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Journal articles on the topic 'Shallow water systems'

Author: Grafiati

Published: 26 October 2024

Last updated: 31 July 2025

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1

Clarkson, Peter A., and Thomas J. Priestley. "Shallow Water Wave Systems." Studies in Applied Mathematics 101, no. 4 (1998): 389–432. http://dx.doi.org/10.1111/1467-9590.00099.

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2

Saxena, Atanu Basu, N. K. "A Review of Shallow-Water Mapping Systems." Marine Geodesy 22, no. 4 (1999): 249–57. http://dx.doi.org/10.1080/014904199273380.

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3

Browning, G. L., and H.-O. Kreiss. "Reduced Systems for the Shallow Water Equations." Journal of the Atmospheric Sciences 44, no. 19 (1987): 2813–22. http://dx.doi.org/10.1175/1520-0469(1987)044<2813:rsftsw>2.0.co;2.

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4

Illes, Ladislav, Tomas Kalina, Martin Jurkovic, and Vladimir Luptak. "Distributed Propulsion Systems for Shallow Draft Vessels." Journal of Marine Science and Engineering 8, no. 9 (2020): 667. http://dx.doi.org/10.3390/jmse8090667.

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The aim of this study was to investigate the impact of distributed propulsion systems used on inland and coastal navigation in shallow water. Five layouts were assessed by computational fluid dynamics (CFD) simulation. The hull/propulsion layout cases have been analyzed for discrete flow speed values in the range 0–6 m/s. All cases have been examined under restricted draft conditions in shallow water with a minimum of 0.3 m under keel clearance (UKC) and under unrestricted draft conditions in deep water. The results show that distributed propulsion consisting of 6 or 8 (in some cases, even mor

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5

Korpusov, M. O., and E. V. Yushkov. "Solution blowup for systems of shallow-water equations." Theoretical and Mathematical Physics 177, no. 2 (2013): 1505–14. http://dx.doi.org/10.1007/s11232-013-0119-9.

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6

Sangapate, P. "Adaptive Control and Synchronization of the Shallow Water Model." Mathematical Problems in Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/529251.

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The shallow water model is one of the important models in dynamical systems. This paper investigates the adaptive chaos control and synchronization of the shallow water model. First, adaptive control laws are designed to stabilize the shallow water model. Then adaptive control laws are derived to chaos synchronization of the shallow water model. The sufficient conditions for the adaptive control and synchronization have been analyzed theoretically, and the results are proved using a Barbalat's Lemma.

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7

Nallathambi, G., and J. G. Robinson. "Performance of Shallow Water Rice for Drought Tolerance." International Rice Research Newsletter 17, no. 4 (1992): 11. https://doi.org/10.5281/zenodo.7218919.

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This article 'Performance of Shallow Water Rice for Drought Tolerance' appeared in the International Rice Research Newsletter series, created by the International Rice Research Institute (IRRI). The primary objective of this publication was to expedite communication among scientists concerned with the development of improved technology for rice and for rice based cropping systems. This publication will report what scientists are doing to increase the production of rice in as much as this crop feeds the most densely populated and land scarce nations in the world.

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8

Hu, Qiaoyi, Zhixin Wu, and Yumei Sun. "Liouville theorems for periodic two-component shallow water systems." Discrete & Continuous Dynamical Systems - A 38, no. 6 (2018): 3085–97. http://dx.doi.org/10.3934/dcds.2018134.

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9

Branco, Brett, Thomas Torgersen, John R. Bean, Gary Grenier, and Dennis Arbige. "A new water column profiler for shallow aquatic systems." Limnology and Oceanography: Methods 3, no. 3 (2005): 190–202. http://dx.doi.org/10.4319/lom.2005.3.190.

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10

Didenkulova, Ira, and Efim Pelinovsky. "Rogue waves in nonlinear hyperbolic systems (shallow-water framework)." Nonlinearity 24, no. 3 (2011): R1—R18. http://dx.doi.org/10.1088/0951-7715/24/3/r01.

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11

Ersing, Patrick, Sven Goldberg, and Andrew R. Winters. "Entropy stable hydrostatic reconstruction schemes for shallow water systems." Journal of Computational Physics 527 (April 2025): 113802. https://doi.org/10.1016/j.jcp.2025.113802.

