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.     

Practical implementation of the fractional flow approach to multi-phase flow simulation

Fractional flow formulations of the multi-phase flow equations exhibit several attractive attributes for numerical simulations. The governing equations are a saturation equation having an advection diffusion form, for which characteristic methods are suited, and a global pressure equation whose form is elliptic. The fractional flow approach to the governing equations is compared with other approaches and the implication of equation form for numerical methods discussed. The fractional flow equations are solved with a modified method of characteristics for the saturation equation and a finite element method for the pressure equation. An iterative algorithm for determination of the general boundary conditions is implemented. Comparisons are made with a numerical method based on the two-pressure formulation of the governing equations. While the fractional flow approach is attractive for model problems, the performance of numerical methods based on these equations is relatively poor when the method is applied to general boundary conditions. We expect similar difficulties with the fractional flow approach for more general problems involving heterogenous material properties and multiple spatial dimensions.     

Topographic forcing of flow partition and flow structures at river bifurcations

This paper presents the predicted flow dynamics from the application of a Reynolds‐averaged Navier–Stokes model to a series of bifurcation geometries with morphologies measured during previous flume experiments. The topography of the bifurcations consists of either plane or bedform‐dominated beds which may or may not possess discordance between the two bifurcation distributaries. Numerical predictions are compared with experimental results to assess the ability of the numerical model to reproduce the division of flow into the bifurcation distributaries. The hydrodynamic model predicts: (1) diverting fluxes in the upstream channel which direct water into the distributaries; (2) super‐elevation of the free surface induced at the bifurcation edge by pressure differences; and (3) counter‐rotating secondary circulation cells which develop upstream of the apex of the bifurcation and move into the downstream channels, with water converging at the surface and diverging at the bed. When bedforms are not present, weak transversal fluxes characterize the upstream channel for almost its entire length, associated with clearly distinguishable secondary circulation cells, although these may be under‐estimated by the turbulence model used in the solution. In the bedform dominated case, the same hydrodynamic conditions were not observed, with the bifurcation influence restricted and depth scale secondary circulation cells not forming. The results also demonstrate the dominant effect bed discordance has upon flow division between the two distributaries. Finally, results indicate that in bedform dominated rivers. Consequently, we suggest that sand‐bed river bifurcations are more likely to have an influence that extends much further upstream and have a greater impact upon water distribution. This may contribute to observed morphological differences between sand‐bedded and gravel‐bedded braided river networks. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of debris flow surges using the theory of uniformly progressive flow

Coarse debris flows develop surges with distinct longitudinal sorting. Although highly unsteady, such flow often appears to attain a steady‐state condition, moving over long distances with approximately constant velocity and maximum depth. Typically, a steep, bouldery front is followed by an accumulation of liquid slurry, which in turn decays into a dilute tail. Such sorting has long been recognized by field workers, but its influence on the dynamic behaviour of debris flow surges has not yet been fully clarified by analysis. A simple model is presented, using the theory of uniformly progressive flow and incorporating zoned longitudinal variation in rheology. It is shown that non‐homogeneity can cause very significant magnification of the peak discharge, depending on the slope angle and on the length of the frontal boulder concentration. The shape of the surge flow profiles is determined not only by the rheology of the retained material, but by the longitudinal variation of material characteristics. As a result, excessive reliance on laboratory‐derived rheological constitutive relationships is not advisable. Models of debris flow surges should be non‐homogeneous and able to incorporate zones of contrasting rheology. Copyright © 2000 John Wiley & Sons, Ltd.     

The development of new analytic elements for transient flow and multiaquifer flow

We deal in this paper with an ongoing development of the analytic element method. We present in outline new analytic line elements that are suitable to model general flow fields, i.e., flow fields that possess a continuously varying areal inflow or outflow. These elements are constructed specifically to model the leakage through leaky layers that separate aquifers in leaky systems and to model transient effects. The leakage or release from storage underneath linear features is modeled precisely by the new elements; the singularity in leakage is matched exactly by the approximate solution. Applications are given for a problem involving leakage and for a case of transient flow. We note that the analytic elements can be used also to reproduce the effect of continuously varying aquifer properties, e.g., the hydraulic conductivity or the elevation of the base of the aquifer. In the latter case, the elements would reproduce the rotation of the flow field caused by the variation in properties, rather than the divergence as for the case of leakage.     

