Wall effects in non-Boussinesq density currents

We report on the results of a numerical study of nearly immiscible contrasted density currents aimed at shedding light on the influence of wall effects on current dynamics in the lock-exchange configuration. The numerical approach is an interface-capturing method which does not involve any explicit reconstruction of the interface. Navier-Stokes equations are solved on a fixed grid and a hyperbolic equation is used for the transport of the local volume fraction of one of the fluids. This allows us to describe the density currents for the complete range of density contrast 10⁻³ ≤ρL/ρH≤ 0.99 (ρL and ρH being the density of the light and heavy fluids) and a wide range of Reynolds number 70 ≤Re≤ 5×10⁴ (based on the channel height and the viscosity of the heavy fluid). The use of free-slip vs. no-slip boundary conditions enables us to separate the dissipation at the interface from the dissipation at the boundaries. Present results reveal that wall effects play a significant role on the propagation of contrasted density currents, unlike dissipation at the interface. It is first shown that when wall friction can be neglected, theoretical models based on the inviscid shallowwater approximations and Benjamin's steady-state result describe fairly well the light and heavy front velocities of density currents for the complete range of density ratio. However, when wall friction cannot be neglected, the results depart significantly from the prediction of inviscid theories. It is observed that most of the dissipation in highly contrasted currents takes place at the bottom wall and is a maximum at the head of the heavy current. This dissipation is shown to be responsible for the decrease of the front velocity. We propose a simple model based on Benjamin's analysis that includes wall friction. Keeping in mind the simplicity and limitations of the present model, the prediction of the front velocity of the heavy and light currents is observed to be in good agreement with the numerical results for the complete range of density contrast. This gives further support to the idea that wall effects are the crucial ingredient for accurately predicting the front velocity of highly contrasted density currents

Flood magnitude-frequency and lithologic control on bedrock river incision in post-orogenic terrain

Mixed bedrock-alluvial rivers - bedrock channels lined with a discontinuous alluvial cover - are key agents in the shaping of mountain belt topography by bedrock fluvial incision. Whereas much research focuses upon the erosional dynamics of such rivers in the context of rapidly uplifting orogenic landscapes, the present study investigates river incision processes in a post-orogenic (cratonic) landscape undergoing extremely low rates of incision (> 5 m/Ma). River incision processes are examined as a function of substrate lithology and the magnitude and frequency of formative flows along Sandy Creek gorge, a mixed bedrock-alluvial stream in arid SE-central Australia. Incision is focused along a bedrock channel with a partial alluvial cover arranged into riffle-pool macrobedforms that reflect interactions between rock structure and large-flood hydraulics. Variations in channel width and gradient determine longitudinal trends in mean shear stress (τb) and therefore also patterns of sediment transport and deposition. A steep and narrow, non-propagating knickzone (with 5% alluvial cover) coincides with a resistant quartzite unit that subdivides the gorge into three reaches according to different rock erodibility and channel morphology. The three reaches also separate distinct erosional styles: bedrock plucking (i.e. detachment-limited erosion) prevails along the knickzone, whereas along the upper and lower gorge rock incision is dependent upon large formative floods exceeding critical erosion thresholds (τc) for coarse boulder deposits that line 70% of the channel thalweg (i.e. transport-limited erosion). The mobility of coarse bed materials (up to 2 m diameter) during late Holocene palaeofloods of known magnitude and age is evaluated using step-backwater flow modelling in conjunction with two selective entrainment equations. A new approach for quantifying the formative flood magnitude in mixed bedrock-alluvial rivers is described here based on the mobility of a key coarse fraction of the bed materials; in this case the d84 size fraction. A 350 m3/s formative flood fully mobilises the coarse alluvial cover with τb200-300 N/m2 across the upper and lower gorge riffles, peaking over 500 N/m2 in the knickzone. Such floods have an annual exceedance probability much less than 10- 2 and possibly as low as 10- 3. The role of coarse alluvial cover in the gorge is discussed at two scales: (1) modulation of bedrock exposure at the reach-scale, coupled with adjustment to channel width and gradient, accommodates uniform incision across rocks of different erodibility in steady-state fashion; and (2) at the sub-reach scale where coarse boulder deposits (corresponding to <i>τ</i><sub>b</sub> minima) cap topographic convexities in the rock floor, thereby restricting bedrock incision to rare large floods. While recent studies postulate that decreasing uplift rates during post-orogenic topographic decay might drive a shift to transport-limited conditions in river networks, observations here and elsewhere in post-orogenic settings suggest, to the contrary, that extremely low erosion rates are maintained with substantial bedrock channel exposure. Although bed material mobility is known to be rate-limiting for bedrock river incision under low sediment flux conditions, exactly how a partial alluvial cover might be spatially distributed to either optimise or impede the rate of bedrock incision is open to speculation. Observations here suggest that the small volume of very stable bed materials lining Sandy Creek gorge is distributed so as to minimise the rate of bedrock fluvial incision over time

