[1] Understanding bed load transport fluctuations in rivers is crucial for development of a transport theory and for choosing a sampling interval for ''mean'' transport rates. Fieldscale studies lack sufficient resolution to statistically characterize these fluctuations, while laboratory experiments are limited in scale and hence cannot be directly compared to field cases. Here we use a natural-scale laboratory channel to examine bed load transport fluctuations in a heterogeneous gravel substrate under normal flow conditions. The novelty of our approach is the application of a geometrical/statistical formalism (called the multifractal formalism), which allows characterization of the ''roughness'' of the series (depicting the average strength of local abrupt fluctuations in the signal) and the ''intermittency'' (depicting the temporal heterogeneity of fluctuations of different strength). We document a rougher and more intermittent behavior in bed load sediment transport series at low-discharge conditions, transitioning to a smoother and less intermittent behavior at high-discharge conditions. We derive an expression for the dependence of the probability distribution of bed load sediment transport rates on sampling interval. Our findings are consistent with field observations demonstrating that mean bed load sediment transport rate decreases with sampling time at low-transport conditions and increases with sampling time at high-transport conditions. Simultaneous measurement of bed elevation suggests that the statistics of sediment transport fluctuations are related to the statistics of bed topography.

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Measurements of the instantaneous wake flow from a model wind turbine placed in a turbulent boundary layer were obtained by wall-parallel oriented particle image velocimetry (PIV) in the St. Anthony Falls Laboratory wind tunnel. PIV velocity vector fields were used to investigate mean (expansion angle, wavelength, and wake velocity) and higher order statistics (local slope, curvature, and correlation) describing meandering motions in the turbine wake. These statistics were used to compare the wakes produced by four different wind turbine operating configurations, which include a single turbine operating at two different tip-speed ratios and two turbines aligned with the mean flow. The origin of meandering motions was identified for all cases in the hub vortex signature, which evolved into a stretched or compressed low speed meander in the wall parallel plane, depending on the turbine operating conditions and on the interaction with the wake shear layer. Finally, both autocorrelation and scale-dependent statistics on the velocity minima fluctuations about the meander signature suggest that small scale vortices, found in the hub shear layer and in the wake shear layer, interact with the hub vortex and govern its spatial evolution into large scale wake meandering.

This paper considers the problem of spatiotemporal bed topography evolution and sediment transport estimation in rivers with migrating bed forms of different types and sizes, in statistical equilibrium conditions. Instead of resorting to bed form classification, we propose to evaluate the evolution of multiscale bed topography as the integral of unit contributions defined through a space‒time Fourier decomposition of bed elevations. Using joint 2‒D spectra in the frequency and wave number domain, a functional relationship between the length scales and the timescales in which migrating bed forms are decomposed is proposed and developed into a dimensionless expression for scale‒dependent convection velocities. This formulation highlights the violation of Taylor's hypothesis for migrating bed forms, confirming statistically that larger bed forms travel slower as compared to smaller bed forms. This phenomenological description leads to a spectral extension of the Simons et al. (1965) formula for sediment transport to incorporate a range of multiscale migrating features. Both the scaling of convection velocities and the spectral estimate of sediment transport rate were validated through extensive bed elevation data from laboratory experiments conducted at the St. Anthony Falls Laboratory, for a range of Froude numbers 0.2

[1] Migrating bed forms strongly influence hydraulics, transport, and habitat in river environments. Their dynamics are exceedingly complex, making it difficult to predict their geometry and their interaction with sediment transport. Acoustic instrumentation now permits high-resolution observations of bed elevation as well as flow velocity. We present a space-time characterization of bed elevation series in laboratory experiments of sand and gravel transport in a large 84 m long, 2.75 m wide flume. We use a simple filtering and thresholding methodology to estimate bed form heights and report that the shape of their probability density function (pdf) remains invariant to discharge for both gravel and sand and has a positive tail slightly thicker than Gaussian. Using a wavelet decomposition, we quantify the presence of a rich multiscale statistical structure and estimate the scaledependent celerity of migrating bed forms, showing the faster movement of smaller bed forms relative to the larger ones. The nonlinear dynamics of gravel and sand bed forms is also examined, and the predictability time, i.e., the interval over which one can typically forecast the system, is estimated. Our results demonstrate that flow rate as well as bed sediment composition exert a significant influence on the multiscale dynamics and degree of nonlinearity and complexity of bed form evolution.Citation: Singh, A., S. Lanzoni, P. R. Wilcock, and E. Foufoula-Georgiou (2011), Multiscale statistical characterization of migrating bed forms in gravel and sand bed rivers, Water Resour. Res., 47, W12526,

Understanding how landscapes respond to climate dynamics in terms of macroscale (average topographic features) and microscale (landform reorganization) is of interest both for deciphering past climates from today's landscapes and for predicting future landscapes in view of recent climatic trends. Although several studies have addressed macro-scale response, only a few have focused on quantifying smaller-scale basin reorganization. To that goal, a series of controlled laboratory experiments were conducted where a self-organized complete drainage network emerged under constant precipitation and uplift dynamics. Once steady state was achieved, the landscape was subjected to a fivefold increase in precipitation (transient state). Throughout the evolution, high-resolution spatiotemporal topographic data in the form of digital elevation models were collected. The steady state landscape was shown to possess three distinct geomorphic regimes (unchannelized hillslopes, debris-dominated channels, and fluvially dominated channels). During transient state, landscape reorganization was observed to be driven by hillslopes via accelerated erosion, ridge lowering, channel widening, and reduction of basin relief as opposed to channel base-level reduction. Quantitative metrics on which these conclusions were based included slope-area curve, correlation analysis of spatial and temporal elevation increments, and wavelet spectral analysis of the evolving landscapes. Our results highlight that landscape reorganization in response to increased precipitation seems to follow ''an arrow of scale'': major elevation change initiates at the hillslope scale driving erosional regime change at intermediate scales and further cascading to geomorphic changes at the channel scale as time evolves.

[1] A series of flume experiments were conducted to study the effect of bed form dynamics on the flow over a gravel bed comprising a wide distribution of grain sizes. Instantaneous high-frequency streamwise flow velocities were sampled using an acoustic Doppler velocimeter at a frequency of 200 Hz, while the simultaneous bed elevations were sampled using sonar transducers at a frequency of 0.2 Hz for a duration of 20 h. Spectral analysis of the measured velocity fluctuations reveals the existence of two distinct power law scaling regimes. At high frequencies, an inertial subrange of turbulence with ∼−5/3 Kolmogorov scaling is observed. At low frequencies, another scaling regime with spectral slope of about −1.1 is found. We interpret this range as the signature of the evolving multiscale bed topography on the near-bed velocity fluctuations. The two scaling ranges are separated by a spectral gap, i.e., a range of intermediate scales with no additional energy contribution. The high-frequency limit of the spectral gap corresponds to the integral scale of turbulence. The low-frequency end of the gap corresponds to the scale of the smallest bed forms identified by the velocity sensor, which depends on the position of the sensor. Our results also show that the temporal scales of the largest bed forms can be potentially identified from spectral analysis of low-resolution velocity measurements collected near the channel bed.

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