Year 2018,
Volume: 6 Issue: 2, 134 - 142, 28.12.2018
İmanverdi Ekberli
,
Coşkun Gülser
References
- Averyanov SF, 1978. Control of salinity in irrigated lands. Kolos Press, Mockow (in Russian), 288 p.
- Barna IF, Matyas L, 2015. Analytic self-similar solutions of the Oberbeck–Boussinesq equations. Chaos, Solitons and Fractals, 78: 249–255.
- Barry DA, Barry SJ, Parlange, JY, 1996. Capillarity correction to periodic solutions of the shallow Flow Approximation, Mixing in Estuaries and Coastal Seas. American Geophysical Union, pp. 496–510.
- Bear J, Zaslavsky D, Irmay S, 1968. Physical principles of water percolation and seepage. UNESCO, Paris, pp. 191-223.
- Bierkens MFP, 1998. Modeling water table fluctuations by means of a stochastic differential equation. Water Resources Research, 34 (10): 2485–2499.
- Bierkens MFP, Knotters M, Geer FC, 1999. Calibration of transfer function-noise models to sparsely or irregularly observed time series. Water Resources Research, 35(6): 1741–1750.
- Boussinesq MJ, 1904. Recherches theoriques sur l’ecoulement des nappes d’eau infiltrées dans le sol et sur debit de sources. Journal de Mathématiques Pures et Appliquées, 10: 5-78.
- Coulibaly P, Anctil F, Aravena R, Bobee B, 2001. Artificial neural network modeling of water table depth fluctuations. Water Resources Research, 37 (4): 885–896.
- Coulibaly P, Baldwin CK, 2005. Nonstationary hydrological time series forecasting using nonlinear dynamic methods. Journal of Hydrology, 307 (1): 164–174.
- Cuthbert MO, 2010. An improved time series approach for estimating groundwater recharge from groundwater level fluctuations. Water Resources Research, 46 (9), 11 p., W09515.
- Darcy H, 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris, 647 p.
- Dupuit J, 1863. Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et a travers les terrains perméables. Dunod, Paris, 364 p.
- Ekberli I, 2006. Determination of initial unconditional solution of heat conductivity equation for evaluation of temperature variance in finite soil layer. Journal of Applied Sciences, 6 (7): 1520-1526.
- Ekberli İ, Dengiz O, Gülser C, Özdemir N, 2016. Benzerlik teorisinin toprak sıcaklığına uygulanabilirliği. Toprak Bilimi ve Bitki Besleme Dergisi, 4 (2), 63-68.
- Ekberli İ, Gülser C, Mamedov A, 2015a. Toprakta bir boyutlu ısı iletkenlik denkleminin incelenmesinde benzerlik teorisinin uygulanması. Süleyman Demirel Üniversitesi Ziraat Fakültesi Dergisi, 10 (2): 69-79.
- Ekberli, İ, Gülser C, Mamedov, A, Özdemir, N, 2018. Faz değişimine bağlı olarak ısı iletkenliği denkleminin incelenmesi ve toprak neminin ısısal yayınıma etkisi. Anadolu Tarım Bilimleri Dergisi, 33 (3): 261-269
- Ekberli İ, Gülser C, Özdemir N, 2014. Toprak deformasyonu ve geriliminin reoloji denklemine göre analitik incelenmesi. Anadolu Tarım Bilimleri Dergisi, 29 (1):79-85.
- Ekberli İ, Gülser C, Özdemir N, 2015b. Toprakta ısı iletkenliğine etki yapan ısısal parametrelerin teorik incelemesi. Anadolu Tarım Bilimleri Dergisi, 30 (3):300-306.
- Ekberli İ, Gülser C, Özdemir N, 2017. Farklı toprak derinliklerindeki sıcaklığın tahmininde parabolik fonksiyonun kullanımı. Toprak Bilimi ve Bitki Besleme Dergisi 5 (1) 34- 38.
- Ekberli İ, Sarılar Y, 2015. Toprak sıcaklığının profil boyunca sönme derinliğinin ve gecikme zamanının belirlenmesi. Ege Üniversitesi Ziraat Fakültesinin Dergisi, 52 (2): 219-225.
