A three-dimensional numerical model of particulate transport for coastal waters

A Lagrangian marker particle in Eulerian finite difference cell solution to the three-dimensional incompressible mass transport equation was developed for predicting particulate transport in coastal and estuarine waters. Special features of the solution procedure include a finite difference grid network which translates horizontally and vertically with the mean particle motion and expands with the dispersive growth of the marker particle cloud. The cartesian vertical coordinate of the three-dimensional mass transport equation has been transformed, using instantaneous water column depth to allow adaptation to flow situations with a temporally and spatially varying bottom topography and free surface. Results from this model for turbulent diffusion and advection of a uniform plug flow of sediment in an unbounded uniform flow field with various sediment settling velocities were in excellent agreement with the corresponding analytic solutions. Using current information from a two-dimensional vertically averaged hydrodynamic's model, the model was utilized to predict the long term diffusion and advection of dilute neutrally and negatively buoyant suspended sediment clouds resulting from a hypothetical instantaneous release of dredge spoil waste at Brown's Ledge in Rhode Island Sound.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 10³dyne/cm²), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 10⁴ dyne/cm², if the flow rate is greater than 10⁵ g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.     

Floc size and settling velocity within a Spartina anglica canopy

There is increasing interest in tidal wetlands as mechanisms for sustainable and long-term coastal defence. The complexities of the interaction between the deposition of suspended particulate matter (SPM) and submerged vegetation, however, is to a large extent poorly understood. Consequently, accurate parameterisation of cohesive sediment settling fluxes in these environments is a crucial requirement for the development of high-resolution numerical models of wetland morphodynamics. A novel laboratory experiment is described in which the turbulent flow structure within a canopy of the halophytic macrophyte Spartina anglica is examined, and floc characteristics quantified using a unique floc camera configuration able to measure directly the full spectral floc size (D) and settling velocity (W_s). We provide the first quantitative observations of floc characteristics from shallow (h<0.5 m), vegetated flows and investigate the potential influence that variations in vegetative density may have on flocculation, and thus depositional fluxes, in comparison to unvegetated flows.     

Sand settling through bedform-generated turbulence in rivers

Fluvial bedforms generate a turbulent wake that can impact suspended-sediment settling in the passing flow. This impact has implications for local suspended-sediment transport, bedform stability, and channel evolution; however, it is typically not well-considered in geomorphologic models. Our study uses a three-dimensional OpenFOAM hydrodynamic and particle-tracking model to investigate how turbulence generated from bedforms and the channel bed influences medium sand-sized particle settling, in terms of the distribution of suspended particles within the flow field and particle-settling velocities. The model resolved the effect of an engineered bedform, which altered the flow field in a manner similar to a natural dune. The modelling scenarios alternated bed morphology and the simulation of turbulence, using detached eddy simulation (DES), to differentiate the influence of bedform-generated turbulence relative to that of turbulence generated from the channel bed. The bedform generated a turbulent wake that was composed of eddies with significant anisotropic properties. The eddies and, to a lesser degree, turbulence arising from velocity shear at the bed substantially reduced settling velocities relative to the settling velocities predicted in the absence of turbulence. The eddies tended to advect sediment particles in their primary direction, diffuse particles throughout the flow column, and reduced settling likely due to production of a positively skewed vertical-velocity fluctuation distribution. Study results suggest that the bedform wake has a significant impact on particle-settling behaviour (up to a 50% reduction in settling velocity) at a scale capable of modulating local suspended transport rates and bedform dynamics. © 2020 John Wiley & Sons, Ltd.     

