Analysis of turbulent flows in fixed and moving permeable media

The ability to realistically model flows through heterogeneous domains, which contain both solid and fluid phases, can benefit the analysis and simulation of complex real-world systems. Environmental impact studies, as well as engineering equipment design, can both take advantage of reliable modelling of turbulent flow in permeable media. Turbulence models proposed for such flows depend on the order of application of volume-and time-average operators. Two methodologies, following the two orders of integration, lead to distinct governing equations for the statistical quantities. This paper reviews recently published methodologies to mathematically characterize turbulent transport in permeable media. A new concept, called double-decomposition, is here discussed and instantaneous local transport equations are reviewed for clear flow before the time and volume averaging procedures are applied to them. Equations for turbulent transport follow, including their detailed derivation and a proposed model for suitable numerical simulations. The case of a moving porous bed is also discussed and transport equations for the mean and turbulent flow fields are presented.     

Explicit data-driven models for prediction of pressure fluctuations occur during turbulent flows on sloping channels

Stochastic Environmental Research and Risk Assessment - Pressure fluctuations are among the favorite topics for hydraulic engineers due to their critical role in the design and safe operation of...     

Modeling the interaction between water flows

Approaches to schematization used in the models of interacting water flows in different media are considered. Studies of the interaction between subsurface and surface waters are analyzed. Specific features of water flow-out from watercourses (channels), pipelines, etc. are discussed. Some steady-state problems are formulated, and their solutions are given. Dynamic effects of pressure changes in water flows are shown based on these solutions. The effects that appear in such cases are explained theoretically and correlated with experiments.     

Modified models for better prediction of infiltration rates in trapezoidal permeable stormwater channels

ABSTRACT

In stormwater management, it is important to accurately quantify the infiltration rates to solve urban runoff-related problems. This study proposes a method to improve estimates of the infiltration rate in permeable stormwater channels. As part of the analysis, five infiltration models were evaluated: the Kostiakov, Horton, modified Kostiakov, Philip and SCS (Soil Conservation Service) models. Infiltration tests with various initial water levels were performed on channel models with differing base width and side slopes. The results show that the addition of three parameters that describe the trapezoidal cross-sectional area, i.e. the depth, side slope and base width, in the infiltration models yielded better estimates of the infiltration rate. A comparison of the infiltration capacity values obtained from the models after the three parameters were added with those that were experimentally obtained, shows that the improved modified Kostiakov model is the most suitable model to predict infiltration rates in trapezoidal permeable stormwater channels.     

Analysis of depth-dependent pressure head of slug tests in highly permeable aquifers

A curve-matching method is developed for the analysis of depth-dependent pressure head responding to a slug test in a highly permeable aquifer. The depth dependency is due to the fact that the pressure transducer is placed at depth relatively far from the initial water level. The Springer and Gelhar solution and a depth correction relation are used to generate theoretical curves of pressure head vs. time. A trial-and-error procedure is established to find the theoretical curve best fitting the field data by adjusting the two unknown parameters, the horizontal hydraulic conductivity, and the effective length of the water column. Analytic relations for some oscillation characteristics of the converted pressure head are derived. A field example indicates that the theoretical relations and the curve-matching method developed herein are suitable to deal with the oscillatory head data dependent on depth of measurement. Nevertheless, it is recognized that placing the pressure transducer close to the initial water level and using a small initial water displacement can effectively avoid complicating the data analysis, such that previous, simpler data analysis methods can be used.     

The incidence and nature of bedload transport during flood flows in coarse-grained alluvial channels

A continuous record reveals that the incidence of bedload in a coarse-grained river channel changes from flood to flood. Long periods of inactivity encourage the channel bed to consolidate sufficiently so that bedload is largely confined to the recession limb of the next flood-wave. But when floods follow each other closely, the bed material is comparatively loose and offers less resistance to entrainment. In this case, substantial amounts of bedload are generated on the rising limb. This is confirmed by values of bed shear stress or stream power at the threshold of initial motion which can be up to five times the overall mean in the case of isolated floods or those which are the first of the season. This produces a complicated relationship between flow parameters and bedload and explains some of the difficulties in establishing bedload rating curves for coarse-grained channels. Besides this, the threshold of initial motion is shown to occur at levels of bed shear stress three times those at the thresholds of final motion. This adds further confusion to attempts at developing predictive bedload equations and clearly indicates at least one reason why equations currently in use are unsatisfactory. Bedload is shown to be characterized by a series of pulses with a mean periodicity of 1.7 hours. In the absence of migrating bedforms, it is speculated that this well-documented pattern reflects the passage of kinematic waves of particles in a slow-moving traction carpet. The general pattern of bedload, including pulsations, is shown to occur more or less synchronously at different points across the stream channel.     

