Organic litter: dominance over stones as a source of interrill flow roughness on low‐gradient desert slopes at Fowlers Gap,arid western NSW,Australia

Thirty‐six runoff plot experiments provide data on flow depths, speeds, and Darcy–Weisbach friction coefficients (f) on bare soil surfaces, and surfaces to which were added sufficient extra plant litter or surface stones to provide projected cover of 5, 10 and 20 per cent. Precision flow depth data were derived with a computer‐controlled gantry and needle gauge for two different discharges for each plot treatment. Taking a fixed flow intensity (Reynolds number, Re = 150) for purposes of comparison shows means of f = 17·7 for bare soil surfaces, f = 11·4 for added stone treatments, and f = 23·8 for added litter treatments. Many individual values of f for stone treatments are lower than for the bare soil surface, but all litter treatments show increases in fcompared to bare soil. The lowering of f in stone treatments relates to the submerged volume that the stones occupied, and the associated concentration of flow onto a smaller part of the plot surface. This leads to locally higher flow intensities and lower frictional drag along threads of flow that the obstacles create. Litter causes higher frictional drag because the particles are smaller, and, for the same cover fraction, are 100 times more numerous and provide 20 times the edge or perimeter length. Along these edges, which in total exceed 2·5 m g^?1 (equivalent to 500 m m^?2 for a loading of 2 t ha^?1), surface tension draws up water from between the litter particles. This reduces flow depth there, and as a consequence of the lower flow intensity, frictional drag rises. Furthermore, no clear passage remains for the establishment of flow threads. These findings apply to shallow interrill flows in which litter is largely immobile. The key new result from these experiments is that under these conditions, a 20 per cent cover of organic litter can generate interrill frictional retardation that exceeds by nearly 41 per cent that of a bare soil surface, and twice that contributed by the same cover fraction of surface stones. Even greater dominance by litter can be anticipated at the many dryland sites where litter covers exceed those tested here. Copyright © 2002 John Wiley & Sons, Ltd.     

Volumetric displacement of flow depth by obstacles,and the determination of friction factors in shallow overland flows

Large roughness elements such as stones or plant stems (obstacles) influence the depth of overland flows in two ways. The first effect is a dynamic one, involving frictional retardation of the flow and associated reduction in flow speeds. The second influence is static, and arises from the upward volumetric displacement of flow depth because of the submerged volume of the obstacles. Depending upon the distribution of submerged obstacle volume with height above the soil surface, the proportion of the flow volume occupied (and so, the perturbation of flow depth arising from volumetric displacement) can vary irregularly or systematically with flow stage. Furthermore, the amount of volumetric displacement of flow depth would vary among surfaces carrying different cover fractions of identical obstacles. Consequently, estimates of the change in friction factors arising from the drag on flow traversing varying obstacle cover fractions are confounded with the parallel shift volumetric displacement. To understand the true frictional drag arising from obstacles, a correction must be made for the volumetric displacement. A method for making this correction is outlined. New laboratory experiments provide precise observations of depths and friction coefficients in laminar flows passing fields of regular obstacles. After making the proposed correction for volumetric displacement, increases of 40 to 75 per cent in the derived value of the Darcy–Weisbach friction factor, f, are found for an obstacle cover of 20 per cent. Many published studies of friction coefficients in shallow overland flows, such as those on stone‐covered dryland soils, involve larger obstacle cover fractions, and evidently involve the significant confounding effect of volumetric displacement. Copyright © 2002 John Wiley & Sons, Ltd.     

Determining friction coefficients for interrill flows: the significance of flow filaments and backwater effects

Friction coefficients in overland flows are customarily estimated from mean flow properties (depth, velocity, slope) that subsume spatial variations in flow arising from two major causes: microtopography and obstacles. This paper uses laboratory experiments in shallow flumes to examine the extent of non‐uniformity in flow conditions associated with each cause. Randomly placed emergent obstacles in a flume with a shallow axial channel generally yielded higher hydraulic roughness than the same pattern of obstacles on a planar flume, as well as greater variation in roughness as the obstacle locations were altered. In both flumes, hydraulic roughness fell with increasing Reynolds number for 10% obstacle cover, showed a flattening trend at 20% cover, and exhibited a convex‐downward trend at 30% obstacle cover. These results indicate the progressive onset of flow controls at narrow gaps in the obstacle field. In such flows, the use of mean flow properties conceals the existence of two main subdivisions of flow: flow filaments and backwater flows. In the experiments, flow filaments involved velocities more than twice the overall mean, whereas backwater flows were much slower than the mean. The existence of fast‐moving flow filaments may be significant in understanding soil transport in surface runoff, and backwater depths may modify splash detachment. Similarly, friction coefficients that fail to reflect these important non‐uniform flow components may not be optimal for hydraulic calculations or in erosion models. It is concluded that new approaches to observing and processing flow data may be required, in order to avoid the loss of important flow detail that is entailed in assuming uniform flow conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