Stratified flow in pyroclastic surges

Stratified flow theory is applied to pyroclatic surges in an effort to gain insight into transport dynamics during explosive eruptions. Particle transport is assumed to be by turbulent suspension, and calculations contained herein show that this is likely for many cases including the 18 May 1980 blast at mount St. Helens. The discussion centers on the Rouse number (Pn), which represents a ratio of particle settling velocity to scale of turbulence; the Brunt-Väisälä frequency (N), which is the maximum possible frequency of internal waves; the Froude number (Fr), representing the ratio of inertial forces to gravitational forces; and the Richardson number (Ri), a ratio of buoyant restoring forces to turbulent mixing forces. The velocity or flow power dependence of bed-form wavelength in surge deposits is related to a velocity dependence of wavelength of internal waves in the turbulent surge. This produces a decrease in dune wavelength with increasing distance from vent. Migration direction of bed forms is related toFr as it is defined for a continuously stratified flow. Proximal to distal facies variations in surge deposits reflect increasingPn andRi as the flows move away from their sources. This produces the progression from sandwave to massive to planar facies with increasing distance from vent. Where the long axis of topography is at low angles to the flow direction, massive facies in topographic lows may from concurrently with sandwave facies on highs, due to the higher particle concentration in the lows. Where long axis of topography is at high angles to flow direction, denser lower parts of the surge may be dammed or blocked. Blocked material tends to form massive flows that may move down slope independent of the overriding surge. A model incorporating turbulent transport, stratified flow, and time evolution of pyroclastic surges is proposed for deposits which have been attributed to both pyroclastic flow and pyroclastic surge transport by various workers. During the initial high energy (waxing) phase of the eruptive event,Pn is sufficiently low that only coarse, but poorly sorted, material is deposited to form relatively coarse bottom layers. As the event wanes, remaining finer material is deposited through a thin bed load to produce overlying bedded and cross-bedded veneer deposits. Throughout most of the event, blocking occurs to produce relatively thick and massive deposits in valley bottoms.     

An absorbing boundary condition for wave propagation in saturated poroelastic media — Part II: Finite element formulation

In a finite element formulation for dynamic soil-structure interaction, an absorbing boundary condition is needed to model wave propagation towards infinity. When the soil is saturated, its dynamic behaviour can be modelled by means of Biot's poroelastic theory. In Part I (Degrande, G. & De Roeck, G., Soil Dynamics & Earthquake Eng., 1993, 12(7), 411-21), a local absorbing boundary condition for wave propagation in saturated poroelastic media has been developed. In the present paper, this boundary condition is implemented in an irreducible finite element formulation for a compressible pore fluid. Spurious reflections for oblique incident waves on the absorbing boundary contribute to the solution errors. Therefore, a spectral element method, based on classical analytical solution techniques, is used to assess the accuracy of the finite element formulation.     

A quadratic element method for evaluating groundwater flow by the inversion of surface tilt with application to the Tono Area, Japan

By modifying a previous method with constant elements, we developed a quadratic element method for more accurately estimating groundwater flow by the inversion of tilt data. In this method: (1) a region of groundwater flow is divided into quadratic elements in which the change in groundwater volume per unit volume of rock (Δv) and the Skempton coefficient (B) vary in a quadratic manner with the coordinates, (2) the values of Δv are set to zero at the boundaries of the region of groundwater flow and (3) the sum of the squared second derivatives of Δv is adopted as a constraining condition that is weighted and added to the sum of the squared errors in tilt. First, analyses were performed for a flow model to determine the accuracy of this method for estimating groundwater flow and also to clarify the effect of the assumed size of a region of groundwater flow. These analyses showed that the quadratic element method proposed in this study gives a much better estimation of Δv than the constant element method and that a large region of groundwater flow should be assumed, rather than a small region, since the values of Δv at points outside of the actual region of groundwater flow are estimated to be nearly zero when a large region is assumed while these values are greatly overestimated when an excessively small region is assumed. Finally, the quadratic element method was applied to the site of the Mizunami Underground Research Laboratory in the Tono area, Japan. Inverse analyses were performed for tilt data measured by four tiltmeters with a resolution of 10⁻⁹ radians during the excavation of two shafts under the assumption that the rock mass is an isotropic and homogeneous half- space. The results showed that the method proposed in this study reproduced the tilt data very accurately. Thus, the distribution of Δv was estimated without sacrificing the reproducibility of the tilt data. The contour maps of B(1 + ν)Δv (ν: Poisson’s ratio) showed that the heterogeneous flow of groundwater occurred at the site and that groundwater volume decreased mainly in the area surrounded by two faults. The latter result is consistent with the finding obtained by previous investigations that these faults have low permeability in the direction perpendicular to the strike and may act as a flow barrier.     

