Analytical Solutions for Steady Phreatic Flow Appearing/Re-emerging Toward/from a Bedrock/Caprock Isobaric Breach: The Polubarinova-Kochina–Numerov and Pavlovsky Problems Revisited

© 2015, Springer Science+Business Media Dordrecht. Analytical solutions for steady, confined and unconfined Darcian flows in aquifers breached by “windows” in caprocks or bedrocks with applications to hillslope hydrology are presented. As compared with classical Polubarinova-Kochina, Numerov and Pavlovsky analytical solutions, the aquifers are sloping and the “window” is a finite-size isobaric segment, which due to the aquifer dip brings about a nonconstant head boundary condition. The velocity hodograph, method of boundary value problems and conformal mappings are used for obtaining solutions of essentially 2D seepage problems with Laplace’s PDE as a governing equation and the nonlinear phreatic surface for an unconfined flow. The second-order hydraulic theory with Picard’s iteration is used for deriving and solving a nonlinear ODE with respect to the shape of the water table, that is, compared with standard Dupuit–Forchheimer computations. The size of the “window,” incident flow parameters upstream of the “window” and the angle of tilt determine the disturbance to a main aquifer, mundanely normal “longitudinal” flow, which may completely dive or unexpectedly extravasate into a commingled adjacent subjacent–superjacent layer

Groundwater flow in hillslopes: Analytical solutions by the theory of holomorphic functions and hydraulic theory

© 2014 Elsevier Inc. Three 2-D steady Darcian flows in an aquifer with a subjacent confining layer of a non-constant slope or a bedding inconformity are studied by two models: a potential theory (conformal mappings, the inverse boundary-value problem method, and the theory of R-linear conjugation) and hydraulic approximation. First, flow over a corner, whose vertex is either a stagnation point or point of infinite Darcian velocity, is analysed as a transition from one "normal" regime upstream to another downstream. The hodograph domain is a circular triangle, which is mapped onto a complex potential strip via an auxiliary half-plane. Parametric equations (backwater curves) for the phreatic surface are obtained. For the same flow problem, a depth-averaged 1-D nonlinear ODE for the thickness of the saturated zone (a generalized Dupuit-Fawer model) is numerically solved showing a perfect match with the potential (2-D) solution. Second, a non-planar aquifuge boundary is reconstructed as a streamline, along which an additional "control" boundary condition holds in the form of pore pressure as a function of an auxiliary variable (a relation between the hydraulic head and vertical Cartesian coordinate). The free surface is found in terms of Cauchy's integrals for the Zhukovskii function, with explicit integrations for selected "controls". Third, a confined flow in a two-layered aquifer having a lens-type semi-circular inclusion in the subjacent stratum and incident velocity parallel to the interface between two aquifers is examined. The conjugation conditions along all four boundaries, across which the hydraulic conductivity jumps, are exactly met. The three velocity fields are explicitly presented, with examination of the flow net, including separatrices ("capture zone" boundaries), demarcating suction/barriering of the lens, and evaluation of the lens-induced cross-flow (commingling) between the two strata

Hydrodynamic modelling of overtopping flow over granular dikes

[EN] This paper presents a comparative analysis of the last advances in depth-averaged modelling of overtopping flow over granular dikes. Among the most relevant models in this field, three families of models are described: (i) non-hydrostatic models with sediment transport, (ii) hydrostatic models with sediment transport and dynamic granular beds, and (iii) hydrostatic models with sediment transport as bed-load. To study their suitability, examples of the three families of models are compared using experimental data of dike overtopping. Whilst the hydrostatic model with bed-load sediment transport shows a fair agreement with the experimental data, the results by the non-hydrostatic model produces a more accurate free surface profile up to the dike crest domain. The results by the hydrostatic model assuming dynamic bed deformation enhances the predictions near the dike toe downstream. Finally, the limitations of the models are discussed.[ES] Este trabajo presenta un análisis comparativo entre los últimos avances en el modelado promediado de flujos sobre diques de materiales sueltos. Entre los modelos más relevantes se encuentran: (i) modelos no hidrostáticos con transporte de sedimentos, (ii) modelos hidrostáticos con transporte de sedimentos y movimiento dinámico granular y (iii) modelos hidrostáticos con transporte de sedimentos por carga de fondo. Los tres tipos de modelos son comparados con datos experimentales para discutir su aplicabilidad. Mientras que el modelo hidrostático con transporte de sedimentos por carga de fondo presenta una solución adecuada en términos generales, el modelo no hidrostático permite mejorar la predicción del flujo en la cresta del dique, mientras que el modelo con movimiento granular dinámico permite mejorar las predicciones cerca del pie del dique. Por último, se discuten las limitaciones de los modelos.Este trabajo ha sido financiado por el Ministerio de Ciencia, Innovación y Universidades a través del proyecto de investigación CTM2017-85171-C2-1-R, el Programa Juan de la Cierva 2016 (FJCI-2016-28009) y el Programa Juan de la Cierva 2017 (FJCI-2017-31781).Cantero-Chinchilla, F.; Bergillos, R.; Castro-Orgaz, O. (2019). Modelización hidrodinámica del flujo sobre diques de materiales sueltos. Ingeniería del Agua. 23(3):215-227. https://doi.org/10.4995/ia.2019.12085SWORD21522723

Efecto de diferentes formulaciones de carga de fondo en flujos transitorios con lecho móvil

El objetivo de este trabajo es realizar un estudio comparativo entre diferentes formulaciones de carga de fondo (García, 2008), y su efecto en transitorios con lecho móvil, tomando como caso de estudio la rotura de presa, a través de la modificación empírica propuesta por Wu y Wang (2007). Para ello se emplean las ecuaciones de Saint-Venant para lecho móvil desarrolladas por Wu y Wang (2007), las cuales se resuelven mediante el uso de un esquema de volúmenes finitos

