Time‐Dependent Linearized Infiltration. I. Point Sources

Warrick, A. W.

doi:10.2136/sssaj1974.03615995003800030008x

Cited by 135 publications

(104 citation statements)

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“…In the first paper of this series [Reval et al, this issue], a field test, we presented an analysis of the limitations of the steady state theory, and we concluded that there is a need to be able to simulate the transient wet-front movement away from drippers. Although time-dependent, the interesting theory of Warrick [1974] is unfortunately linearized, so that in a practical sense, it cannot be used to predict the penetration of the wet front [Clothier and Scatter, 1982]. So currently, there is no concise analytical theory that can encompass both the shorttime, capillary-dominated flow around a dripper as well as the geometrically and gravity-induced steady regime.…”

Section: Introductionmentioning

confidence: 99%

Infiltration from a surface point source and drip irrigation: 2. An approximate time‐dependent solution for wet‐front position

Revol¹,

Clothier²,

Mailhol³

et al. 1997

Water Resources Research

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Abstract. Raats' [1971] steady state theory is here extended to provide an approximate analysis of the transient pattern of wetting around a point source. The assumption that a steady state regime prevails behind the wet front and the use of the Clothier [1984] and Philip [1984] theories on water movement along the streamlines allows an approximate transient solution for surface point source infiltration to be developed. This procedure was previously tested against absorption theory and laboratory experiments [Revol et al., 1995], but now this new analysis is evaluated via a field test. The vertical elongating influence of gravity is found to be well predicted. Application of this analysis to design purposes is also mentioned. The role of the macroscopic characteristic capillary length of unsaturated flow, Xc, is highlighted by this approximate solution. Finally, we propose a method that allows estimation of Xc from a point-source infiltration experiment. IntroductionThe lateral spread of water away from a dripper, compared to its depth of penetration, is determined by the relative importance of the soil's capillarity and its hydraulic conductivity. The ability to predict the dimensions of the wetted bulb is important, both to ensure efficient irrigation and to avoid the environmentally deleterious passage of irrigation water beyond the root zone. The main advantage of analytical solutions is their fewer parameters requirements and the generalization they offer in relating inputs to system response, which are essential for making general inferences and developing recommendations. Existing analytical theories for three-dimensional infiltration, which can be used for drip irrigation, either are applicable only to the early stages of wetting [

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Section: Introductionmentioning

confidence: 99%

Infiltration from a surface point source and drip irrigation: 2. An approximate time‐dependent solution for wet‐front position

Revol¹,

Clothier²,

Mailhol³

et al. 1997

Water Resources Research

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“…Tanto a teoria, assim como os dados experimentais, indicam que para as condições estudadas, um incremento na taxa de descarga resulta num incremento do molhamento horizontal em detrimento do molhamento vertical. Parlange (1972) derivou expressões analíticas para a absorção de água a partir de cavidades cilíndricas e esféricas e Warrick (1974) analisou a infiltração em função do tempo utilizando uma equação de fluxo linearizada. Levin et al (1979) compararam a distribuição de umidade sob fontes pontuais a partir de dados obtidos experimentalmente e dados simulados empregando o modelo de Bresler (1975), encontrando uma boa concordância entres os dados simulados e os observados.…”

Section: Fluxo E Distribuição De áGua Sob Irrigação Por Gotejamentounclassified

“…Modelos de infiltração e redistribuição para fontes pontiformes foram apresentados por Brandt et al (1971), Warrick (1974), Ben-Asher et al (1978) e Warrick (1986, entre outros. Mmolawa (2000b) relatou que a dinâmica de água e solutos no solo, em ausência de culturas, pode ser representada adequadamente por soluções analíticas do fluxo transitório a partir de fontes puntiformes.…”

Section: Introductionunclassified

Modelagem da dinâmica da água e do potássio na irrigação por gotejamento superficial.

Rivera¹

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“…The quasi-linear approximation uses the exponential variation of relative hydraulic conductivity with pressure head as applied by Gardner [1958] to the modeling of soil properties. Combining this result with Kirchoff's Transformation and requiring that moisture content vary linearly with relative hydraulic conductivity as determined by Warrick [1974] allows the linearization of Richards' equation for both steady state and transient cases. Also important to note is that if the PDE is solved for the moisture content instead of pressure head, a linear PDE occurs naturally without the need for a transformation when using the above assumptions.…”

Section: Previous Workmentioning

confidence: 99%

Clean two‐ and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers

Tracy

2006

Water Resources Research

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[1] This technical note derives clean analytical solutions of Richards' equation for threedimensional unsaturated groundwater flow. Clean means that the boundary conditions and steady state solutions are closed form expressions and the transient solutions have relatively simple additional Fourier series terms. Two-dimensional versions of these solutions are also given. The primary purpose for the solutions is to test linear and nonlinear solvers in finite difference/volume/element computer programs for accuracy and scalability using architectures ranging from PCs to parallel high-performance computers. This derivation starts from the quasi-linear assumption of relative hydraulic conductivity varying exponentially with pressure head and the separate approximation that relative hydraulic conductivity varies linearly with moisture content. This allows a transformation to be used to create a linear partial differential equation. Separation of variables and Fourier series are then used to obtain the final solution. Physically reasonable material properties are also used. A total of four solutions are given in this technical note (steady state and transient solutions for two different boundary conditions of the sample problem).

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Time‐Dependent Linearized Infiltration. I. Point Sources

Cited by 135 publications

References 0 publications

Infiltration from a surface point source and drip irrigation: 2. An approximate time‐dependent solution for wet‐front position

Infiltration from a surface point source and drip irrigation: 2. An approximate time‐dependent solution for wet‐front position

Modelagem da dinâmica da água e do potássio na irrigação por gotejamento superficial.

Clean two‐ and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers

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