Textural analysis and flow mechanism of the Donzurubo subaqueous pyroclastic flow deposits

The Donzurubo subaqueous pyroclastic flow deposits deposited in subaqueous environments maintaining high temperatures (about 500°C). Each flow unit of these pyroclastic flow deposits shows some characteristic size distributions in its stratigraphic column. The concentration of pumice at the top clearly defines the top facies of a flow unit. Median diameter (Md Ø) and the averages of the largest ten essential dense debris increase gradually starting from both the top and the bottom of the flow unit. The maximum points of Md Ø and the averages of the largest ten essential dense debris are usually found in the middle zone of each flow unit, but the Md Ø maximum points are generally in a lower position than the averages. Mechanical analyses show that the deposits consist of polymodal populations. They show, on the whole, an asymmetrical distribution, which is mainly due to the absence of the coarser fractions of the main population. The size distribution characteristics and the C-M pattern of the deposits suggest that these subaqueous pyroclastic flow deposits were not originated by homogeneously suspended turbulent flows but by incandescent turbulent flows with layered suspension.     

Classification of natural flow regimes in Iran to support environmental flow management

Abstract

Development of environmental flow standards at the regional scale has been proposed as a means to manage the influence of hydrological alterations on riverine ecosystems in view of the rapid pace of global water resources management. Flow regime classification forms a critical part in such environmental flow assessments. We present a national-scale classification of hydrological regimes for Iran based on a set of hydrological metrics. It describes ecologically relevant characteristics of the natural hydrological regime derived from 15- to 47-year-long records of daily mean discharge data for 539 streamgauges within a 47-year period. The classification was undertaken using a fuzzy partitional method within Bayesian mixture modelling. The analysis resulted in 12 classes of distinctive flow regime types that differ in various hydrological aspects. This classification is being used for further research in regional-scale environmental flow studies in Iran.

Editor D. Koutsoyiannis     

Plume heat flow is much lower than CMB heat flow

Plumes rising from the core–mantle boundary (CMB) are often assumed to transport most, or all, of the heat conducted across the CMB. Here this assumption is explored using numerical convection models in idealized geometries that lead to a single plume under steady-state or near steady state conditions. Plume heat transport is calculated for different internal heating rates using two methods and compared to the CMB heat flux. For these conditions, it is found that the heat flux transported by plumes in the upper mantle is only a fraction of the core heat flux and, thus, core heat flow estimates derived from observed hotspots could be multiplied by a factor of several.     

Diverging overland flow

This study investigates divering overland flow utilizing kinematic wave theory, which does not appear to have been dealt with previously. Explicit analytical solutions are derived in dimensionless form for space-time invariant rainfall. Analytical solutions do not seem to be tractable for time-varying rainfall. Depending upon the duration of rainfall, equilibrium and partial equilibrium cases are distinguished explicitly. The effect of divergence parameter on the hydrograph shape is shown. The adequacy of kinematic approximation for characterization of diverging overland flow is tested against laboratory watershed results. The diverging overland flow model is found to yield results which compare well with observations and with those of a plane model.     

Approaches to the simulation of unconfined flow and perched groundwater flow in MODFLOW

Various approaches have been proposed to manage the nonlinearities associated with the unconfined flow equation and to simulate perched groundwater conditions using the MODFLOW family of codes. The approaches comprise a variety of numerical techniques to prevent dry cells from becoming inactive and to achieve a stable solution focused on formulations of the unconfined, partially-saturated, groundwater flow equation. Keeping dry cells active avoids a discontinuous head solution which in turn improves the effectiveness of parameter estimation software that relies on continuous derivatives. Most approaches implement an upstream weighting of intercell conductance and Newton-Raphson linearization to obtain robust convergence. In this study, several published approaches were implemented in a stepwise manner into MODFLOW for comparative analysis. First, a comparative analysis of the methods is presented using synthetic examples that create convergence issues or difficulty in handling perched conditions with the more common dry-cell simulation capabilities of MODFLOW. Next, a field-scale three-dimensional simulation is presented to examine the stability and performance of the discussed approaches in larger, practical, simulation settings.     

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 transition of flow patterns through critical stagnation points in two-dimensional groundwater flow

A flow pattern is characterized by aquifer features and the number, type, and distribution of stagnation points (locations where the discharge is zero). This article identifies a condition for transition of flow patterns in two-dimensional groundwater flow obeying Darcy’s law by examining changes in stagnation points, using the Taylor series expansion of the discharge vector. It is found that the three standard types of stagnation points (minimums, maximums, and saddle points) are completely characterized by the first-order term containing the discharge gradient tensor. However, when the determinant of the tensor becomes zero, stagnation points of other types characterized by higher-order terms come into existence. In this article, we call these zero-determinant stagnation points as critical stagnation points; they may emerge suddenly, split to a set of new stagnation points, or disappear from the flow, resulting in transitions of flow patterns. Examples of both transient and steady flows are used to illustrate the usefulness and significance of critical stagnation points.     