- Faibishenko BA, 1986. Water-salt rejime of soils under irrigation. Agropromizdat, Moscow (in Russian), 304 p.
- Gülser C, Ekberli İ (2002). Toprak sıcaklığının profil boyunca değişimi. Ondokuz Mayıs Üniversitesi Ziraat Fakültesinin Dergisi, 17(3): 43-47.
- Jeong J, Park E, 2017. A shallow water table fluctuation model in response to precipitation with consideration of unsaturated gravitational flow. Water Resources Research, 53: 3505-3512.
- Jeong J, Park E, Han WS, Kim K-Y, Suk H, Jo SB, 2018. A generalized groundwater fluctuation model based on precipitation for estimating water table levels of deep unconfined aquifers. Journal of Hydrology, 562: 749–757.
- Kats DM, Shestakov VM, 1992. Melioration hydrogeology. Moscow State University Press, Mockow (in Russian), pp. 71-92.
- Knotters M, Bierkens MFP, 2000. Physical basis of time series models for water table depths. Water Resources Research, 36 (1): 181–188.
- Kong J, Shen CJ, Xin P, Song Z, Li L, Barry DA, Jeng DS, Stagnitti F, Lockington, DA, Parlange JY, 2013. Capillary effect on water table fluctuations in unconfined aquifers. Water Resources Research, 49 (5): 3064-3069.
- Kong J, Xin P, Hua G-F, Luo ZY, Shen C-J, Chen, D, Li L, 2015. Effects of vadose zone on groundwater table fluctuations in unconfined aquifers. Journal of Hydrology, 528: 397-407.
- Kostyakov AN, 1960. Fundamentals of land reclamation. Selhozgis, Mockow (in Russian), 622 p.
- Li L, Barry DA, Parlange JY, Pattiaratchi CB, 1997. Beach water table fluctuations due to wave run-up: capillarity effects. Water Resources Research, 33 (5): 935-945.
- Lockington DA, Parlange J.-Y, Parlange MB, Selker J, 2000. Similarity solution of the Boussinesq equation. Advances in Water Resources, 23: 725-729.
- Luikov AV, 1948. Heat conductivity of nonstationary processes (in Russian). State Energy Press (Gosudarstvennoye energetiçeskoye izdatelstvo), Moscow-Leningrad, 232 p.
- Luikov AV, 1967. Theory of thermal conductivity (in Russian). Vysshaya Shkola Press, Moscow, 599 p.
- Luikov AV, Mikhailov YuA, 1965. Theory of energy and mass transfer. Pergamon Press, Oxford, England, 392 p.
- Luthin JN (Editor), 1964. Drainage of agricultural lands. Kolos Press, Mockow (in Russian), 719 p.
- Morel CRG, van Reeuwijk M, Graf T, 2015. Systematic investigation of non-Boussinesq effects in variable-density groundwater flow simulations. Journal of Contaminant Hydrology, 183: 82–98.
- Neto DC, Chang HK, van Genuchten MT, 2015. A mathematical view of water table fluctuations in a shallow aquifer in Brazil. Groundwater, 54 (1): 82–91.
- Özdemir N, 1998. Toprak Fiziği. Ondokuz Mayıs Üniversitesi Ziraat Fakültesi Ders Kitabı No:30, Samsun.
- Park E, Parker JC, 2008. A simple model for water table fluctuations in response to precipitation. Journal of Hydrology, 356 (3): 344–349.
- Rai SN, Manglik A, Singh VS, 2006. Water table fluctuation owing to time-varying recharge pumping and leakage. Journal of Hydrology, 324 (1–4): 350–358.
- Rai, SN, Manglik A, 1999. Modelling of water table variation in response to time-varyingrecharge from multiple basins using the linearised Boussinesq equation. Journal of Hydrology, 220: 141-148.
- Su N, 2017. The fractional Boussinesq equation of groundwater flow and its applications. Journal of Hydrology, 547, 403–412.
- Szilagyi J, Parlange MB, 1998. Baseflow separation based on analytical solutions of the Boussinesq equation. Journal of Hydrology, 204: 251-260.
- Tang G, Alshawabkeh AN, 2006. A semi-analytical time integration for numerical solution of Boussinesq equation. Advances in Water Resources, 29: 1953–1968.
