A numerical study on the occurrence of flowing wells in the discharge area of basins due to the upward hydraulic gradient induced wellbore flow

The occurrence of flowing wells in basins has been found to be closely related to the discharge area with an upward hydraulic gradient. Unfortunately, previous studies on upward gradient induced wellbore flow with equaling total inflow (Q_in) in the deep and total outflow (Q_out) in the shallow could not explain the occurrence of flowing wells. By representing wells using the MNW2 Package imbedded in MODFLOW 2005, we obtain the exchange of groundwater between the aquifer and the well in the discharge area of 3D unit basins and identify three scenarios: Q_in = Q_out, Q_in > Q_out > 0 and Q_in > Q_out = 0. The relationship of Q_in > Q_out well explains why flowing wells only develop in a limited part of the discharge area. Sensitivity analysis shows that well location, water table undulation, and basin length–depth ratio do not change the profile of the ratio of cumulative flow rate in a flowing well to total inflow (Q_v/Q_in) versus the relative elevation in the inflow segment, z_in*, but could significantly change the length of the inflow segment; well depth could change both the length of the inflow segment and the profile of Q_v/Q_in versus z_in*. Based on the numerical results in homogeneous and isotropic basins with different basin length–depth ratios in the current study, the ratio of inflow in the lower half part of a flowing well to the total inflow is found to be at least 67% and could be close to 100%, indicating that water at the outlets of flowing wells with long open sections is mainly from the deep part of the well.     

Assessing the dye‐tracer correction factor for documenting the mean velocity of sheet flow over smooth and grassed surfaces

In the investigation of overland flow hydraulics, mean flow velocity (V) is frequently estimated using the measured surface flow velocity (Vs) multiplied by a correction factor, α. In total, 291 tests were performed in a flume with three beds [smooth glass (GL), sandpaper (SD), and plastic grass (GR)] to investigate α under submerged and non‐submerged flows, and Vs was observed using dye‐tracer method whilst V was calculated by the measured water depth and flow rate. For GL with 5.2% slope and 100 < Re < 5000 [Reynolds number (Re)], α ranged from 0.35 to 0.79, with an average of 0.54. For SD with slopes ranging from 2.6% to 25.9% and 300 < Re < 1200, α varied from 0.18 to 0.48 with an average of 0.32. Raindrop impacts decreased α for GL at 5.2% slope, but the effect diminished for SD as the slope increased. The α‐values less than the theoretical value of 0.67 in laminar flows may be attributed to the greater spatial variability in overland flow compared with channel flow. For GR with non‐submerged flows and Re < 4200, α varied inversely with sediment concentration (SC) at 5.2% slope but was only slightly related to SC at steep slopes of 15.6% and 25.9%. The α‐values were approximately 0.8 for turbulent flows and even greater than 1.0 under high flow discharges. This finding may relate to sheet flow disturbance and retarded surface velocity due to the protruding scattered grass stems. For each surface, α varied positively with Re; α was inversely related to slope for SD but positively related to slope for GR. There was a positive relation between h and α for GL and SD but a negative relation for GR, which highlights the importance of flow inundation status to α. The inundation ratio (h/Δ) is a promising indicator for predicting α; thus, further investigations using different submerged and non‐submerged surfaces are required to predict α effectively based on (h/Δ). Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.     

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.     

Near surface velocity and QS structure of the Quaternary sediment in Bohai basin,China

Heavily populated by Beijing and Tianjin cities, Bohai basin is a seismically active Cenozoic basin suffering from huge lost by devastating earthquakes, such as Tangshan earthquake. The attenuation (Q_P and Q_S) of the surficial Quaternary sediment has not been studied at natural seismic frequency (1?10 Hz), which is crucial to earthquake hazards study. Borehole seismic records of micro earthquake provide us a good way to study the velocity and attenuation of the surficial structure (0?500 m). We found that there are two pulses well separated with simple waveforms on borehole seismic records from the 2006 M_W4.9 Wen'an earthquake sequence. Then we performed waveform modeling with generalized ray theory (GRT) to confirm that the two pulses are direct wave and surface reflected wave, and found that the average v_P and v_S of the top 300 m in this region are about 1.8 km/s and 0.42 km/s, leading to high v_P/v_S ratio of 4.3. We also modeled surface reflected wave with propagating matrix method to constrain QS and the near surface velocity structure. Our modeling indicates that Q_S is at least 30, or probably up to 100, much larger than the typically assumed extremely low Q (~10), but consistent with Q_S modeling in Mississippi embayment. Also, the velocity gradient just beneath the free surface (0?50 m) is very large and velocity increases gradually at larger depth. Our modeling demonstrates the importance of borehole seismic records in resolving shallow velocity and attenuation structure, and hence may help in earthquake hazard simulation.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