Limits to scale invariance in alluvial rivers

Assumptions about fluvial processes and process–form relations are made in general models and in many site‐specific applications. Many standard assumptions about reach‐scale flow resistance, bed‐material entrainment thresholds and transport rates, and downstream hydraulic geometry involve one or other of two types of scale invariance: a parameter (e.g. critical Shields number) has the same value in all rivers, or doubling one variable causes a fixed proportional change in another variable in all circumstances (e.g. power‐law hydraulic geometry). However, rivers vary greatly in size, gradient, and bed material, and many geomorphologists regard particular types of river as distinctive. This review examines the tension between universal scaling assumptions and perceived distinctions between different types of river. It identifies limits to scale invariance and departures from simple scaling, and illustrates them using large data sets spanning a wide range of conditions. Scaling considerations and data analysis support the commonly made distinction between coarse‐bed and fine‐bed reaches, whose different transport regimes can be traced to the different settling‐velocity scalings for coarse and fine grains. They also help identify two end‐member sub‐types: steep shallow coarse‐bed ‘torrents’ with distinctive flow‐resistance scaling and increased entrainment threshold, and very large, low‐gradient ‘mega rivers’ with predominantly suspended load, subdued secondary circulation, and extensive backwater conditions

Pebble abrasion during fluvial transport: Experimental results and implications for the evolution of the sediment load along rivers

International audienceIn actively eroding landscapes, fluvial abrasion modifies the characteristics of the sediment carried by rivers and consequently has a direct impact on the ability of mountain rivers to erode their bedrock and on the characteristics and volume of the sediment exported from upland catchments. In this experimental study, we use a novel flume replicating hydrodynamic conditions prevailing in mountain rivers to investigate the role played by different controlling variables on pebble abrasion during fluvial transport. Lithology controls abrasion rates and processes, with differences in abrasion rates exceeding two orders of magnitude. Attrition as well as breaking and splitting are efficient processes in reducing particle size. Mass loss by attrition increases with particle velocity but is weakly dependent on particle size. Fragment production is enhanced by the use of large particles, high impact velocities and the presence of joints. Based on our experimental results, we extrapolate a preliminary generic relationship between pebble attrition rate and transport stage (τ*/τ*c), where τ* = fluvial Shields stress and τ*c = critical Shields stress for incipient pebble motion. This relationship predicts that attrition rates are independent of transport stage for (τ*/τ*c) ≤ 3 and increase linearly with transport stage beyond this value. We evaluate the extent to which abrasion rates control downstream fining in several different natural settings. A simplified model predicts that the most resistant lithologies control bed load flux and fining ratio and that the concavity of transport-limited river profiles should rarely exceed 0.25 in the absence of deposition and sorting

Field calibration of sediment flux dependent river incision

Bed erosion and sediment transport are ubiquitous and linked processes in rivers. Erosion can either be modeled as a “detachment limited” function of the shear stress exerted by the flow on the bed, or as a “transport limited” function of the sediment flux capacity of the flow. These two models predict similar channel profiles when erosion rates are constant in space in time, but starkly contrasting behavior in transient settings. Traditionally detachment limited models have been used for bedrock rivers, whereas transport limited models have been used in alluvial settings. In this study we demonstrate that rivers incising into a substrate of loose, but very poorly sorted relict glacial sediment behave in a detachment limited manner. We then develop a methodology by which to both test the appropriate incision model and constrain its form. Specifically we are able to tightly constrain how incision rates vary as a function of the ratio between sediment flux and sediment transport capacity in three rivers responding to deglaciation in the Ladakh Himalaya, northwest India. This represents the first field test of the so-called “tools and cover” effect along individual rivers