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12

Pivnev, P. P., A. P. Voloshchenko, and S. P. Tarasov. "Monitoring of Bioresources in Shallow Water by Parametric Systems." IOP Conference Series: Earth and Environmental Science 459 (April 15, 2020): 042089. http://dx.doi.org/10.1088/1755-1315/459/4/042089.

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13

Gonzalo, Fernando del Ama, and Juan A. Hernandez Ramos. "Testing of Water Flow Glazing in Shallow Geothermal Systems." Procedia Engineering 161 (2016): 887–91. http://dx.doi.org/10.1016/j.proeng.2016.08.742.

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14

Yaşar, Emrullah, and Teoman Özer. "Conservation laws for one-layer shallow water wave systems." Nonlinear Analysis: Real World Applications 11, no. 2 (2010): 838–48. http://dx.doi.org/10.1016/j.nonrwa.2009.01.028.

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15

Lastra, Miguel, José M. Mantas, Carlos Ureña, Manuel J. Castro, and José A. García-Rodríguez. "Simulation of shallow-water systems using graphics processing units." Mathematics and Computers in Simulation 80, no. 3 (2009): 598–618. http://dx.doi.org/10.1016/j.matcom.2009.09.012.

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16

Hoekstra, N. J., J. A. Finn та A. Lüscher. "The effect of drought and interspecific interactions on the depth of water uptake in deep- and shallow-rooting grassland species as determined by <i>δ</i><sup>18</sup>O natural abundance". Biogeosciences Discussions 11, № 3 (2014): 4151–86. http://dx.doi.org/10.5194/bgd-11-4151-2014.

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Abstract. Increased incidence of weather drought, as predicted under climate change, has the potential to negatively affect grassland production. Compared to monocultures, vertical belowground niche complementarity between shallow- and deep-rooting species may be an important mechanism resulting in higher yields and higher resistance to drought in grassland mixtures. However, very little is known about the belowground responses in grassland systems and increased insight into these processes may yield important information both to predict the effect of future climate change and better design ag

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17

Zhang, Zhujun, Wei Fan, Weicheng Bao, Chen-Tung A. Chen, Shuo Liu, and Yong Cai. "Recent Developments of Exploration and Detection of Shallow-Water Hydrothermal Systems." Sustainability 12, no. 21 (2020): 9109. http://dx.doi.org/10.3390/su12219109.

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A hydrothermal vent system is one of the most unique marine environments on Earth. The cycling hydrothermal fluid hosts favorable conditions for unique life forms and novel mineralization mechanisms, which have attracted the interests of researchers in fields of biological, chemical and geological studies. Shallow-water hydrothermal vents located in coastal areas are suitable for hydrothermal studies due to their close relationship with human activities. This paper presents a summary of the developments in exploration and detection methods for shallow-water hydrothermal systems. Mapping and me

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18

Zahoor, F., M. A. Malik, R. Anser, et al. "Water Use Efficiency and Rain Water Productivity of Wheat under Various Tillage-Glyphosate Interactive Systems." Cercetari Agronomice in Moldova 48, no. 1 (2015): 25–36. http://dx.doi.org/10.1515/cerce-2015-0014.

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Abstract Rainfed wheat is generally grown in rotation with summer fallow in medium to high rainfall zone of Pothwar plateau of Pakistan. The present study was, therefore, conducted to investigate the impact of shallow and deep tillage practices, with and without herbicide (glyphosate) application, on moisture conservation and subsequent wheat yields. The study also aimed to examine the feasibility of substituting intensive shallow tillage with single application of glyphosate. The experiment was laid out in randomized complete block design with three replicates and net plot size of 14 m x 10 m

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19

Hammer, Donald A., and Robert L. Knight. "Designing Constructed Wetlands for Nitrogen Removal." Water Science and Technology 29, no. 4 (1994): 15–27. http://dx.doi.org/10.2166/wst.1994.0148.

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Many constructed wetlands adequately treat BOD5, TSS, and bacteria. However, a review of nitrogen (N) data from 52 constructed and natural wetlands in the North American data base confirmed that N removal was variable. Nitrification and denitrification require aerobic and anaerobic conditions. This paper presents case histories of systems that use alternating shallow and deep water zones to create both environments. Regression analysis of N removal and N loadings in 18 shallow-deep water systems suggested that NH4+ loading (kg N/ha/day) could be used to predict effluent NH4+ values. Combinatio

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20

Prieto, Iván, Francisco I. Pugnaire, and Ronald J. Ryel. "Water uptake and redistribution during drought in a semiarid shrub species." Functional Plant Biology 41, no. 8 (2014): 812. http://dx.doi.org/10.1071/fp13300.