Macroscale surface roughness and frictional resistance in overland flow

The hydraulics of overland flow on rough granular surfaces can be modelled and evaluated using the inundation ratio rather than the flow Reynolds number, as the primary dimensionless group determining the flow behaviour. The inundation ratio describes the average degree of submergence of the surface roughness and is used to distinguish three flow regimes representing partially inundated, marginally inundated and well-inundated surfaces. A heuristic physical model for the flow hydraulics in each regime demonstrates that the three states of flow are characterized by very different functional dependencies of frictional resistance on the scaled depth of flow. At partial inundation, flow resistance is associated with the drag force derived from individual roughness and therefore increases with depth and percentage cover. At marginal inundation, the size of the roughness elements relative to the depth of flow controls the degree of vertical mixing in the flow so that frictional resistance tends to decrease very rapidly with increasing depth of flow. Well-inundated flows are described using rough turbulent flow hydraulics previously developed for open channel flows. These flows exhibit a much more gradual decrease in frictional resistance with increasing depth than that observed during marginal inundation. A data set compiled from previously published studies of overland flow hydraulics is used to assess the functional dependence of frictional resistance on inundation ratio over a wide range of flow conditions. The data confirm the non-monotonic dependence predicted by the model and support the differentiation of three flow regimes based on the inundation ratio. Although the percentage cover and the surface slope may be of importance in addition to the inundation ratio in the partially and marginally inundated regimes, the Reynolds number appears to be of significance only in describing well-inundated flows at low to moderate Reynolds numbers. As these latter conditions are quite rare in natural environments, the inundation ratio rather than the Reynolds number should be used as the primary dimensionless group when evaluating the hydraulics of overland flow on rough surfaces. © 1997 by John Wiley & Sons, Ltd.     

Resistance to flow in rough supercritical sheet flow

Shallow water depths on steep slopes of as much as fifty per cent can be measured easily by weighing a light flume and the water it contains. Because water accelerates along the flume, a good approximation of the steady state depth is obtained when the recording balance is fixed to its bottom end. From the unit discharge and the depth, and not from measurements of the surface velocity, the Darcy-Weisbach friction coefficient can be calculated. The present results show that this friction coefficient is larger in thin sheet flows than that calculated from the equation for rough turbulent flow. This latter could fit at a Reynolds Number of 50,000. When the regime is laminar (Re < 2,440) the Darcy-Weisbach friction coefficient always exceeds the theoretical value of 96/Re. The great relative depth of standing and travelling waves could account for this discrepancy together with turbulence and wake formation around bottom grains. Herein it is assumed that a regime can prevail where a laminar superlayer glides over a turbulent sublayer in the vicinity of bottom grains, because the ratio of the surface velocity to the mean velocity can greatly exceed 1.5, especially on steep slopes. Until photographs of the streamlines are taken, no statement about flow regimes in supercritical sheet flow can be made.     

Instantaneous dynamic pressure effects on the behaviour of lithic boulders in pyroclastic flows: the Abrigo Ignimbrite,Tenerife, Canary Islands

A method for estimating the instantaneous dynamic pressure near the base of ancient pyroclastic flows, using large lithic boulders from the late Pleistocene Abrigo Ignimbrite, is proposed here. The minimum instantaneous dynamic pressure is obtained by determining the minimum aerodynamic drag force exerted by a pyroclastic flow onto a stationary boulder that will allow the boulder to overcome static friction with the underlying substrate, and move within the flow. Consideration is given to the properties of the boulder (shape, roughness, size, density and orientation relative to the flow), substrate (type and hill slope angle), boulder-substrate interface (looseness of boulder, coefficient of static friction) and flow (coefficient of aerodynamic drag). Nineteen boulders from massive, lithic-rich ignimbrite deposits at two localities on Tenerife were assessed in this study. Minimum dynamic pressures required for Abrigo pyroclastic flows to move these boulders ranged from 5 to 38 kPa, which are comparable to dynamic pressures previously calculated from observations of the damage caused by recent pyroclastic flows. Considering the maximum possible range in flow density, the derived minimum velocity range for the Abrigo pyroclastic flows is 1.3 to 87 m s⁻¹.     