- Telyakovskiy AS, Braga GA, Kurita S, Mortensen J, 2010. On a power series solution to the Boussinesq equation. Advances in Water Resources, 33: 1128–1129.
- Telyakovskiy AS, Kurita S, Allen MB, 2016. Polynomial-based approximate solutions to the Boussinesq equation near a well. Advances in Water Resources, 96: 68–73.
- Turcotte DL, Schubert G, 1982. Geodynamics: Application of Continuum Physics to Geological Problems. Wiley & Sons, 450 p.
- Isachenko VP, Osipova VA, Sukomel AS. 1981. Heat transfer (in Russian). Energoizdat Press, Moscow, 417 p.
- Yang F, Liang D, Xiao Y, 2018. Influence of Boussinesq coefficient on depth-averaged modelling of rapid flows. Journal of Hydrology, 559: 909-919.
- Yao Y, Tang Z, Jiang C, He W, Liu Z, 2018. Boussinesq modeling of solitary wave run-up reduction by emergent vegetation on a sloping beach. Journal of Hydro-environment Research, 19: 78–87.
- Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK, 2011. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology, 396 (1): 128–138.
- Zavala M, Fuentes C, Saucedo H, 2007. Non-linear radiation in the Boussinesq equation of the agricultural drainage. Journal of Hydrology, 332: 374-380.
- Zaydelman FR, 1987. Soil reclamation. Moscow State University Press, Mockow (in Russian), pp. 160-167.
Boussinesq denkleminin çözümüne bağlı olarak taban suyu seviyesi yüksekliğinin incelenmesi
Year 2018,
Volume: 6 Issue: 2, 134 - 142, 28.12.2018
İmanverdi Ekberli
,
Coşkun Gülser
Abstract
Bu çalışmada geçirgen toprak katmanında Dupuit yaklaşımı ve Darcy yasasına bağlı olarak taban suyu seviyesindeki değişimin belirlenmesi için Boussinesq denkleminin ilave edilmesi ve çözümü açıklanmıştır. Yavaş (0.44 cm sa-1), oldukça yavaş (1.05 cm sa-1) ve orta (3.12 cm sa-1) hidrolik iletkenlik değerlerine sahip topraklara aynı hacimde su uygulanması durumunda, farklı toprak kesitlerinden farklı sürelerde oluşacak drenaj koşulları için taban suyu seviyesindeki değişimler hesaplanmıştır. Genel olarak taban suyu seviyesi, drenajın gerçekleştiği kesit mesafesinin daralması ile yükselmekte, kesit mesafesinin artması ile alçalmaktadır. Taban suyu seviyesindeki değişim drenaj süresi arttıkça aynı geçirgenlik sınıfı için sabit bir değere yaklaşmaktadır. Toprak ortamına ilave olunan su miktarına bağlı olarak taban suyu seviyesinin değişiminde, drenaj kesit mesafesinin, zamanın ve hidrolik iletkenliğin temel faktörler olduğu belirlenmiştir.
References
- Averyanov SF, 1978. Control of salinity in irrigated lands. Kolos Press, Mockow (in Russian), 288 p.
- Barna IF, Matyas L, 2015. Analytic self-similar solutions of the Oberbeck–Boussinesq equations. Chaos, Solitons and Fractals, 78: 249–255.
- Barry DA, Barry SJ, Parlange, JY, 1996. Capillarity correction to periodic solutions of the shallow Flow Approximation, Mixing in Estuaries and Coastal Seas. American Geophysical Union, pp. 496–510.
- Bear J, Zaslavsky D, Irmay S, 1968. Physical principles of water percolation and seepage. UNESCO, Paris, pp. 191-223.
- Bierkens MFP, 1998. Modeling water table fluctuations by means of a stochastic differential equation. Water Resources Research, 34 (10): 2485–2499.
- Bierkens MFP, Knotters M, Geer FC, 1999. Calibration of transfer function-noise models to sparsely or irregularly observed time series. Water Resources Research, 35(6): 1741–1750.
- Boussinesq MJ, 1904. Recherches theoriques sur l’ecoulement des nappes d’eau infiltrées dans le sol et sur debit de sources. Journal de Mathématiques Pures et Appliquées, 10: 5-78.