Magnetosheath Interaction with the High Latitude Magnetopause

We present both statistical and case studies of magnetosheath interaction with the high-latitude magnetopause on the basis of Interball-1 and other ISTP spacecraft data. We discuss those data along with recently published results on the topology of cusp-magnetosheath transition and the roles of nonlinear disturbances in mass and energy transfer across the high-latitude magnetopause. For sunward dipole tilts, a cusp throat is magnetically open for direct interaction with the incident flow that results in the creation of a turbulent boundary layer (TBL) over an indented magnetopause and downstream of the cusp. For antisunward tilts, the cusp throat is closed by a smooth magnetopause; demagnetized ‘plasma balls’ (with scale ∼ few R_E, an occurrence rate of ∼25% and trapped energetic particles) present a major magnetosheath plasma channel just inside the cusp. The flow interacts with the ‘plasma balls’ via reflected waves, which trigger a chaotization of up to 40% of the upstream kinetic energy. These waves propagate upstream of the TBL and initiate amplification of the existing magnetosheath waves and their cascade-like decays during downstream passage throughout the TBL. The most striking feature of the nonlinear interaction is the appearance of magnetosonic jets, accelerated up to an Alfvenic Mach number of 3. The characteristic impulsive local momentum loss is followed by decelerated Alfvenic flows and modulated by the TBL waves; momentum balance is conserved only on time scales of the Alfvenic flows (1/f_A ∼12 min). Wave trains at f_A∼1.3 mHz are capable of synchronizing interactions throughout the outer and inner boundary layers. The sonic/Alfvenic flows, bounded by current sheets, control the TBL spectral shape and result in non-Gaussian statistical characteristics of the disturbances, indicating the fluctuation intermittency. We suggest that the multi-scale TBL processes play at least a comparable role to that of macro-reconnection (remote from or in the cusp) in solar wind energy transformation and population of the magnetosphere by the magnetosheath plasma. Secondary micro-reconnection constitutes a necessary chain at the small-scale (∼ion gyroradius) edge of the TBL cascades. The thick TBL transforms the flow energy, including deceleration and heating of the flow in the open throat, ‘plasma ball’ and the region downstream of the cusp.     

The amplitude of turbulent shear flow

A new formulation of the problem of the statistical stability of fully turbulent shear flow is proposed, in which one seeks mean fields that bound the observed flow from the stable side. In the spirit of maximum transport theory, this formulation admits a larger set of “flows” than are dynamically possible. A sequence of constraints derived from the equations of motion can narrow this set, permitting at each step the determination of a “most stable” field free of any empirical elements. Turbulent channel flow is proposed as the first application and test of this quantitative theory. Past deductive theories for this flow, from “mean field” to “transport upper bounds,” are assessed. It is shown why these theories do not retain the significant destabilizing mechanisms of the actual flow. The implications for turbulent flow of recent work on the nonlinear and three-dimensional instability of laminar shearing flow are described. In first exploration of the “decoupled mean” stability theory proposed here, approximate analytical and numerical stability methods are used to find an amplitude and structure for the averaged flow propoerties. The quantitative results differ by considerably less than two from the observed values, providing an incentive for a more complete numerical study and for further constraints on the admitted class of flows. In the language now current for nonlinear stability theory, evidence is advanced here that anN-dimensional central manifold is adjacent to the realized turbulent flow, whereN has the largest possible value compatible with the dynamical relations.     

Modeling Water Flow in the Presence of Higher Vegetation

The notions of hydromechanics of continuum with a complicated structure are used to formulate a closed spatially homogeneous mathematical model of water flow within higher aquatic vegetation (HAV) canopy. Model equations are applied to the analysis of the vertical structure of a turbulent flow in a vegetated open channel. Test calculations are made. The results of calculations and experimental studies of water flow characteristics within vegetation communities in some water bodies [1, 6–8, 10, 14] are shown. The difficulties in implementing such experiments require improving the methods of mathematical simulation of water flows through HAV.     

