Coupled dynamics of the co-evolution of gravel bed topography, flow turbulence and sediment transport in an experimental channel
A series of flume experiments were conducted in a large experimental channel at the St. Anthony Falls Laboratory to understand the coupled dynamics of flow and bed forms above the sediment-water interface. Simultaneous high resolution measurements of velocity fluctuations, bed elevations and sediment flux at the downstream end of the channel, were made for a range of discharges. The probability density functions (pdfs) of bed elevation increments and instantaneous Reynolds stress reveal a power law tail behavior and a wavelet cross-correlation analysis depicts a strong dependence of these series across a range of scales, indicating a feedback between bed form dynamics and near-bed turbulence. These results complement our previous findings in which the signature of bed form evolution on the near-bed velocity fluctuations was confirmed via the presence of a spectral gap and two distinct power law scaling regimes in the spectral density of velocity fluctuations. We report herein a strong asymmetry in the probability distribution of bed elevation increments and instantaneous Reynolds stresses, the latter being further analyzed and interpreted via a quadrant analysis of velocity fluctuations in the longitudinal and vertical directions. We also report the presence of intermittency (multifractality) in bed elevation increments and interpret it, in view of the asymmetric nature of the pdfs, as the result of scale coupling. In other words, the geometric asymmetry at the bed form scale gets transferred down to a probabilistic asymmetry at all smaller scales indicating a local anisotropy in the energy transfer. Finally, we propose a predictive relationship between bed form averaged sediment transport rates and bed form averaged instantaneous Reynolds stress and validate it using our experimental data.