Assessment of environmental flow requirements

Flow is considered to be the master variable for a river because the fluvial processes and health of its ecosystem critically depend upon flow. Increasing water withdrawals from many rivers of the world are leading to severe degradation in river ecosystems. Water is allocated for environmental needs so that a river can perform its natural functions. This article discusses the concept of environmental flow, methods to assess it, and issues in implementation. Copyright © 2012 John Wiley & Sons, Ltd.     

Factors governing the flow lineation of a large-scale pyroclastic flow — An example in the ata pyroclastic flow deposit,Japan

Schmincke andSwanson (1967) explained laminar flowage structures as indicators for flow direction of pyroclastic flows that show a radial flow pattern away from the source. Several other authors have reported similar examples, but the influence of pre-flow topographic relief has not been analyzed. Flow lineations were measured for the Ata pyroclastic flow deposit, southwestern Japan. This deposit has covered an undulating basement topography. Preferred orientation of crystals and lithic fragments were measured on thin sections cut parallel to sedimentary layering. The following three factors which control the flow lineation have been recognized. 1) Flow lineations oriented radially away from the source, as described by previous authors, were obtained only for samples collected from the surface of the pyroclastic flow plateau where the basement valleys were nearly filled by earlier flow units. 2) Lineations near the floor of narrow valleys were parallel to the strike of the valley. 3) Flow lineations near the wall of valleys tend to be parallel to the dip of the valley walls. These data suggest that the initial radial movement of pyroclastic flows from the source gradually changes direction to parallel the strike of deep valleys due to confining effect of valley wall. Flows which are trapped within a valley, tends to move towards the bottom of the valley just prior to the final settlement. After the basement topographic relief has been filled up with earlier flow units, the later flows maintain their original radial movement until final settlement.     

The instability of precessing flow

Abstract

An explanation is put forward for the instability observed within a precessing, rotating spheroidal container. The constant vorticity solution for the flow suggested by Poincaré is found to be inertially unstable through the parametric coupling of two inertial waves by the underlying constant strain field. Such resonant couplings are due either to the elliptical or shearing strains present which elliptically distort the circular streamlines and shear their centres respectively. For the precessing Earth's outer core, the shearing of the streamlines and the ensuing shearing instability are the dominant features. The instability of some exact, linear solutions for finite precessional rates is established and used to corroborate the asymptotic analysis. A complementary unbounded analysis of a precessing, rotating fluid is also presented and used to deduce a likely upperbound on the growth rate of a small disturbance. Connection is made with past experimental studies.     

Estimation of ecological high flow

Floods can destroy fish habitat. During a flood a fish has to seek shelters (refuges) to survive. It is necessary to know the maximum discharge that the fish can sustain against the strong current. Ecological and hydraulic engineers can simulate the flow condition of high flow for designing the refuge when restoring and enhancing the rivers are needed. Based on the average ratio of the mean and maximum velocities invariant with time, discharge and water level, this paper tries to introduce the concept of ecological high flow. The mean‐maximum velocity ratio can be used to estimate the mean velocity of the river. If the maximum velocity of the cross section is replaced by the maximum sustained swimming speeds of fish, the mean velocity of ecological high flow can be calculated with the constant ratio. The cross‐sectional area can be estimated by the gage height. Then the ecological high flow can be estimated as the product of mean velocity of ecological high flow multiplied by the cross‐sectional area. The available data of the upstream of the Dacha River where is the habitat of the Formosan landlocked salmon were used to illustrate the estimation of the ecological high flow. Any restoration project at Sonmou that try to improve the stream habitat can use the ecological high flow to design the hydraulic structure at suitable location to offer refuges for the Formosan landlocked salmon that is an endangered species in Taiwan Copyright © 2005 John Wiley & Sons, Ltd.     

One-dimensional modelling of mantle flow

A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 10²¹ N s m^–2 with a free-slip bottom boundary.     

A two-grid method for coupled free flow with porous media flow

This paper presents a two-grid method for solving systems of partial differential equations modelling incompressible free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numerical errors and convergence rates for solutions obtained from the two-grid method are presented. CPU times for the two-grid algorithm are shown to be significantly less than those obtained by solving the fully coupled problem.