Turbulence in vegetated flows: Volume-average analysis and modelling aspects

Two approaches for the modelling of turbulence in vegetated flows have been developed in the past. The “microscopic” approach which is straightforward but limited to simple cases and the “macroscopic” approach which is based on Volume Average Theory (VAT). In this study, aspects of Volume-Average (VA) analysis and modelling are investigated for turbulent vegetated flow using computed three-dimensional results from the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations around a representative vegetal element. In particular (a) the VA transport equations for k and ε, based on VAT, are properly derived, (b) the Boussinesq hypothesis for the VA quantities, employed in 〈k〉-〈ε〉 turbulence models is tested, and (c) the values of the coefficients used in such turbulence models are assessed in comparison with those used in the classical turbulence models.     

A facies interpretation of the eruption and emplacement mechanisms of the upper part of the Neapolitan Yellow Tuff,Campi Flegrei,southern Italy

This study focuses on the upper part, Member B, of the Neapolitan Yellow Tuff (NYT). Detailed measurements of stratigraphic sections within the unlithified pozzolana facies show that Member B is composed of at least six distinct depositional units which each record a complex fluctuation between different styles of deposition from pyroclastic density flows. Six lithofacies have been identified: (1) massive valleyponded facies, the product of non-turbulent flows; (2) inverse-graded facies formed by flows that were turbulent for the majority of transport but were deposited through a non-tubulent basal regime; (3) regressive sand-wave facies, the product of high-concentration, turbulent flows; (4) stratified facies, the product of deposition from turbulent, low-particle-concentration, flows; (5) particle aggregate and (6) vesicular ash lithofacies, both of which are considered to have formed by deposition from turbulent, low-concentration flows. Although the whole eruption may have been phreatomagmatic, facies 1–4 are interpreted to be the product of dry eruptive activity, whereas facies 5 and 6 are considered to be of wet phreatomagmatic eruptive phases. Small-scale horizontal variations between facies include inverse-graded lithofacies that pass laterally into regressive sand-wave structures and stratified deposits. This indicates rapid transition from non-turbulent to turbulent deposition within the same flow. Thin vesicular ash and particle aggregate layers pass laterally into massive valley-ponded vesicular lithofacies, suggesting contemporaneous wet pyroclastic surges and cohesive mud flows. Three common vertical facies relations were recognised. (1) Massive valley-ponded and inverse-graded facies are overlain by stratified facies, suggesting decreasing particle concentration with time during passage of a flow. (2) Repeated vertical gradation from massive up into stratified facies and back into massive beds, is indicative of flow fluctuating between non-turbulent and turbulent depositional conditions. (3) Vertical alternation between particle aggregates and vesicular facies is interpreted as the product of many flow pulses, each of which involved deposition of a single particle aggregate and vesicular ash layer. It is possible that the different facies record stages in a continuum of flow processes. The deposits formed are dependent on the presence, thickness and behaviour of a high-concentration, non-turbulent boundary layer at the base of the flow. The end members of this process are (a) flows that transported and deposited material from a non-turbulent flow regime and (b) flows that transported and deposited material from a turbulent flow regime.     

Lattice Boltzmann simulation of turbulence-induced flocculation of cohesive sediment

Both the floc formation and floc breakup of cohesive sediment are affected by turbulent shear which is recognized as one of the most important parameters, and thus, on the settling and transport of cohesive sediment. In this study, the development of floc characteristics at early stage and steady-state of flocculation were investigated via a three-dimensional lattice Boltzmann numerical model for turbulence-induced flocculation. Simulations for collision and aggregation of various size particles, floc growth, and breakup in isotropic and homogenous turbulent flows with different shear stresses were conducted. Model results for the temporal evolution of floc size distribution show that the normalized floc size distributions is time-independent during early stage of flocculation, and at steady-state, shear rate has no effect on the shape of normalized floc size distribution. Furthermore, the size, settling velocity, and effective density of flocs at the non-equilibrium flocculation stage do not change significantly for shear stresses in the range 0–0.4 N m^?2. The relationships between floc size and settling velocity established during floc growth stages and that during steady-states are different.     

