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This study investigated the effects of fluctuating boundary water levels and surface recharge on groundwater flow within unconfined aquifers. We aimed to understand how changes in recharge patterns and variable boundary water levels, such as those from rivers or canals, affect groundwater levels over time and space. To achieve this, we solved the linearized Boussinesq equation using the time-marching method alongside the generalized integral transformation method. Our analysis focused on how different types of recharge affect groundwater level variations and flow dynamics. We found that boundary effects on groundwater level change propagate from the edges toward the aquifer's center, becoming more pronounced with increased boundary water levels. Over time, the system stabilizes, leading to a steady water table height and flow rate, which depend on the disparity between the boundary water levels. Our analytical model demonstrated flexibility and practical applicability by allowing for the consideration or omission of various influencing factors, thus facilitating complete knowledge about groundwater variations and offering future strategic insights for sustainable groundwater resource management. [ABSTRACT FROM AUTHOR]

The groundwater level in an unconfined aquifer near a river is strongly affected by rainfall and river level. The linearized Boussinesq equation has been used in numerous studies to analytically investigate the changes in groundwater level. A perturbation method was used to determine the non-linear term of the Boussinesq equation. The generalized integral transform technique (GITT) was subsequently used to obtain a semi-analytical solution. We compared this solution with a linearized analytical and non-linear numerical solution and investigated the influence of each parameter that affects the number of convergent terms in analytical solutions. To estimate the recharge volume, two methods, the Horton infiltration formula and a method in which the fraction of rainfall intensity is considered, were employed. Subsequently, the simulated groundwater levels were compared with the field data. Finally, the recharge type, namely unimodal, with and without the Horton infiltration formula was used to model the groundwater flow. [ABSTRACT FROM AUTHOR]

In nature, a soil profile generally consists of several heterogeneous layers. This study is aimed at discussing the interactive problem of oscillatory water waves and flow passing over multilayered soils. The soil behavior is considered as viscoelastic in the present mathematical model modified from Biot's poroelastic theory. Employing this model, the dynamic response including the profiles of pore water pressure and effective stress in the multilayered soils is discussed. The results reveal that the perturbed pore pressure is different from that inside a single-layered soil where the thickness of the first soil layer is less than the water wavelength. The discrepancy of the vertical effective stresses between multilayered and single-layered soils is even much more apparent under the same conditions. Moreover, seepage force is examined and is found to be larger near the bed surface and the bottom of the first soil layer where soils are easily disturbed by external disturbance. The locations where soil failure might happen are found near the troughs of surface water waves. DOI: 10.1061/(ASCE)0733-9399(2007)133:3(357) CE Database subject headings: Water waves; Viscoelasticity; Seepage; Multimedia.

This study examines low Reynolds number flow over vegetated sloping ground. Instead of using the traditional empirical formula related to resistance or frictional roughness, a new approach is presented by considering the flow inside the vegetation layer as porous media flow governed by Blot's poroelastic theory as well as inside the soil layer. There is a discrepancy in the velocity distributions of flow over vegetative mantle area and bare area, respectively. Due to the change of the vegetation density, the effects of vegetation porosity and vegetation blockage on surface water flow are discussed. DOI: 10.1061/(ASCE)0733-9429(2007)133:3(335) CE Database subject headings: Laminar flow; Vegetation; Reynolds number; Slopes; Surface waters.

The problem of the dynamic interaction of water waves, current, and a hard poroelastic bed is dealt with in this study. Finite-depth homogeneous water with harmonic linear water waves passing over a semi-infinite poroelastic bed is investigated. In order to reveal the importance of viscous effect for different bed forms, viscosity of water is considered herein. In a boundary layer correction approach, the governing equations of the poroelastic material are decoupled without losing physical generality. The contribution of pressure effect and shear effect to the hard poroelastic bed, which is a valuable indication to the mechanism of ripple formation, is clarified in the present study. This approach will be helpful in saving time and storage capacity when it is applied to numerical computation. DOI: 10.1061/(ASCE)0733-9399(2003)129:6(655) CE Database subject headings: Laminar flow; Viscosity; Water waves; Beds; Porous media.

