Exact analytical expressions for the piezometric profile and water exchange between stream and groundwater during and after a uniform rise of the stream level

Boufadel, Michel C.; Peridier, Vallorie J.

doi:10.1029/2001wr000780

Cited by 15 publications

(10 citation statements)

References 17 publications

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“…These results are in conformity with the results obtained by Boufadel and Peridier (2002). One can also derive the expressions for the asymptotic cases of very fast and very slow rise of the water in the stream by taking γ → 0 and γ → ∞ in Eqs.…”

Section: Problem Formulation and Analytical Solutionsupporting

confidence: 74%

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Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

Bansal¹,

Das²

2009

Journal of Hydrology and Hydromechanics

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This paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate. Príspevok obsahuje analytické riešenie rovnice neustáleného prúdenia vzhľadom na neustálenú hydraulickú výšku, rýchlosť prúdenia a objemové toky vo zvodnenom kolektore s napätou hladinou, ktorý je v kontakte s konštantnou piezometrickou výškou na jednej strane a s tokom s konštantne sa zvyšujúcou hladinou vody na strane druhej.Zvodnený kolektor je tiež napájaný konštantnou rýchlosťou infiltrovanou vodou zo zrážok. Rovnica neustáleného prúdenia podzemnej vody je riešená s použitím Laplaceovej transformácie, aby sme získali neustálenú tlakovú výšku na ľavej aj pravej strane a objemový prítok vody na rozhraní zvodnený kolektortok.Výsledky analytického riešenia, ktoré predkladáme, ukazujú vplyv infiltrácie zrážok na doplňovanie podzemnej vody a odhaľujú podmienky, za ktorých prítok do zvodneného kolektora môže byť kladný, negatívny, alebo nulový. Získané výsledky umožňujú určiť neustálené hydraulické výšky pre dva extrémne scenáre: (i) veľmi pomalé a (ii) veľmi rýchle zvýšenie hladiny vody v toku. Analytické riešenie ukazuje, že objem vody, ktorou je zvodnený kolektor doplňovaný, môže byť kladný, záporný, alebo nulový, v závislosti na intenzite infiltrácie a rýchlosti zvyšovania sa hladiny vody v toku.KĽÚČOVÉ SLOVÁ: piezometrická výška, rýchlosť prúdenia, prítok do podzemných vôd, ohraničený zvodnený kolektor, analytické riešenia, Laplaceova transformácia.

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Section: Problem Formulation and Analytical Solutionsupporting

confidence: 74%

“…Exhaustive reference on earlier works can be obtained from the monographs of Polubarinova-Kochina (1962) and Huisman (1978). Recently Boufadel and Peridier (2002) have presented the analytical expressions for hydraulic head and volumetric exchange of water between an aquifer and a constantly rising stream under no recharge condition.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

Bansal¹,

Das²

2009

Journal of Hydrology and Hydromechanics

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“…The rise rate of the stream water plays an important role in determining the free surface as well as its stabilization. A fast rising stream reduces the outflow at stream-aquifer interface, leading to growth in the water table (Boufadel and Peridier 2002). It is evident from Fig.…”

Section: Discussion Of Resultsmentioning

confidence: 96%

Response of an Unconfined Sloping Aquifer to Constant Recharge and Seepage from the Stream of Varying Water Level

Bansal

Das

2010

Water Resour Manage

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This paper presents analytical solution of one-dimensional linearized Boussinesq equation characterizing unsteady groundwater flow in an unconfined aquifer, overlying an impervious downward sloping bed. At one end, the aquifer is in contact with a constant water level and at the other end; water level is rising exponentially from an adjoining stream. The aquifer also receives constant or cycle of time-varying vertical recharge. Analytical expressions for hydraulic head and flow rate in the aquifer are obtained by solving the seepage model using Laplace transform. The expressions derived here can explain sudden rise or very slow rise in the stream water related to sloping or horizontal beds and are represented under asymptotic case. Response of a short and long aquifer to the variation in bed slope, recharge rate and rise rate of the stream water is illustrated with the help of numerical examples. The sensitivity of the flow rate is also analyzed with respect to various parameters. NomenclatureK hydraulic conductivity [LT −1 ] h 0 piezometric head at the left boundary [L] initial water level in the stream [L] x horizontal x-axis [L] t time [T] t r time period in which recharge changes from N 1 to N 2 [T] S specific yield [-] h water table height above impermeable bed [L] H normalized water head height [-] . L length of the domain [L] D aquifer's depth [L] N(t) time-varying recharge rate [LT −1 ] N 1 , N 2 constant recharge rates [LT −1 ] p linearization constant [-] X distance ratio x/L [-] A, B constants [-] H* normalized steady-state value of water head q flow rate [steady-state flow rate at x = 0 [-] Q * (x = L) normalized steady-state flow rate at x = L [-] β Slope angle of the aquifer's bed [-] λ Rise constant [T −1 ] α (L tan β)/2pD. τ normalized time [-] τ r normalized time corresponding to t = t r [-]

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“…Among these studies are numerical simulations of the hydraulics of the CF, the interactions of the CF with the water table, and the impact of these interactions on the behavior of groundwater systems. Boufadel et al (1999) and Boufadel and Peridier (2002), for example, report on numerical studies in which they demonstrate that the CF has significant impact on the formation of seepage faces and that this impact is significantly different under transient flow than under steady flow. Theoretical studies have also been compared to field observations.…”

Section: Introductionmentioning

confidence: 97%

Demonstration of microbial transport into the capillary fringe via advection from below the water table

Dunn

Silliman

Dhamwichukorn

et al. 2005

Journal of Hydrology

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Exact analytical expressions for the piezometric profile and water exchange between stream and groundwater during and after a uniform rise of the stream level

Cited by 15 publications

References 17 publications

Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

Response of an Unconfined Sloping Aquifer to Constant Recharge and Seepage from the Stream of Varying Water Level

Demonstration of microbial transport into the capillary fringe via advection from below the water table

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