Mathematical Modeling of Tidal Effects in Groundwater

Ondovčin, Tomáš; Mls, J.; Herrmann, Leopold

doi:10.1007/s11242-012-0056-3

Cited by 3 publications

(7 citation statements)

References 13 publications

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“…For the purposes of sensitivity analysis, the forward problem was solved for multiple values of one of the parameters, while the others were fixed. As stated in [16], values of K, µ and M N were the most influencing. Low hydraulic conductivity K of the aquitard does not affect the amplitude of tidal oscillations.…”

Section: Sensitivity Analysismentioning

confidence: 79%

“…Comparison between the measurement in Police Basin in [19] and prediction from theory of [16] shows that the theory produces realistic oscillations in terms of their amplitude and overall character (see Fig. 9).…”

Section: Discussionmentioning

confidence: 97%

“…Rice and Cleary [15] introduced compressibility of both phases. Since the deformation is very small and slow and the process is considered to be drained, Biot's (1941) theory was rearranged and utilized in [16] in the form…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Two conceptual models were presented in [16] to predict the parameters of tidal oscillations. Each prescribes a special form of the function T .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The tidal force was computed using the tidal potential catalogue HW95 of [18]. See [16] for a detailed development of the forward problem. …”

Section: Mathematical Modelmentioning

confidence: 99%

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Models of earth-tide-induced groundwater oscillations in the Police Basin, Czech Republic

Ondovčin¹,

Mls²,

Herrmann³

2014

Advances in Fluid Mechanics X

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Earth-tide induced oscillations of hydraulic head occurring in a confined aquifer in an isolated block of rocks in the Police Basin, Czech Republic were studied. Two models were developed to demonstrate how earth-tide induced groundwater oscillations originate in the area. Due to the nature of the process, it was useful to utilize Biot's theory to predict the tidal oscillations. The resulting theory was applied in connection with two conceptual models involving geological structure of the site. This paper presents a sensitivity study of these models.

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Section: Sensitivity Analysismentioning

confidence: 79%

Section: Discussionmentioning

confidence: 97%

Section: Mathematical Modelmentioning

confidence: 99%

“…Two conceptual models were presented in [16] to predict the parameters of tidal oscillations. Each prescribes a special form of the function T .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The tidal force was computed using the tidal potential catalogue HW95 of [18]. See [16] for a detailed development of the forward problem. …”

Section: Mathematical Modelmentioning

confidence: 99%

See 3 more Smart Citations

Models of earth-tide-induced groundwater oscillations in the Police Basin, Czech Republic

Ondovčin¹,

Mls²,

Herrmann³

2014

Advances in Fluid Mechanics X

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Temperature fluctuations underneath the ice in Diamond Lake, Hennepin County, Minnesota

et al. 2013

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[1] Diamond Lake in Minnesota is covered every winter with ice and snow providing a modified thermal insulation between water and air. Autonomous temperature sensors, data loggers, were placed in this lake so that hourly measurements could be obtained from the snow-covered ice and water. The sensors that became frozen measured damped and delayed thermal response from the air-temperature fluctuation. Those sensors that were deeper within the snow-covered ice measured continuous, almost constant, temperature values near freezing. Several of them were within the liquid water and responded with a fluctuation of 24 h periods of amplitudes up to 0.2 C. Our analysis of the vertical temperature profiles suggested that the source of periodic water heating comes from the lake bottom. Because of the absence of daily temperature variations of the snow-covered ice, the influence of the airtemperature fluctuation can be ruled out. We attribute the heating process to the periodic inflow of groundwater to the lake and the cooling to the heat diffusion to the overlying ice cover. The periodic groundwater inflow is interpreted due to solid Earth tides, which cause periodic fluctuations of the groundwater pressure head.

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Oscillatory Solutions of Some Autonomous Partial Differential Equations with a Parameter

Herrmann

2018

J Math Sci

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A class of partial differential equations of evolution (stemming from the groundwater flow problems) depending on a parameter τ is studied. The existence of an open interval T 0 of parameter τ and of a function τ → Θ(τ ), Θ : T 0 → (0, +∞), is proved with the property that any nonzero global solution u : R + × Ω → R of the equation cannot remain nonnegative (nonpositive) throughout the set J × Ω, where J ⊂ R + is any interval the length of which is greater than Θ(τ ). In other words, such solutions are globally oscillatory and Θ(τ ) is the uniform oscillatory time. The interval T 0 as well as the function Θ are explicitly determined.Вивчається клас еволюцiйних диференцiальних рiвнянь з частинними похiдними iз параметром τ, якi розглядаються в задачах течiї пiдземних вод. Доведено iснування вiдкритого iнтервалу T 0 параметра τ та функцiї τ → Θ(τ ), Θ : T 0 → (0, +∞), якi задовольняють таку властивiсть: будь-який ненульовий глобальний розв'язок u : R + × Ω → R рiвняння не може залишатися невiд'ємним (недодатним) на множинi J × Ω, де J ⊂ R + -будь-який iнтервал, довжина якого перевищує Θ(τ ). Iншими словами, такi розв'язки є глобально коливними, а Θ(τ ) -рiвномiрним коливним часом. Iнтервал T 0 та функцiю Θ знайдено в явному виглядi.

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Mathematical Modeling of Tidal Effects in Groundwater

Cited by 3 publications

References 13 publications

Models of earth-tide-induced groundwater oscillations in the Police Basin, Czech Republic

Models of earth-tide-induced groundwater oscillations in the Police Basin, Czech Republic

Temperature fluctuations underneath the ice in Diamond Lake, Hennepin County, Minnesota

Oscillatory Solutions of Some Autonomous Partial Differential Equations with a Parameter

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