A rational sediment transport scaling relation based on dimensionless stream power

The concept of stream channel grade – according to which a stream channel reach will adjust its gradient, S, in order to transport the imposed sediment load having magnitude Q_b and characteristic grain size D_b, with the available discharge Q (Mackin, 1948 , Geological Society of America Bulletin 59 : 463–512; Lane, 1955 , American Society of Civil Engineers, Proceedings 81 : 1–17) is one of the most influential ideas in fluvial geomorphology. Herein, we derive a scaling relation that describes how externally imposed changes in either Q_b or Q can be accommodated by changes in the channel configuration, described by the energy gradient, mean flow depth, characteristic grain size and a parameter describing the effect of bed surface structures on grain entrainment. One version of this scaling relation is based on the dimensionless bed material transport parameter (W*) presented by Parker and Klingeman ( 1982 , Water Resources Research 18 : 1409–1423). An equivalent version is based on a new dimensionless transport parameter (E*) using dimensionless unit stream power. This version is nearly identical to the relation based on W*, except that it is independent of flow resistance. Both versions of the scaling relation are directly comparable to Lane's original relation. In order to generate this stream power‐based scaling relation, we derived an empirical transport function relation relating E* to dimensionless stream power using data from a wide range of stable, bed load‐dominated channels: the form of that transport function is based on the understanding that, while grain entrainment is related to the forces acting on the bed (described by dimensionless shear stress), sediment transport rate is related to the transfer of momentum from the fluid to the bed material (described by dimensionless stream power). Copyright © 2010 John Wiley & Sons, Ltd.     

THE PROBLEM OF LONG-TERM STORAGE IN RESERVOIRS

Abstract

The geometry of a meandering stream depends strongly on the relative stream size (Q ^2/5 / g ^1/5)/D, on the valley slope, Sv, and on the charge, Q _s/Q, where Q and Q _s are the fluid and sediment discharges respectively, g is acceleration due to gravity and D is the mean sediment size. The geometry depends less strongly on the relative settling size of sediment, D/(v ^2/3 / g ^1/3), where v is the kinematic viscosity. For constant values of Q, S _v and D, the effect of increase of charge reduces the meander length, M _L, and the mean channel surface width, B, whereas meander width, M _B, bend radius, R _M, and mean channel depth, H, increase, For a constant value of (Q ^2/5 / g^1/5)/D the values of M _L, M _B, R _M and B increase with the increase of valley slope but the value of H tends to decrease.     

Spatial and depth variability of streambed vertical hydraulic conductivity under the regional flow regimes

This study investigated the influence of the regional flow on the streambed vertical hydraulic conductivity (K_v) within the hyporheic zone in three stream reaches of the Weihe River in July 2016. The streambed K_v with two connected depths was investigated at each test reach. Based on the sediment characteristics, the three test reaches could be divided into three categories: a sandy streambed without continuous silt and clay layer, a sandy streambed with continuous silt and clay layer, and a silt–clay streambed. The results demonstrate that the streambed K_v mainly decreases with the depth at the sandy streambed (without continuous silt and clay layer) and increases with the depth at the other two test reaches. At the sandy streambed (with continuous silt and clay layer) where streambed K_v mainly decreases with the depth, the regional upward flux can suspend fine particles and enhance the pore spacing, resulting in the elevated K_v in the upper sediment layers. At another sandy streambed, the continuous silt and clay layer is the main factor that influences the vertical distribution of fine particles and streambed K_v. An increase in streambed K_v with the depth at the silt/clay streambed is attributed to the regional downward movement of water within the sediments that may lead to more fine particles deposited in the pores in the upper sediment layers. The streambed K_v is very close to the bank in the sandy streambed without continuous silt and clay layer and the channel centre in the other two test reaches. Differences in grain size distribution of the sediments at each test reach exercise a strong controlling influence on the streambed K_v. This study promotes the understanding of dynamics influencing the interactions between groundwater and surface water and provides guidelines to scientific water resources management for rivers.     

