analyzed. The wavelet-based spectral analysis shows that the slopes of the elevation spectrums are -2 and -3 for gravel and sand bed surfaces, respectively. The slope -3 indicates that the surface is self-similar, in another words, the ratios of bed form heights and lengths for different bed forms are the same; however, the slope of -2 indicates that the surface is self-affine, and in such case (-2) the ratios of bed form heights and lengths for different bed forms are not correlated at all. We interpret that the relative size of grain and boundary layer affects the bed form characteristics significantly, e.g., grain size of sand is of the same scale as the thickness of boundary layer, but both are much smaller than the grain size of gravel. Our results suggest that the PDFs of bed elevation increments for both gravel and sand beds can be fitted well with two-sided asymmetric exponential function. Furthermore, we show that the flow resistance (Darcy-Weisbach coefficients f) are much higher for sand bed than gravel bed, and the former is contributed by form drags, which is much larger than grain drags. For gravel bed, f and the skewness of bed elevation increments increases with flow discharge whereas for the sand bed, both f and the skewness of bed elevation increments decreases which corresponds to the transition in hydraulic conditions for dune to dynamic flat surface in our experiments. The analysis highlights the need to incorporate several different topics such as boundary layer, bed form development, flow resistance and bed load transport together.