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

The Coefficient of Friction in Channel Flows

The dimensionless Darcy–Weisbach coefficient of friction is used to evaluate the drag in channel flows. A developed turbulent flow with a quadratic drag law is considered. The dependence of the coefficient of friction on the cross-section shape of the channel flow is examined. A coefficient of the channel shape is introduced, which depends on the wetted perimeter and the flow width and allows the complicated geometry of the river cross-section to be taken into account in calculating the drag. The drag estimates calculated using the suggested technique are compared with other authors' estimates for flumes and rivers.     

Estimation of friction parameters and laws in 1.5D shallow-water gravity currents on the f-plane, by data assimilation

A 1.5-dimensional, 1.5-layer shallow water model and an ensemble Kalman filter are used to evaluate the feasibility of estimating friction parameters and determining friction laws of oceanic gravity currents. The two friction laws implemented are a linear Rayleigh friction and a quadratic drag law. We demonstrate that the assimilation procedure rapidly estimates the total frictional force, whereas the distinction between the two laws is evolving on a slower time scale. We also demonstrate that parameter estimation can, in this way, choose between different parametrisations and help to discriminate between physical laws of nature by estimating the coefficients presented in such parametrisations.     

Numerical resolution of well-balanced shallow water equations with complex source terms

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.     

Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation

Vegetation is a key aspect of water resources and ecology in natural rivers, floodplains and irrigation channels. The hydraulic resistance of the water flow is greatly changed when submerged vegetation is present. Three kinds of drag coefficients, i.e., the drag coefficient for an isolated cylinder, the bulk drag coefficient of an array of cylinders and the vertically distributed or local drag coefficient, have been commonly used as parameters to represent the vegetation drag force. In this paper, a comprehensive experimental study of submerged stems in an open channel flow is presented. Empirical formulae for the three drag coefficients were obtained based on our experimental results and on data from previous studies. A two-layer model was developed to solve the mean momentum equation, which was used to evaluate the vertical mean velocity profile with each of the drag coefficients. By comparing the velocity distribution model predictions and the measurement results, we found that the model with the drag coefficient for an isolated cylinder and the local drag coefficient was good fit. In addition, the model with the bulk drag coefficient gave much larger velocity values than measurements, but it could be improved by adding the bed friction effect and making choice of the depth-averaged velocity within the canopy layer.     

Vertical structure of tidal current in a typically coastal raft-culture area

In this paper vertical structure of tidal current in a typically coastal raft-culture area is discussed by field measurement and a numerical model. The observations show that the vertical structure changed dramatically. A tidal surface boundary layer (SBL) is well formed due to the frictional effects induced by extensive, high-density suspended culture as surface obstruction. Both the aquaculture drag and the bottom friction are much higher than those in non-raft-culture areas, and show an obvious variation with tidal flow. The significant earlier ebbing and earlier flooding appear in the upper water column instead of the seabed. And the maximal phase lag is about 1 h within one tide cycle. A 1D hydrodynamic model was modified to include the SBL and parameterized with the field data. It replicated the observed velocity profile and was then used to investigate the impacts of varying culture density and bottom friction on the vertical tidal-current structure. Modeling results indicate that the surface current velocity was largely damped because culture activities enhanced the frictional effects on flow intensively. The magnitude and vertical structure of tidal current are determined together with aquaculture drag and bottom friction. In addition, the vertical velocity structure has a nonlinear trend along with culture density and bottom friction. This study is a theoretical foundation for optimizing aquaculture configuration through regulating culture density and species distribution.     

The wave-induced boundary layer under long internal waves

The boundary layer formed under the footprint of an internal solitary wave is studied by numerical simulation for waves of depression in a two-layer model of the density stratification. The inviscid outer flow, in the perspective of boundary-layer theory, is based on an exact solution for the long wave-phase speed, yielding a family of fully nonlinear solitary wave solutions of the extended Korteweg–de Vries equation. The wave-induced boundary layer corresponding to this outer flow is then studied by means of simulation employing the Reynolds-averaged Navier–Stokes (RANS) formulation coupled with a turbulence closure model validated for wall-bounded flows. Boundary-layer characteristics are computed for an extensive range of environmental conditions and wave amplitudes. Boundary-layer transition, identified by monitoring the eddy viscosity, is correlated in terms of a boundary-layer Reynolds number. The frictional drag is evaluated for laminar, transitional, and turbulent cases, and correlations are presented for the friction coefficient plus relevant measures of the boundary-layer thickness.     