Reconciling pyroclastic flow and surge: the multiphase physics of pyroclastic density currents

Two end-member types of pyroclastic density current are commonly recognized: pyroclastic surges are dilute currents in which particles are carried in turbulent suspension and pyroclastic flows are highly concentrated flows. We provide scaling relations that unify these end-members and derive a segregation mechanism into basal concentrated flow and overriding dilute cloud based on the Stokes number (S_T), the stability factor (Σ_T) and the dense-dilute condition (D_D). We recognize five types of particle behaviors within a fluid eddy as a function of S_T and Σ_T: (1) particles sediment from the eddy, (2) particles are preferentially settled out during the downward motion of the eddy, but can be carried during its upward motion, (3) particles concentrate on the periphery of the eddy, (4) particles settling can be delayed or ‘fast-tracked’ as a function of the eddy spatial distribution, and (5) particles remain homogeneously distributed within the eddy. We extend these concepts to a fully turbulent flow by using a prototype of kinetic energy distribution within a full eddy spectrum and demonstrate that the presence of different particle sizes leads to the density stratification of the current. This stratification may favor particle interactions in the basal part of the flow and D_D determines whether the flow is dense or dilute. Using only intrinsic characteristics of the current, our model explains the discontinuous features between pyroclastic flows and surges while conserving the concept of a continuous spectrum of density currents.     

A laboratory investigation into the effects of slope on lava flow morphology

In an attempt to model the effect of slope on the dynamics of lava flow emplacement, four distinct morphologies were repeatedly produced in a series of laboratory simulations where polyethylene glycol (PEG) was extruded at a constant rate beneath cold sucrose solution onto a uniform slope which could be varied from 1° through 60°. The lowest extrusion rates and slopes, and highest cooling rates, produced flows that rapidly crusted over and advanced through bulbous toes, or pillows (similar to subaerial “toey” pahoehoe flows and to submarine pillowed flows). As extrusion rate and slope increased, and cooling rate decreased, pillowed flows gave way to rifted flows (linear zones of liquid wax separated by plates of solid crust, similar to what is observed on the surface of convecting lava lakes), then to folded flows with surface crusts buckled transversely to the flow direction, and, at the highest extrusion rates and slopes, and lowest cooling rates, to leveed flows, which solidified only at their margins. A dimensionless parameter, Ψ, primarily controlled by effusion rate, cooling rate and flow viscosity, quantifies these flow types. Increasing the underlying slope up to 30° allows the liquid wax to advance further before solidifying, with an effect similar to that of increasing the effusion rate. For example, conditions that produce rifted flows on a 10° slope result in folded flows on a 30° slope. For underlying slopes of 40°, however, this trend reverses, slightly owing to increased gravitational forces relative to the strength of the solid wax. Because of its significant influence on heat advection and the disruption of a solid crust, slope must be incorporated into any quantitative attempt to correlate eruption parameters and lava flow morphologies. These experiments and subsequent scaling incorporate key physical parameters of both an extrusion and its environment, allowing their results to be used to interpret lava flow morphologies on land, on the sea floor, and on other planets.     

Depositional mechanics of turbulent nuées ardentes (surges) from their grain sizes

The ability of turbulent nuées ardentes (surges) to transport coarse pyroclasts has been questioned on the basis that settling velocities of coarse fragments in the deposits are much too high for them to have been supported by turbulence in a dilute gas suspension. A computer model is used to evaluate the settling velocity of pyroclasts in suspensions of varying concentration and temperature. Since suspension of grains in low-concentration surges occurs if the shear velocity exceeds the settling velocity, the shear velocities related to the 16th and 84th percentiles, and the mean of the grain-size distribution are compared in surge deposits of the Vulsini, with the shear velocity necessary to move the coarsest grain on the bed surface (the Shields criterion). The results show that the settling velocities do not vary significantly in gaseous suspensions having volume concentrations lower than 15%, and that an increase in concentration to 25% is not sufficient to decrease the settling velocity of the coarser fraction, if it represents flow shear velocity. It is shown that the settling velocity of the mean grain size (M _z ) best depicts the shear velocity of a dilute turbulent suspension. Applying the results to the May 1902 paroxysmal nuées ardentes of Mount Pelée shows that the estimated mean velocities are well within the observed velocities, and sufficient to support all the clasts in dilute, turbulent suspensions.     