- Coulibaly P, Anctil F, Aravena R, Bobee B, 2001. Artificial neural network modeling of water table depth fluctuations. Water Resources Research, 37 (4): 885–896.
- Coulibaly P, Baldwin CK, 2005. Nonstationary hydrological time series forecasting using nonlinear dynamic methods. Journal of Hydrology, 307 (1): 164–174.
- Cuthbert MO, 2010. An improved time series approach for estimating groundwater recharge from groundwater level fluctuations. Water Resources Research, 46 (9), 11 p., W09515.
- Darcy H, 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris, 647 p.
- Dupuit J, 1863. Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et a travers les terrains perméables. Dunod, Paris, 364 p.
- Ekberli I, 2006. Determination of initial unconditional solution of heat conductivity equation for evaluation of temperature variance in finite soil layer. Journal of Applied Sciences, 6 (7): 1520-1526.
- Ekberli İ, Dengiz O, Gülser C, Özdemir N, 2016. Benzerlik teorisinin toprak sıcaklığına uygulanabilirliği. Toprak Bilimi ve Bitki Besleme Dergisi, 4 (2), 63-68.
- Ekberli İ, Gülser C, Mamedov A, 2015a. Toprakta bir boyutlu ısı iletkenlik denkleminin incelenmesinde benzerlik teorisinin uygulanması. Süleyman Demirel Üniversitesi Ziraat Fakültesi Dergisi, 10 (2): 69-79.
- Ekberli, İ, Gülser C, Mamedov, A, Özdemir, N, 2018. Faz değişimine bağlı olarak ısı iletkenliği denkleminin incelenmesi ve toprak neminin ısısal yayınıma etkisi. Anadolu Tarım Bilimleri Dergisi, 33 (3): 261-269
- Ekberli İ, Gülser C, Özdemir N, 2014. Toprak deformasyonu ve geriliminin reoloji denklemine göre analitik incelenmesi. Anadolu Tarım Bilimleri Dergisi, 29 (1):79-85.
- Ekberli İ, Gülser C, Özdemir N, 2015b. Toprakta ısı iletkenliğine etki yapan ısısal parametrelerin teorik incelemesi. Anadolu Tarım Bilimleri Dergisi, 30 (3):300-306.
- Ekberli İ, Gülser C, Özdemir N, 2017. Farklı toprak derinliklerindeki sıcaklığın tahmininde parabolik fonksiyonun kullanımı. Toprak Bilimi ve Bitki Besleme Dergisi 5 (1) 34- 38.
- Ekberli İ, Sarılar Y, 2015. Toprak sıcaklığının profil boyunca sönme derinliğinin ve gecikme zamanının belirlenmesi. Ege Üniversitesi Ziraat Fakültesinin Dergisi, 52 (2): 219-225.
- Faibishenko BA, 1986. Water-salt rejime of soils under irrigation. Agropromizdat, Moscow (in Russian), 304 p.
- Gülser C, Ekberli İ (2002). Toprak sıcaklığının profil boyunca değişimi. Ondokuz Mayıs Üniversitesi Ziraat Fakültesinin Dergisi, 17(3): 43-47.
- Jeong J, Park E, 2017. A shallow water table fluctuation model in response to precipitation with consideration of unsaturated gravitational flow. Water Resources Research, 53: 3505-3512.
- Jeong J, Park E, Han WS, Kim K-Y, Suk H, Jo SB, 2018. A generalized groundwater fluctuation model based on precipitation for estimating water table levels of deep unconfined aquifers. Journal of Hydrology, 562: 749–757.
- Kats DM, Shestakov VM, 1992. Melioration hydrogeology. Moscow State University Press, Mockow (in Russian), pp. 71-92.
- Knotters M, Bierkens MFP, 2000. Physical basis of time series models for water table depths. Water Resources Research, 36 (1): 181–188.
- Kong J, Shen CJ, Xin P, Song Z, Li L, Barry DA, Jeng DS, Stagnitti F, Lockington, DA, Parlange JY, 2013. Capillary effect on water table fluctuations in unconfined aquifers. Water Resources Research, 49 (5): 3064-3069.
- Kong J, Xin P, Hua G-F, Luo ZY, Shen C-J, Chen, D, Li L, 2015. Effects of vadose zone on groundwater table fluctuations in unconfined aquifers. Journal of Hydrology, 528: 397-407.
