Space time evolution of sand bed topography and associated flow turbulence: experiments with statistical analysis
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A series of flume experiments were conducted with varying the flow discharges at the Fluvial Mechanics Laboratory of Indian Statistical Institute (Kolkata) to understand the co-evolution patterns of generating bed forms and the corresponding flow turbulence. Instantaneous bed elevations and velocity components were recorded continuously for sufficient time using high resolution instruments, such as, Ultrasonic Ranging System and acoustic Doppler velocimeter, at some spatial location over the deformed bed for each flow discharge. Increase in mean bed elevations and bed-slopes was found to be increased in discharge. Heavy-tailed nature of the probability density functions of magnitude of bed elevation increments, magnitude of single continuous bed elevation increments and instantaneous Reynolds shear stresses along three planes were analyzed using Pareto and truncated Pareto distributions. The spectral analysis of bed elevations revealed that the slope of log–log linearity increased with increase in flow discharge. Wavelet cross-correlations depicted strong dependence of bed form evolution on the corresponding instantaneous Reynolds shear stress along xz-plane. A Gram–Charlier type of distribution was used to estimate the probability density function of fluctuating velocity components, instantaneous Reynolds shear stresses along three planes and the joint probability density functions of the fluctuating velocity components, which showed good fit with the experimental data.
KeywordsTurbulence Bed form evolution Pareto and truncated Pareto distributions Gram–Charlier distribution Acoustic Doppler velocimeter (ADV) 5-MHz Ultrasonic Ranging System (URS)
Authors would like to acknowledge the Editor-in-Chief and two anonymous reviewers for their fruitful comments and suggestions for improvement of the paper. Authors also acknowledge Professor Fotis Sotiropoulos for providing some of their important papers on this topic during revision.
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