Depositional processes and gas pore pressure in pyroclastic flows: an experimental perspective

The depositional processes and gas pore pressure in pyroclastic flows are investigated through scaled experiments on transient, initially fluidized granular flows. The flow structure consists of a sliding head whose basal velocity decreases backwards from the front velocity (U _f) until onset of deposition occurs, which marks transition to the flow body where the basal deposit grows continuously. The flows propagate in a fluid-inertial regime despite formation of the deposit. Their head generates underpressure proportional to U _f ² whereas their body generates overpressure whose values suggest that pore pressure diffuses during emplacement. Complementary experiments on defluidizing static columns prove that the concept of pore pressure diffusion is relevant for gas-particle mixtures and allow characterization of the diffusion timescale (t _d) as a function of the material properties. Initial material expansion increases the diffusion time compared with the nonexpanded state, suggesting that pore pressure is self-generated during compaction. Application to pyroclastic flows gives minimum diffusion timescales of seconds to tens of minutes, depending principally on the flow height and permeability. This study also helps to reconcile the concepts of en masse and progressive deposition of pyroclastic flow units or discrete pulses. Onset of deposition, whose causes deserve further investigation, is the most critical parameter for determining the structure of the deposits. Even if sedimentation is fundamentally continuous, it is proposed that late onset of deposition and rapid aggradation in relatively thin flows can generate deposits that are almost snapshots of the flow structure. In this context, deposition can be considered as occurring en masse, though not strictly instantaneously.     

Typical properties of dynamic systems and the instability of hydrodynamic flows

Summary Based on Peixot's theorem of topological dynamics, the unstable behaviour of hydrodynamic flows on a two-dimensional annuloid T ² is analysed. The generating property is the curvature of the group of S ₀ Diff T ² diffeomorphisms of the (Riemannian) flow region T ² . This group is the configuration space of the ideal fluid flowing on T ² .

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a m ma u mn u ¶rt;uauu ¶rt;am mu n¶rt;uu¶rt;¶rt;uauu nm a ¶rt; m T ² u¶rt; mu. ¶rt;au m m a m uuann S ₀ Diff T ² ¶rt;uu amu mu ( uaa) T ² . manna m uau nmam ¶rt; u¶rt;a u¶rt;mu a T ² .

     

A laboratory model of surface crust formation and disruption on lava flows through non-uniform channels

Crust formation on basaltic lava flows dictates conditions of both flow cooling and emplacement. For this reason, flow histories are dramatically different depending on whether lava is transported through enclosed lava tubes or through open channels. Recent analog experiments in straight uniform channels (Griffiths et al. J Fluid Mech 496:33–62, 2003) have demonstrated that tube flow, dictated by a stationary surface crust, can be distinguished from a mobile crust regime, where a central solid crust is separated from channel walls by crust-free shear zones, by a simple dimensionless parameter ϑ, such that ϑ<25 produces tube flow and ϑ>25 describes the mobile crust regime. ϑ combines a previously determined parameter ψ, which describes the balance between the formation rate of surface solid and the shear strain that disrupts the solid crust, with the effects of thermal convection (described by the Rayleigh number Ra).Here we explore ways in which ϑ can be used to describe the behavior of basaltic lava channels. To do this we have extended the experimental approach to examine the effects of channel irregularities (expansions, contractions, sinuosity, and bottom roughness) on crust formation and disruption. We find that such changes affect local flow behavior and can thus change channel values of ϑ. For example, gradual widening of a channel results in a decrease in flow velocity that causes a decrease in ϑ and may allow a down-flow transition from the mobile crust to the tube regime. In contrast, narrowing of the channel causes an increase in flow velocity (increasing ϑ), thus inhibiting tube formation.We also quantify the fraction of surface covered by crust in the mobile crust regime. In shallow channels, variations in crust width (d _c) with channel width (W) are predicted to follow d _c∼W ^5/3. Analysis of channelized lava flows in Hawaii shows crustal coverage consistent with this theoretical result along gradually widening or narrowing channel reaches. An additional control on crustal coverage in both laboratory and basaltic flows is disruption of surface crust because of flow acceleration through constrictions, around bends, and over breaks in slope. Crustal breakage increases local rates of cooling and may cause local blockage of the channel, if crusts rotate and jam in narrow channel reaches. Together these observations illustrate the importance of both flow conditions and channel geometry on surface crust development and thus, by extension, on rates and mechanisms of flow cooling. Moreover, we note that this type of analysis could be easily extended through combined use of FLIR and LiDAR imaging to measure crustal coverage and channel geometry directly.Editorial responsibility: A. Harris     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

The calibration and use of pressure transducers in tensiometer systems

The uncertainty in a transducer/tensiometer system was assessed with temperature and pressure calibrations. A reference transducer/tensiometer pair was used to factor out temperature related deviations from two monitoring pairs. The reference pair removed most of the deviations, resulting in a high estimate of precision. In contrast to earlier reports of high accuracy, these estimates of accuracy were considerably reduced by a time correlated residual pattern. The calibrations suggested that the electronic components may be responsible for these residual errors and illustrated the need for experimentation which isolates the error among groups of components. The complexity of transducer/tensiometer networks, and the differing response of each component to thermal loading, demonstrated the necessity of using a reference system, which when properly designed can yield reliable pressure readings for soil water.     