Capabilities of Large-scale Particle Image Velocimetry to characterize shallow free-surface flows

Irrespective of their spatial extent, free-surface shallow flows are challenging measurement environments for most instruments due to the relatively small depths and velocities typically associated with these flows. A promising candidate for enabling measurements in such conditions is Large-scale Particle Image Velocimetry (LSPIV). This technique uses a non-intrusive approach to measure two-dimensional surface velocity fields with high spatial and temporal resolutions. Although there are many publications documenting the successful use of LSPIV in various laboratory and field open-channel flow situations, its performance has not been equally substantiated for measurement in shallow flows. This paper aims at filling in this gap by demonstrating the capabilities of LSPIV to: (a) accurately evaluate complex flow patterns in shallow channel flows; and (b) estimate depth in shallow flows using exclusively LSPIV measurements. The demonstration is provided by LSPIV measurements in three shallow flow laboratory situations with flow depths ranging from 0.05 to 0.31 m. The obtained measurements illustrate the LSPIV flexibility and reliability in measuring velocities in shallow and low-velocity (near-zero) flows. Moreover, the technique is capable to evaluate and map velocity-derived quantities that are difficult to document with alternative measurement techniques (e.g. vorticity and shear stress distributions and mapping of large-scale structure in the body of water).     

Effect of saltating sediment on flow resistance and bed roughness in overland flow

The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.     

The effects of ice cover on flow characteristics in a subarctic meandering river

The effects of ice cover on flow characteristics in meandering rivers are still not completely understood. Here, we quantify the effects of ice cover on flow velocity, the vertical and spatial flow distribution, and helical flow structure. Comparison with open‐channel low flow conditions is performed. An acoustic doppler current profiler (ADCP) is used to measure flow from up to three meander bends, depending on the year, in a small sandy meandering subarctic river (Pulmanki River) during two consecutive ice‐covered winters (2014 and 2015). Under ice, flow velocities and discharges were predominantly slower than during the preceding autumn open‐channel conditions. Velocity distribution was almost opposite to theoretical expectations. Under ice, velocities reduced when entering deeper water downstream of the apex in each meander bend. When entering the next bend, velocities increased again together with the shallower depths. The surface velocities were predominantly greater than bottom/riverbed velocities during open‐channel flow. The situation was the opposite in ice‐covered conditions, and the maximum velocities occurred in the middle layers of the water columns. High‐velocity core (HVC) locations varied under ice between consecutive cross‐sections. Whereas in ice‐free conditions the HVC was located next to the inner bank at the upstream cross‐sections, the HVC moved towards the outer bank around the apex and again followed the thalweg in the downstream cross‐sections. Two stacked counter‐rotating helical flow cells occurred under ice around the apex of symmetric and asymmetric bends: next to the outer bank, top‐ and bottom‐layer flows were towards the opposite direction to the middle layer flow. In the following winter, no clear counter‐rotating helical flow cells occurred due to the shallower depths and frictional disturbance by the ice cover. Most probably the flow depth was a limiting factor for the ice‐covered helical flow circulation, similarly, the shallow depths hinder secondary flow in open‐channel conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Fault rock analysis of the northern part of the Chelungpu Fault and its relation to earthquake faulting of the 1999 Chi-Chi earthquake, Taiwan