Near-critical free-surface flows: Real fluid flow analysis

An open channel flow with a flow depth close to the critical depth is characterised by a curvilinear streamline flow field that results in steady free surface undulations. Near critical flows of practical relevance encompass the undular hydraulic jump when the flow changes from supercritical (F > 1) to subcritical (F 1). So far these flows were mainly studied based on ideal fluid flow computations, for which the flow is assumed irrotational and, thus, shear forces are absent. While the approach is accurate for critical flow conditions (F = 1) in weir and flumes, near-critical flows involve long distances reaches, and the effect of friction on the flow properties cannot be neglected. In the present study the characteristics of near-critical free-surface flows are reanalysed based on a model accounting for both the streamline curvature and friction effects. Based on the improved model, some better agreement with experimental results is found, thereby highlighting the main frictional features of the flow profiles

A Bayesian assessment of an approximate model for unconfined water flow in sloping layered porous media

The prediction of water table height in unconfined layered porous media is a difficult modelling problem that typically requires numerical simulation. This paper proposes an analytical model to approximate the exact solution based on a steady-state Dupuit–Forchheimer analysis. The key contribution in relation to a similar model in the literature relies in the ability of the proposed model to consider more than two layers with different thicknesses and slopes, so that the existing model becomes a special case of the proposed model herein. In addition, a model assessment methodology based on the Bayesian inverse problem is proposed to efficiently identify the values of the physical parameters for which the proposed model is accurate when compared against a reference model given by MODFLOW-NWT, the open-source finite-difference code by the U.S. Geological Survey. Based on numerical results for a representative case study, the ratio of vertical recharge rate to hydraulic conductivity emerges as a key parameter in terms of model accuracy so that, when appropriately bounded, both the proposed model and MODFLOW-NWT provide almost identical results

Analytical determination of irrotational flow profiles in open-channel transitions

Transitional free surface flow profiles with a critical point occur with weak vorticity and viscosity effects and thus can be modeled with an irrotational flow approach. Important examples in hydraulic engineering include flow over low obstacles, transition structures in canals, and flow over high spillways. While solving Laplace’s equation is relatively simple, the determination of the unknown free surface and energy head of the flow is challenging. Both hydraulic quantities need to be iterated before solving the Laplace equation. Former models iterated the energy head on a trial-and-error basis, assuming that the linked free surface profile is smooth, i.e., free of waves. The iteration of the free surface for a given head is frequently accomplished using the Newton–Rapshon method, which is difficult for the challenging case of spillway flow, giving no solution in some cases. An alternative method of computing irrotational flow profiles in transitional flows involving a critical point is proposed in this work. The model contains three elements: mapping of Laplace’s equation to directly track the streamlines, determination of the critical point and unknown energy head using a critical flow condition for irrotational flows, and determination of the water surface position using an exact analytical solution. The proposed model is favorably compared with experimental data from different sources and CFD results, indicating a reasonable agreement

Analytical Solutions for Steady Phreatic Flow Appearing/Re-emerging Toward/from a Bedrock/Caprock Isobaric Breach: The Polubarinova-Kochina–Numerov and Pavlovsky Problems Revisited

© 2015, Springer Science+Business Media Dordrecht. Analytical solutions for steady, confined and unconfined Darcian flows in aquifers breached by “windows” in caprocks or bedrocks with applications to hillslope hydrology are presented. As compared with classical Polubarinova-Kochina, Numerov and Pavlovsky analytical solutions, the aquifers are sloping and the “window” is a finite-size isobaric segment, which due to the aquifer dip brings about a nonconstant head boundary condition. The velocity hodograph, method of boundary value problems and conformal mappings are used for obtaining solutions of essentially 2D seepage problems with Laplace’s PDE as a governing equation and the nonlinear phreatic surface for an unconfined flow. The second-order hydraulic theory with Picard’s iteration is used for deriving and solving a nonlinear ODE with respect to the shape of the water table, that is, compared with standard Dupuit–Forchheimer computations. The size of the “window,” incident flow parameters upstream of the “window” and the angle of tilt determine the disturbance to a main aquifer, mundanely normal “longitudinal” flow, which may completely dive or unexpectedly extravasate into a commingled adjacent subjacent–superjacent layer

Analytical Solutions for Steady Phreatic Flow Appearing/Re-emerging Toward/from a Bedrock/Caprock Isobaric Breach: The Polubarinova-Kochina–Numerov and Pavlovsky Problems Revisited

© 2015, Springer Science+Business Media Dordrecht. Analytical solutions for steady, confined and unconfined Darcian flows in aquifers breached by “windows” in caprocks or bedrocks with applications to hillslope hydrology are presented. As compared with classical Polubarinova-Kochina, Numerov and Pavlovsky analytical solutions, the aquifers are sloping and the “window” is a finite-size isobaric segment, which due to the aquifer dip brings about a nonconstant head boundary condition. The velocity hodograph, method of boundary value problems and conformal mappings are used for obtaining solutions of essentially 2D seepage problems with Laplace’s PDE as a governing equation and the nonlinear phreatic surface for an unconfined flow. The second-order hydraulic theory with Picard’s iteration is used for deriving and solving a nonlinear ODE with respect to the shape of the water table, that is, compared with standard Dupuit–Forchheimer computations. The size of the “window,” incident flow parameters upstream of the “window” and the angle of tilt determine the disturbance to a main aquifer, mundanely normal “longitudinal” flow, which may completely dive or unexpectedly extravasate into a commingled adjacent subjacent–superjacent layer