The analytic solutions of inviscid and viscous water waves passing over a submerged rectangular dike are investigated. Owing to the fact that the orthogonality of eigenfunctions is invalid for viscous wave problem, two newly developed orthogonal inner products are applied to reduce the mathematical difficulty of viscous wave problem. Both inviscid and viscous water wave solutions are obtained under the assumption of linear water wave without separation. It shows that two solutions have no significant kinematic difference but the viscous contribution of dynamic effect is not negligible. Beside giving a better theoretical approach, which reduces the error of the conventional minimal squares method, the result of the present analytical solution can be used to quantitatively evaluate the correctness of experiments and also provides helpful information such as near wall boundary layer thickness and oscillating free surface for computational use. DOI: 10.1061/(ASCE)0733-9399(2003) 129:6(613) CE Database subject headings: Water waves; Dikes; Viscous flow; Submerging.

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Blot's theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength. DOI: 10.1061/(ASCE)0733-9399(2003)129:2(210) CE Database keywords: Water waves; Boundary processes; Beds; Thickness.

SUMMARY This work investigates the profiles of surface water flow over a pervious pavement, for example, highway, during a uniform rainfall. The pavement, such as porous asphalt or open-graded asphalt friction course, is regarded as a porous medium, and the flow inside the layer is porous media flow. At first, the velocity distributions are solved based on the simplified Navier-Stokes equations and Biot's theory of poroelasticity for the water layer and the permeable layer, respectively. Then, the flow profiles can be found via the continuity equation. Because the closed form of the water depth cannot be obtained, a numerical technique is employed to find the flow profiles on the pavement surface. A critical permeability factor related to the material and structure of pavement is illustrated to be η = 1.36 × 10− 4 m as the half road width L = 20 m, the cross slope S = 0.02,the pavement thickness H = 0.05 m, and rainfall intensity i = 100 mm/ h. The water on the road surface can be drained very fast, whereas the parameter is greater than the critical value. Another illustration of allowable/safety water depth is made for the design of the pavement thickness. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY A new approach is proposed to analyze the surface flow and subsurface flow passing over a pervious ground under a uniform rainfall excess. The flow field is divided into two regions that are called water layer and soil layer. To figure out the hydraulic behavior of overland flow on an inclined plane under a rainfall event, the simplified Navier-Stokes equations are employed for the surface water flow, and the flow inside the soil layer is porous media flow, which is governed by Biot's (1956, 1962) theory of poroelasticity. The velocity distribution of overland flow is nonzero at the ground surface. The relation between water depth and slope length was developed first. The profile of surface water flow was then found backwards from the downstream end of the flow section by the Runge-Kutta method. After that, the flow velocity and flow discharge of each layer could also be obtained via the water depth. Finally, the variation of fluid shear stress inside the soil layer is also discussed. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A direct analytical approach is proposed to study the turbulent surface water flow on a slope. Both unplanted ground and grassed ground are investigated by dividing the flow field into two layers-homogenous water layer/vegetation layer and permeable soil layer, respectively. The soil and vegetation layers are regarded as porous media, and Biot's poroelastic theory is applied. The effect of vegetation on flow velocity is also analyzed. As the Reynolds stresses become larger, the turbulent strength increases, and the velocity distributions become more uniform. The average velocity is compared with that calculated by Manning's formula and the kinematic-wave equation. The result shows that the average velocity using the kinematic-wave equation is the highest, and the present solution is the smallest for both cases. [ABSTRACT FROM AUTHOR]

Abstract: This study is aimed at investigating the vertical velocity profile of flow passing over a vegetal area by an analytical approach. The soil ground is considered as pervious and thus non-zero velocity at the ground surface can be estimated. The soil and vegetation layers are regarded as homogeneous and isotropic porous media. Therefore the solution of the flow can be obtained by applying the theory of turbulent flow and Biot’s theory of poroelasticity after dividing the flow field into three layers: homogenous water, vegetation and pervious soil. The velocity distribution is compared with the experimental data of [Rowiński PM, Kubrak J. A mixing-length model for predicting vertical velocity distribution on flows through emergent vegetation. J Hydrol Sci 2002;47(6):893–904] to show its validity. In addition, five dimensionless parameters denoting the variation of slope, permeability of soil, Reynolds stress, density of vegetation, and relative height of vegetation are proposed to reveal their effects on the surface water flow. The analytical solutions of flow velocity can also be simplified into simpler expressions to describe the flow passing over a non-vegetated area. [Copyright &y& Elsevier]