How river rocks round: resolving the shape-size paradox

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.Comment: 11 pages, 5 figure

River-bed armoring as a granular segregation phenomenon

Gravel-river beds typically have an "armored" layer of coarse grains on the surface, which acts to protect finer particles underneath from erosion. River bed-load transport is a kind of dense granular flow, and such flows are known to vertically segregate grains. The contribution of granular physics to river-bed armoring, however, has not been investigated. Here we examine these connections in a laboratory river with bimodal sediment size, by tracking the motion of particles from the surface to deep inside the bed, and find that armor develops by two distinct mechanisms. Bed-load transport in the near-surface layer drives rapid segregation, with a vertical advection rate proportional to the granular shear rate. Creeping grains beneath the bed-load layer give rise to slow but persistent segregation, which is diffusion dominated and insensitive to shear rate. We verify these findings with a continuum phenomenological model and discrete element method simulations. Our results suggest that river beds armor by granular segregation from below --- rather than fluid-driven sorting from above --- while also providing new insights on the mechanics of segregation that are relevant to a wide range of granular flows

The Pulse of Calm Fan Deltas

At the heart of interpreting the history of Earth surface evolution preserved in the rock record is distinguishing environmental (allogenic) forcing from internally generated (autogenic) “noise.” Allogenic deposits classically have been recognized by their cyclic nature, which apparently results from periodic changes in base level, sediment supply, or tectonics. Autogenic deposits, which are quite variable in their origin and scale, are caused by the nonlinearity of sediment transport and might be expected to have a random or scale-free (fractal) signature. Here we describe a robust mechanism that generates cyclic deposits by an autogenic process in experimental fan deltas. Sheet flow over the fan surface induces deposition and an increase in fluvial slope and curvature to a point where the surface geometry is susceptible to a channelization instability, similar to channel initiation on hillslopes. Channelized flow results in incision and degrading of the fan surface to a lower slope, releasing a pulse of sediment that pushes the shoreline forward. Sheet flow resumes once the surface is regraded, and the cycle repeats in a surprisingly periodic fashion to produce cyclic foreset accretions. We use simple scaling and a one-dimensional fan evolution model to (1) demonstrate how time-varying flow width can cause pulses in sediment discharge at the shoreline in agreement with experiments and (2) reinterpret cyclic deposits reported in the field. Alternating sheet and channelized flows are known to operate on noncohesive fans in nature. Our results suggest that rather than reflecting variation in environmental forcing, many observed cyclic sedimentation packages may be a signature of the autogenic “pulse” of fan deltas under calm environmental conditions

A Unified Model for Subaqueous Bed Form Dynamics

Bed form evolution remains dynamic even in the special case of steady, uniform flow. Data from the sandy, braided North Loup River, Nebraska, show that roughness features on the channel bottom display a statistical steady state and robust scaling that are maintained through the collective interactions of transient (short-lived) bed forms. Motivated by such field data, and laboratory observations of bed form growth, we develop a nonlinear stochastic surface evolution model for the topography of bed load dominated sandy rivers in which instantaneous sediment flux explicitly depends on local elevation and slope. This model quantitatively reproduces laboratory observations of initial growth and saturation of bed forms from a flat surface, and also generates long-term dynamical behavior characteristic of natural systems. We argue that the variability in geometry and kinematics of bed forms in steady flow, and the existence of roughness at all wavelengths up to the largest dunes, are a consequence of the nonlinear relationship between sediment flux and topography, subject to noise

Shredding of Environmental Signals by Sediment Transport

Landscapes respond to climate, tectonic motions and sea level, but this response is mediated by sediment transport. Understanding transmission of environmental signals is crucial for predicting landscape response to climate change, and interpreting paleo-climate and tectonics from stratigraphy. Here we propose that sediment transport can act as a nonlinear filter that completely destroys (“shreds”) environmental signals. This results from ubiquitous thresholds in sediment transport systems; e.g., landsliding, bed load transport, and river avulsion. This “morphodynamic turbulence” is analogous to turbulence in fluid flows, where energy injected at one frequency is smeared across a range of scales. We show with a numerical model that external signals are shredded when their time and amplitude scales fall within the ranges of morphodynamic turbulence. As signal frequency increases, signal preservation becomes the exception rather than the rule, suggesting a critical re-examination of purported sedimentary signals of external forcing

A Potential Vorticity Theory for the Formation of Elongate Channels in River Deltas and Lakes