Modeling multiple wave systems in the eastern equatorial Pacific

Ocean Dynamics - While moderate wind and wave conditions prevail in the eastern equatorial Pacific, modeling waves in this area remains challenging due to the presence of multiple wave systems...     

Convection in rotating annular channels heated from below. Part 1. Linear stability and weakly nonlinear mean flows

Convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral rigid sidewalls, stress-free top and bottom, uniformly heated from below is investigated. The sidewalls are assumed to be either perfectly insulating or conducting. Three different types of convection are identified when the channel is rotating sufficiently fast: (i) global oscillatory convection preferred for small Prandtl numbers in channels with intermediate or large aspect ratios (width to height ratio), (ii) wall-localized oscillatory convection representing the most unstable mode for moderate or large Prandtl numbers in channels with intermediate or large aspect ratios and (iii) global stationary convection preferred in channels with sufficiently small aspect ratios regardless of the size of the Prandtl number. The corresponding weakly nonlinear problem describing differential rotation and meridional circulation is also examined, showing that geostrophic, multiple-peaked (two prograde and two retrograde) differential rotation can be maintained by the Reynolds stresses in wall-localized convective eddies in a rapidly rotating channel.     

The law of increasing air content and the length of the aeration development zone in accelerated turbulent flows in prismatic channels

The distribution law of averaged coefficients of aeration is established for the aeration zone in accelerated turbulent flows in prismatic channels, and a technique is proposed for the evaluation of the length of this zone. Both the results are in agreement with the data of special laboratory studies. The estimation of the length of the aeration zone is based on relationships derived by the author and verified for flow-controlling parameters varying within wide limits. The law of increasing air content was also confirmed by field measurement data.     

Modeling of pyroclastic flows of Colima Volcano,Mexico: implications for hazard assessment

The 18–24 January 1913 eruption of Colima Volcano consisted of three eruptive phases that produced a complex sequence of tephra fall, pyroclastic surges and pyroclastic flows, with a total volume of 1.1 km³ (0.31 km³ DRE). Among these events, the pyroclastic flows are most interesting because their generation mechanisms changed with time. They started with gravitanional dome collapse (block-and-ash flow deposits, Merapi-type), changed to dome collapse triggered by a Vulcanian explosion (block-and-ash flow deposits, Soufrière-type), then ended with the partial collapse of a Plinian column (ash-flow deposits rich in pumice or scoria,). The best exposures of these deposits occur in the southern gullies of the volcano where Heim Coefficients (H/L) were obtained for the various types of flows. Average H/L values of these deposits varied from 0.40 for the Merapi-type (similar to the block-and-ash flow deposits produced during the 1991 and 1994 eruptions), 0.26 for the Soufrière-type events, and 0.17–0.26 for the column collapse ash flows. Additionally, the information of 1991, 1994 and 1998–1999 pyroclastic flow events was used to delimit hazard zones. In order to reconstruct the paths, velocities, and extents of the 20th Century pyroclastic flows, a series of computer simulations were conducted using the program FLOW3D with appropriate Heim coefficients and apparent viscosities. The model results provide a basis for estimating the areas and levels of hazard that could be associated with the next probable worst-case scenario eruption of the volcano. Three areas were traced according to the degree of hazard and pyroclastic flow type recurrence through time. Zone 1 has the largest probability to be reached by short runout (<5 km) Merapi and Soufrière pyroclastic flows, that have occurred every 3 years during the last decade. Zone 2 might be affected by Soufriere-type pyroclastic flows (∼9 km long) similar to those produced during phase II of the 1913 eruption. Zone 3 will only be affected by pyroclastic flows (∼15 km long) formed by the collapse of a Plinian eruptive column, like that of the 1913 climactic eruption. Today, an eruption of the same magnitude as that of 1913 would affect about 15,000 inhabitants of small villages, ranches and towns located within 15 km south of the volcano. Such towns include Yerbabuena, and Becerrera in the State of Colima, and Tonila, San Marcos, Cofradia, and Juan Barragán in the State of Jalisco.