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.     

Flow threads in surface run‐off: implications for the assessment of flow properties and friction coefficients in soil erosion and hydraulics investigations

Soil surface microtopography produces non‐uniform surface run‐off, in which narrow threads of relatively deep and fast ?ow move within broader, shallower, slower‐moving regions. This kind of ?ow is probably widespread, given that microtopography is itself common. Methods used to record the properties of surface run‐off include grid‐ or transect‐based depth observations, with a single mean ?ow speed derived by calculation from V = Q/WD, and the use of dye timing to estimate velocity, with an effective mean depth calculated from D = Q/WV. Because these methods allow only single, ?ow‐?eld mean values to be derived for V or D, neither is well suited to non‐uniform ?ows. The use of depth data to derive a ?ow‐?eld mean V furthermore implicitly applies area weighting to the depth data; likewise, the use of dye speeds for V inherently overestimates mean V because dye dominantly follows the faster ?ow threads. The associated errors in derived parameters such as friction coef?cients are not readily quanti?ed and appear not to have been addressed previously. New ?eld experiments made on untilled soil surfaces in arid western NSW, Australia, explore these circumstances and the implications for deriving meaningful measures of ?ow properties, including friction coef?cients. On surfaces deliberately chosen for their very subtle microtopography, average thread velocities are shown to be commonly 2·5 times greater than the ?ow‐?eld mean, and locally 6–7 times greater. On the other hand, non‐thread ?ow speeds lie below the ?ow‐?eld mean, on average reaching only 84 per cent of this value, and often considerably less. Flow‐?eld means conceal the existence of regions of the ?ow ?eld whose properties are statistically distinct. Results con?rm that a reliance on ?ow‐?eld average depths yields estimates of friction coef?cients that are biased toward the shallower, high‐roughness parts of the ?ow, while if dye speeds are relied upon the results are biased toward the deeper, smoother threads of ?ow. A new approach to the evaluation of friction coef?cients in non‐uniform ?ows is advanced, involving the determination of separate coef?cients for threads and non‐thread zones of the ?ow ?eld. In contrast, ?ow‐?eld friction coef?cients as they are customarily derived in run‐off plot experiments subsume these distinct coef?cients in proportions that are generally unknown. The value of such coef?cients is therefore questionable. Copyright © 2004 John Wiley & Sons, Ltd.     

A new drain spacing formula

Abstract

A drain spacing formula is derived considering the variation in radial flux and the area above the drain level in the radial flow zone. The extent of the radial flow zone is ascertained by applying a mass balance and differentiability criterion of the water surface profile at the interface of radial and Dupuit-Forchheimer flow zones. The radial flow zone extends from the centre of the tile drain a distance of 2/π times the depth to impervious layer below the drain. For a normal ratio of recharge rate to hydraulic conductivity (R/K ≤ 0.0025), the water surface profile in the radial flow zone computed using Hooghoudt's formula is very different from the profile obtained by the new drain spacing formula; however, Hooghoudt's formula computes the maximum water table height which marginally differs from that found by the present method. For a ratio of high recharge rate to hydraulic conductivity (R/K = 0.1) and close drain spacing (L/D = 2), the difference in the maximum heights is 21%. Hooghoudt's formula overestimates the maximum water table position for L/D < 40. Unlike Hooghoudt's equivalent depth, the equivalent depth obtained using the present method is a function of the ratio of recharge rate to hydraulic conductivity.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

Inundation flow velocity of tsunami on land

An estimation of tsunami inundation flow velocity is one of the most challenging issues among tsunami research. Based on field data of inundation depth and inundation flow velocity u estimated using Bernoulli's theorem and inundation depth, fundamental characteristics of the relationship between inundation flow velocity and inundation depth are examined. Fundamental characteristics of the velocity coefficient where g is gravitational acceleration, h_f and h_r are inundation depths at the front and the back of structures such as a rectangular building with vertical walls, respectively) implicitly included in the relationship are examined through hydraulic experiments. As a result, C_v = 0.6 is recommended as its simple and practical value. It is confirmed through these examinations that the Froude number, defined by where , ranges 0.7–2.0, and when C_v = 0.6 is adopted this Froude number ranges 0.42–1.2. By using the relationship and C_v = 0.6, two simple and practical relationships are presented for two cases where inundation flow velocity exerts the largest or the smallest fluid force on structures. These relationships can be used to roughly grasp the practical side of tsunami damage, and estimate fluid force acting on individual structures, moving velocity and collision force of floating objects and sediment transport such as boulder and sand. Fundamental characteristics of the waterline (tsunami trace) distribution around/on the typical object model (square pillar, corn and column) are also examined through steady flow experiments, and it is confirmed that the maximum and the minimum values of h_f/h₀ in the full type model of the square pillar are almost the same as those of h_f/h_r obtained by field surveys where h₀ is uniform flow depth. It is also confirmed that h_r ? h₀ when the Froude number, defined by where u₀ is uniform flow velocity, is much less than 1.0. Using a newly defined velocity coefficient, tsunami inundation flow velocity on land can be estimated practically and would be useful for checking proposed sediment transport models that are now being developed by tsunami geologists.     