Abstract   The 1999 Chi-Chi earthquake in Taiwan ( M _w = 7.6) produced a surface rupture along the north–south-striking Chelungpu thrust fault with pure dip-slip (east side up) and left lateral strike-slip displacements. Near-field strong-motion data for the northern part of the fault illustrate a distinct lack of the high-frequency seismic radiation associated with a large slip (10–15 m) and a rapid slip velocity (2–4 m/s), suggesting a smooth seismic slip associated with low dynamic frictional resistance on the fault. A drillhole was constructed at shallow depths in the possible fault zones of the northern part of the Chelungpu Fault, which may have slipped during the 1999 earthquake. One of the zones consists of a 20-cm-thick, unconsolidated fault breccia with a chaotic texture lacking both discrete slip surfaces (e.g. Riedel shears) and grain crushing. Other possible fault zones are marked by the narrow (less than a few centimeters) gouge zone in which clayey material intrudes into the damaged zone outside of the gouge zone. These characteristic fault rock textures suggest that the slip mechanisms at shallow levels during the earthquake involved either granular flow of initially unconsolidated material or slip localization under elevated pore pressure along the narrow clayey gouge zone. Because both mechanisms lead to low dynamic frictional resistance on the fault, the rapid seismic slip in the deep portions of the fault (i.e. the source region of strong-motion radiation) could have been accommodated by frictionless slip on the shallow portions of the fault. The combination of strong-motion data and fault rock analysis suggests that smooth slip associated with low dynamic friction occurred on both the deep and shallow portions of the fault, resulting in a large slip between the source region and the surface in the northern region.     

Variations of tidally driven three-layer residual circulation in fjords

Residual, or tidally averaged, circulation in fjords is generally assumed to be density driven and two layered. This circulation consists of a thin surface layer of outflow and a thick bottom layer of sluggish inflow. However, development of different vertical structures in residual circulation in fjords can arise from wind, remote, and tidal forcing that may modify the two-layer circulation. Particularly, theoretical results of tidal residual flows in homogeneous semienclosed basins indicate that their vertical structure is determined by the dynamical depth of the system. This dynamical depth can be considered as the ratio between the water column depth and the depth of frictional influence in an oscillatory flow (inverse of Stokes number). When the frictional depth occupies the entire water column, the tidal residual flow is one layered as in shallow basins. But when the frictional depth is only a small portion of the water column (>6 times smaller), the tidal residual is three layered. In relatively deep fjords (say deeper than 100 m), where frictional depths typically occupy a small portion of the water column, the tidal residual flow is expected to be three layered. Ample observational evidence presented here shows a three-layered exchange flow structure in fjords. On the basis of observational and theoretical evidence, it is proposed that the water exchange structure in deep fjords (more than six frictional layers deep, or inverse Stokes number >6) is tidally driven and is three layered. The tidally driven three-layer structure of residual flows could be regarded in some cases as the fundamental structure. However, this structure will only be observed sporadically as it will be masked by wind forcing, remote forcing from the ocean, and freshwater pulses.     

A depth-dependent study of the topographic rectification of tidal currents

Abstract

A depth-dependent model for the topographic rectification of tidal currents in a homogeneous rotating fluid is used to examine the dependence of the rectified mean flow on various tidal, topographic and frictional parameters. Friction is parameterized through a vertically-uniform, time-independent vertical eddy viscosity and a bottom stress law applied near the top of the constant stress layer. The model neglects the interaction of mean and tidal currents, assumes uniformity along isobaths, and is closed with the assumption of zero depth-averaged mean flow across isobaths.

In the limit of depth-independence, the model reduces to that considered by Huthnance (1973) and Loder (1980) which, for weak friction, favours anticyclonic mean circulation around shallow regions and Lagrangian flow which is significantly reduced from the Eulerian. With the inclusion of vertical structure, the magnitude of the anticyclonic flow is amplified suggesting that depth-independent models may underestimate the along-isobath flow. For strong friction the direction of the mean flow depends on the orientation of the tidal ellipse relative to the isobaths. The depthindependent model again underestimates the magnitude of the along-isobath flow, but this can be offset with an appropriate reduction of the bottom friction coefficient.

The cross-isobath mean flows are one to two orders of magnitude weaker than the along-isobath flows and generally have more vertical structure. There is also a significant Stokes drift in the cross-isobath direction. Although there is some tendency for the cross-isobath mean bottom current to be down the cross-isobath mean pressure gradient, it appears that it is not generally possible to infer this current from depth-independent models.     

Tidal friction in a sea with two equal semidiurnal tidal constituents

The effect of quadratic friction on tidal currents consisting of equal M₂ and S₂ constituents is considered. It is shown by two separate arguments—one based on an energy balance, the other on harmonic analysis of the frictional force—that, for rectilinear and parallel currents, the drag coefficient applicable to either constituent considered in isolation should be 1.70 times greater than that applied to the two constituents propagating together. The results of a numerical model of the tides in Gulf St Vincent, Australia (where equal M₂ and S₂ tides occur) are consistent with this prediction. A general result of this work is that the drag coefficients predicted by harmonic analysis of the friction force give the correct rate of energy dissipation for any number of tidal constituents, equal or not.