- Kostyakov AN, 1960. Fundamentals of land reclamation. Selhozgis, Mockow (in Russian), 622 p.
- Li L, Barry DA, Parlange JY, Pattiaratchi CB, 1997. Beach water table fluctuations due to wave run-up: capillarity effects. Water Resources Research, 33 (5): 935-945.
- Lockington DA, Parlange J.-Y, Parlange MB, Selker J, 2000. Similarity solution of the Boussinesq equation. Advances in Water Resources, 23: 725-729.
- Luikov AV, 1948. Heat conductivity of nonstationary processes (in Russian). State Energy Press (Gosudarstvennoye energetiçeskoye izdatelstvo), Moscow-Leningrad, 232 p.
- Luikov AV, 1967. Theory of thermal conductivity (in Russian). Vysshaya Shkola Press, Moscow, 599 p.
- Luikov AV, Mikhailov YuA, 1965. Theory of energy and mass transfer. Pergamon Press, Oxford, England, 392 p.
- Luthin JN (Editor), 1964. Drainage of agricultural lands. Kolos Press, Mockow (in Russian), 719 p.
- Morel CRG, van Reeuwijk M, Graf T, 2015. Systematic investigation of non-Boussinesq effects in variable-density groundwater flow simulations. Journal of Contaminant Hydrology, 183: 82–98.
- Neto DC, Chang HK, van Genuchten MT, 2015. A mathematical view of water table fluctuations in a shallow aquifer in Brazil. Groundwater, 54 (1): 82–91.
- Özdemir N, 1998. Toprak Fiziği. Ondokuz Mayıs Üniversitesi Ziraat Fakültesi Ders Kitabı No:30, Samsun.
- Park E, Parker JC, 2008. A simple model for water table fluctuations in response to precipitation. Journal of Hydrology, 356 (3): 344–349.
- Rai SN, Manglik A, Singh VS, 2006. Water table fluctuation owing to time-varying recharge pumping and leakage. Journal of Hydrology, 324 (1–4): 350–358.
- Rai, SN, Manglik A, 1999. Modelling of water table variation in response to time-varyingrecharge from multiple basins using the linearised Boussinesq equation. Journal of Hydrology, 220: 141-148.
- Su N, 2017. The fractional Boussinesq equation of groundwater flow and its applications. Journal of Hydrology, 547, 403–412.
- Szilagyi J, Parlange MB, 1998. Baseflow separation based on analytical solutions of the Boussinesq equation. Journal of Hydrology, 204: 251-260.
- Tang G, Alshawabkeh AN, 2006. A semi-analytical time integration for numerical solution of Boussinesq equation. Advances in Water Resources, 29: 1953–1968.
- Telyakovskiy AS, Braga GA, Kurita S, Mortensen J, 2010. On a power series solution to the Boussinesq equation. Advances in Water Resources, 33: 1128–1129.
- Telyakovskiy AS, Kurita S, Allen MB, 2016. Polynomial-based approximate solutions to the Boussinesq equation near a well. Advances in Water Resources, 96: 68–73.
- Turcotte DL, Schubert G, 1982. Geodynamics: Application of Continuum Physics to Geological Problems. Wiley & Sons, 450 p.
- Isachenko VP, Osipova VA, Sukomel AS. 1981. Heat transfer (in Russian). Energoizdat Press, Moscow, 417 p.
- Yang F, Liang D, Xiao Y, 2018. Influence of Boussinesq coefficient on depth-averaged modelling of rapid flows. Journal of Hydrology, 559: 909-919.
- Yao Y, Tang Z, Jiang C, He W, Liu Z, 2018. Boussinesq modeling of solitary wave run-up reduction by emergent vegetation on a sloping beach. Journal of Hydro-environment Research, 19: 78–87.
- Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK, 2011. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology, 396 (1): 128–138.
- Zavala M, Fuentes C, Saucedo H, 2007. Non-linear radiation in the Boussinesq equation of the agricultural drainage. Journal of Hydrology, 332: 374-380.
- Zaydelman FR, 1987. Soil reclamation. Moscow State University Press, Mockow (in Russian), pp. 160-167.