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Parlange, J.‐Y.; Hogarth, W. L.; Govindaraju, Rao S.; Parlange, M. B.; Lockington, David

doi:10.1023/a:1006504527622

Cited by 49 publications

(9 citation statements)

References 4 publications

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“…It should be noted that the linearization of the nonlinear Boussinesq equation (without term with first head derivative) is widely adopted in the previous studies (Chang & Yeh, 2010;Govindaraju & Koelliker, 1994;Liang et al, 2018;Liang & Zhang, 2012a;Liang & Zhang, 2012b;Pauwels & Troch, 2010;Rotzoll et al, 2008;Troch et al, 2004;Verhoest & Troch, 2000) because the nonlinear Boussinesq equation is difficult to solve analytically except for a few special cases (Guo, 1997;Parlange et al, 2000;Serrano, 1995). Boundaries of linearization validity have been firmly established since early studies (Bear, 1972, Section 8.4).…”

Section: Problem Statementmentioning

confidence: 99%

Diagnostic Analysis of Bank Storage Effects on Sloping Floodplains

Liang

Zlotnik

Zhang

et al. 2020

Water Resources Research

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Stream bank storage effects during floods have received limited attention, despite the significant role of such floods in aquifer water budgets. One reason is the complexity of geometry of the problem, which commonly has been treated numerically. Using a simple model in a domain with moving boundary, a semianalytical solution for bank storage effects is proposed to account for stream stage hydrograph, floodplain slope, and aquifer parameters. The results extend classic solutions by Cooper and Rorabaugh (1963, https://doi.org/10.3133/wsp1536J) for idealized vertical streambanks but applied to realistic floodplain cross sections. The accuracy of the semianalytical solution is verified by a one‐dimensional numerical method and compared to a vertical two‐dimensional variably saturated‐flow numerical model. Comparison indicates that a robust solution is valid for diagnostic analyses of modeling bank storage effects on floodplains. The semianalytical solution is applied to laboratory experiments as well. The results indicate that the present solution provides reasonable estimates of peak timing and head of groundwater flow response in the sloping bank during varying stream stage.

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Section: Problem Statementmentioning

confidence: 99%

Diagnostic Analysis of Bank Storage Effects on Sloping Floodplains

Liang

Zlotnik

Zhang

et al. 2020

Water Resources Research

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“…[15] Subsequently, the Boussinesq equation (3) has been solved exactly for only a limited number of boundary and/ or initial conditions, all in the absence of rainfall recharge. Parlange et al [2000] found a solution for initially parabolic water tables in a horizontal and finite aquifer. For what is, as far as we know, the only known exact solution for a sloping aquifer, Daly and Porporato [2004] described the evolution of a groundwater mound in an aquifer that is Figure 1.…”

Section: Exact Solutionsmentioning

confidence: 99%

The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange

et al. 2013

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[1] Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interactions, hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to Dupuit and Forchheimer. Boussinesq (1877) derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes, resulting in a remarkably accurate and applicable family of results, though often challenging to solve due to its nonlinear form. Under certain conditions, the Boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics. The Boussinesq equation has been extended to account for flow divergence/convergence as well as for nonuniform bedrock slope (concave/convex). The extended Boussinesq equation has been favorably compared to numerical solutions of the three-dimensional Richards equation, confirming its validity under certain geometric conditions. Analytical solutions of the linearized original and extended Boussinesq equations led to the formulation of similarity indices for baseflow recession analysis, including scaling rules, to predict the moments of baseflow response. Validation of theoretical recession parameters on real-world streamflow data is complicated due to limited measurement accuracy, changing boundary conditions, and the strong coupling between the saturated aquifer with the overlying unsaturated zone. However, recent advances are shown to have mitigated several of these issues. The extended Boussinesq equation has been successfully applied to represent baseflow dynamics in catchment-scale hydrological models, and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models. From the review, it is clear that Wilfried Brutsaert and Jean-Yves Parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling.Citation: Troch, P. A., et al. (2013), The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange, Water Resour. Res., 49,[5099][5100][5101][5102][5103][5104][5105][5106][5107][5108][5109][5110][5111][5112][5113][5114][5115][5116]

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“…Therefore, solutions of the Boussinesq equation are important, and the topic of reaching either analytical or approximate solutions remains an active research topic. The current set of known solutions is by no means exhaustive, and many analytical solutions are being continuously proposed by considering different initial and boundary conditions representative for the problem under investigation [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase

Gravanis,

Akylas,

Sarris

2024

Water

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We construct approximate analytical solutions of the Boussinesq equation for horizontal unconfined aquifers in the buildup phase under constant recharge and zero-inflow conditions. We employ a variety of methods, which include wave solutions, self-similar solutions, and two classical linear approximations of the Boussinesq equation (linear and quadratic), to explore the behavior and performance of the solutions derived from each method against the Boussinesq equation and the exact (non-closed form) analytical solutions. We find that the wave approximation, which is of a conceptual nature, encapsulates quite faithfully the characteristics of the nonlinear Boussinesq equation solution and, overall, performs much better than the other methods, for which the relatively low performance can be attributed to the specific mathematical features of their construction. These endeavors might be useful for theoretical and modeling purposes related to this problem.

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Untitled

Cited by 49 publications

References 4 publications

Diagnostic Analysis of Bank Storage Effects on Sloping Floodplains

Diagnostic Analysis of Bank Storage Effects on Sloping Floodplains

The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange

Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase

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