Rivers empty into oceans and lakes as turbulent sediment-laden jets, which can be characterized by a Gaussian horizontal velocity profile that spreads and decays downstream because of shearing and lateral mixing at the jet margins. Recent experiments demonstrate that this velocity field controls river-mouth sedimentation patterns. In nature, diffuse jets are associated with mouth bar deposition forming bifurcating distributary networks, while focused jets are associated with levee deposition and the growth of elongate channels that do not bifurcate. River outflows from elongate channels are similar in structure to cold filaments observed in ocean currents, where high potential vorticity helps to preserve coherent structure over large distances. Motivated by these observations, we propose a hydrodynamic theory that seeks to predict the conditions under which elongate channels form. Our approach models jet velocity patterns using the flow vorticity. Both shearing and lateral spreading are directly related to the vertical component of vorticity. We introduce a new kind of potential vorticity that incorporates sediment concentration and thus allows study of jet sedimentation patterns. The potential vorticity equation reduces the number of fluid momentum equations to one without losing generality. This results in a compact analytical solution capable of describing the streamwise evolution of the potential vorticity of a sediment-laden jet from initial conditions at the river mouth. Our theory predicts that high potential vorticity is a necessary condition for focused levee deposition and the creation of elongate channels. Comparison to numerical, laboratory, and field studies indicates that potential vorticity is a primary control on channel morphology. Our results may be useful for designing river delta restoration schemes such as the proposed Mississippi Delta diversion

Interactions Between Bed Forms: Topography, Turbulence, and Transport

Results are presented examining the interaction between two sandy bed forms under low–sediment transport conditions in a small laboratory flume. The initial artificially made bed forms were out of equilibrium with the flow field. Temporal evolution of bed forms was monitored using time-lapse photography in order to characterize bed form adjustment to the imposed flow. Velocity measurements were collected using an acoustic Doppler velocimeter to characterize both mean flow and turbulence associated with different bed form geometries. Sandy bed forms all had identical initial geometries; however, the initial distance between bed form crests was varied between experiments. Overall deformation of the bed varied as a function of initial bed form spacing; however, bed forms evolved unpredictably as periods of relatively slow change were punctuated by periods of rapidly changing geometry. Subtle changes in bed form trough geometry were found to have a strong influence on turbulence and therefore sediment transport. Comparison with field studies suggests that the mechanisms described herein are active in natural systems

Real and Apparent Changes in Sediment Deposition Rates Through Time

Field measurements show that estimated sediment deposition rate decreases as a power law function of the measurement interval. This apparent decrease in sediment deposition has been attributed to completeness of the sedimentary record; the effect arises because of incorporation of longer hiatuses in deposition as averaging time is increased. We demonstrate that a heavy-tailed distribution of periods of nondeposition (hiatuses) produces this phenomenon and that observed accumulation rate decreases as tγ−1, over multiple orders of magnitude, where 0 \u3c γ ≤ 1 is the parameter describing the tail of the distribution of quiescent period length. By using continuous time random walks and limit theory, we can estimate the actual average deposition rate from observations of the surface location over time. If geologic and geometric constraints place an upper limit on the length of hiatuses, then average accumulation rates approach a constant value at very long times. Our model suggests an alternative explanation for the apparent increase in global sediment accumulation rates over the last 5 million years

Transience and Persistence in the Depositional Record of Continental Margins

Continental shelves and coastal plains are large persistent depositional landforms, which are stationary (nonmigrating) at their proximal ends and characterized by relatively steady long-term growth. In detail, however, their surface form and stratigraphic record is built of transient freely migrating landscape elements. We derive the timescales of crossover from transient to persistent topographic forms using empirical scaling relations for mean sediment accumulation as a function of averaging time, based upon tens of thousands of empirical measurements. A stochastic (noisy) diffusion model with drift predicts all the gross features of the empirical data. It satisfies first-order goals of describing both the surface morphology and stratigraphic completeness of depositional systems. The model crossover from noise-dominated to drift-dominated behavior corresponds to the empirical crossover from transport-dominated (autogenic) transient behavior to accommodation-dominated (subsidence) persistent behavior, which begins at timescales of 102–103 years and is complete by scales of 104–105 years. Because the same long-term scaling behavior emerges for off-shelf environments, it is not entirely explicable by steady subsidence. Fluctuations in sediment supply and routing probably have significant influence. At short-term (transient) scales, the exponents of the scaling relations vary with environment, particularly the prevalence of channeled sediment transport. At very small scales, modeling sediment transport as a diffusive process is inappropriate. Our results indicate that some of the timescales of interest for climate interpretation may fall within the transitional interval where neither accommodation nor transport processes are negligible and deconvolution is most challenging