Changes in stream flow regime in headwater catchments of the Yellow River basin since the 1950s

The headwater catchments of the Yellow River basin generate over 35% of the basin's total stream flow and play a vital role in meeting downstream water resources requirements. In recent years the Yellow River has experienced significant changes in its hydrological regime, including an increased number of zero‐flow days. These changes have serious implications for water security and basin management. We investigated changes in stream flow regime of four headwater catchments since the 1950s. The rank‐based non‐parametric Mann–Kendall test was used to detect trends in annual stream flow. The results showed no significant trend for the period 1956 to 2000. However, change‐point analysis showed that a significant change in annual stream flow occurred around 1990, and hence the stream‐flow data can be divided into two periods: 1956–1990 and 1991–2000. There was a considerable difference in average annual stream flow between the two periods, with a maximum reduction of 51%. Wet‐season rainfall appears to be the main factor responsible for the decreasing trend in annual stream flow. Reductions in annual stream flow were associated with decreased interannual variability in stream flow. Seasonal stream flow distribution changed from bimodal to unimodal between the two periods, with winter stream flow showing a greater reduction than other seasons. Daily stream flow regime represented by flow duration curves showed that all percentile flows were decreased in the second period. The high flow index (Q₅/Q₅₀) reduced by up to 28%, whereas the reduction in the low flow index (Q₉₅/Q₅₀) is more dramatic, with up to 100% reduction. Copyright © 2006 John Wiley & Sons, Ltd.     

Depth‐dependent hydraulic conductivity distribution patterns of a streambed

Characterization of streambed hydraulic conductivity from the channel surface to a great depth below the channel surface can provide needed information for the determination of stream‐aquifer hydrologic connectedness, and it is also important to river restoration. However, knowledge on the streambed hydraulic conductivity for sediments 1 m below the channel surface is scarce. This study describes a method that was used to determine the distribution patterns of streambed hydraulic conductivity for sediments from channel surface to a depth of 15 m below. The method includes Geoprobe's direct‐push techniques and Permeameter tests. Direct‐push techniques were used to generate the electrical conductivity (EC) logs and to collect sequences of continuous sediment cores from river channels, as well as from the alluvial aquifer connected to the river. Permeameter tests on these sediment cores give the profiles of vertical hydraulic conductivity (K_v) of the channel sediments and the aquifer materials. This method was applied to produce K_v profiles for a streambed and an alluvial aquifer in the Platte River Valley of Nebraska, USA. Comparison and statistical analysis of the K_v profiles from the river channel and from the proximate alluvial aquifer indicates a special pattern of K_v in the channel sediments. This depth‐dependent pattern of K_v distribution for the channel sediments is considered to be produced by hyporheic processes. This K_v‐distribution pattern implied that the effect of hyporheic processes on streambed hydraulic conductivity can reach the sediments about 9 m below the channel surface. Copyright © 2010 John Wiley & Sons, Ltd.     

Accuracy of kinematic wave and diffusion wave for spatial‐varying rainfall excess over a plane

The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF₀² > 5, where K is the kinematic‐wave number and F₀ is the Froude number. Therefore, the regions (KF₀², F₀) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF₀² ≥ 20 with F₀ ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF₀² > 35 with F₀ ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF₀² ≥ 15 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF₀² ≥ 30 with F₀ ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF₀² > 10 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF₀² > 15 with F₀ ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF₀² > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF₀² > 12·5 with F₀ ≤ 1. The lower limits of the regions, defined on KF₀², can be considered generally valid for both approximations, but for F₀ < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd.     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.