Near-bottom stratified currents and sediment transport in reservoirs and lakes

Results of field and theoretical studies of suspension transport by density currents are presented. The suspension transport is described by a mathematical model taking into account turbulent roiling and involvement, sedimentation, and bed erosion, variations in the vertical component of mean velocity, the relationship between the particles’ settling velocity and the distribution of their concentrations between the near-bottom and the overlaying water, on the one hand, and flow stability and velocity, on the other hand. The theoretical distributions of suspension concentrations are compared with those measured in 20 flows in nine reservoirs and lakes.     

The 1975 sub-terminal lavas, mount etna: a case history of the formation of a compound lava field

The 1975 sub-terminal activity was characterised by low effusion rates (0.3–0.5 m³ s⁻¹) and the formation of a compound lava field composed of many thousands of flow units. Several boccas were active simultaneously and effusion rates from individual boccas varied from about 10⁻⁴ to 0.25 m³s⁻¹. The morphology of lava flows was determined by effusion rate (E): aa flows with well-developed channels and levees formed when E > 2 × 10⁻³ m³ s⁻¹, small pahoehoe flows formed when 2 × 10⁻³ m³ s⁻¹ >E > 5 > 10⁻⁴ m³ s⁻¹ and pahoehoe toes formed when E < 5 × 10⁻⁴ m³ s⁻¹. There was very little variation with time in the effusion temperature, composition or phenocryst content of the lava.New boccas were commonly formed at the fronts of mature lava flows which had either ceased to flow or were moving slowly. These secondary boccas developed when fluid lava in the interior of mature aa flows either found a weakness in the flow front or was exposed by avalanching of the moving flow front. The resulting release of fluid lava was accompanied by either partial drainage of the mature flow or by the formation of a lava tube in the parent flow. The temperature of the lava forming the new bocca decreased with increasing distance from the source bocca (0.035°C m⁻¹). It is demonstrated from the rate of temperature decrease and from theoretical considerations that many of the Etna lavas still contained a substantial proportion of uncooled material in their interior as they came to rest. The formation of secondary boccas is postulated to be one reason why direct measurements of effusion rates tend, in general, to overestimate the total effusion rates of sub-terminal Etna lava fields.     

Energy losses in compound open channels

This paper investigates energy losses in compound channel under non-uniform flow conditions. Using the first law of thermodynamics, the concepts of energy loss and head loss are first distinguished. They are found to be different within one sub-section (main channel or floodplain). Experimental measurements of the head within the main channel and the floodplain are then analyzed for geometries with constant or variable channel width. Results show that head loss differs from one sub-section to another: the classical 1D hypothesis of unique head loss gradient appears to be erroneous. Using a model that couple 1D momentum equations, called “Independent Sub-sections Method (ISM)”, head losses are resolved. The relative weights of head losses related to bed friction, turbulent exchanges and mass transfers between sub-sections are estimated. It is shown that water level and the discharge distribution across the channel are influenced by turbulent exchanges for (a) developing flows in straight channels, but only when the flow tends to uniformity; (b) flows in skewed floodplains and symmetrical converging floodplains for small relative flow depth; (c) flows in symmetrical diverging floodplains for small and medium relative depth. Flow parameters are influenced by the momentum flux due to mass exchanges in all non-prismatic geometries for small and medium relative depth, while this flux is negligible for developing flows in straight geometry. The role of an explicit modeling of mass conservation between sub-sections is eventually investigated.