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In arid systems, most plant mortality occurs during long drought periods when water is not available for plant uptake. In these systems, plants often benefit from scarce rain events occurring during drought but some of the mechanisms underlying this water use remain unknown. In this context, plant water use and redistribution after a large rain event could be a mechanism that allows deep-rooted shrubs to conservatively use water during drought. We tested this hypothesis by comparing soil and plant water dynamics in Artemisia tridentata ssp. vaseyana (Rydb.) Beetle shrubs that either received a

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21

Hoekstra, N. J., J. A. Finn, D. Hofer та A. Lüscher. "The effect of drought and interspecific interactions on depth of water uptake in deep- and shallow-rooting grassland species as determined by δ<sup>18</sup>O natural abundance". Biogeosciences 11, № 16 (2014): 4493–506. http://dx.doi.org/10.5194/bg-11-4493-2014.

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Abstract. Increased incidence of drought, as predicted under climate change, has the potential to negatively affect grassland production. Compared to monocultures, vertical belowground niche complementarity between shallow- and deep-rooting species may be an important mechanism resulting in higher yields and higher resistance to drought in grassland mixtures. However, very little is known about the belowground responses in grassland systems and increased insight into these processes may yield important information both to predict the effect of future climate change and better design agricultur

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22

Kurganov, Alexander. "Finite-volume schemes for shallow-water equations." Acta Numerica 27 (May 1, 2018): 289–351. http://dx.doi.org/10.1017/s0962492918000028.

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Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, f

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23

Bresch, Didier, Mathieu Colin, Khawla Msheik, Pascal Noble, and Xi Song. "Lubrication and shallow-water systems Bernis-Friedman and BD entropies." ESAIM: Proceedings and Surveys 69 (2020): 1–23. http://dx.doi.org/10.1051/proc/202069001.

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This paper concerns the results recently announced by the authors, in C.R. Acad. Sciences Maths volume 357, Issue 1, 1-6 (2019), which make the link between the BD entropy introduced by D. Bresch and B. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF in our paper) dissipative entropy introduced to study the lubrication equations. More precisely different dissipative BF entropies are obtained from the BD entropies playing with drag terms and capillarity formula for viscous shallow water type equations. This is the main idea in the paper which makes the link

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24

Negri, Marco, and Stefano Malavasi. "Wave Energy Harnessing in Shallow Water through Oscillating Bodies." Energies 11, no. 10 (2018): 2730. http://dx.doi.org/10.3390/en11102730.

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This paper deals with wave energy conversion in shallow water, analyzing the performance of two different oscillating-body systems. The first one is a heaving float, which is a system known in the literature. The second one is obtained by coupling the heaving float with a surging paddle. In order to check the different behaviors of the multibody system and the single-body heaving float, physical models of the two systems have been tested in a wave flume, by placing them at various water depths along a sloping bottom. The systems have been tested with monochromatic waves. For each water depth,

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25

Macêdo, Antônia B. M., Raimundo N. T. Costa, Danielle F. de Araújo, and Kenya G. Nunes. "Water productivity with localized irrigation using groundwater and reuse water in the cultivation of plant species." Revista Brasileira de Engenharia Agrícola e Ambiental 24, no. 4 (2020): 219–24. http://dx.doi.org/10.1590/1807-1929/agriambi.v24n4p219-224.

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ABSTRACT This study aimed to analyze the water saving potential of replacing the traditional, furrow-irrigated banana crop in the Curu-Pentecoste Irrigated Perimeter with localized systems by inserting new cropping plans and sources of groundwater and reuse water. An analysis of the support capacity in shallow tube wells for irrigation was also performed, considering the scenario of full recharge and water scarcity. The economic analysis was performed using the profitability indicators of the investment analysis: benefit/cost ratio, net present value, internal rate of return and payback period

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26

Allen, Diana M., Peter Bayer, Grant Ferguson, and Philipp Blum. "Preface: Hydrogeology of shallow thermal systems." Hydrogeology Journal 22, no. 1 (2013): 1–6. http://dx.doi.org/10.1007/s10040-013-1082-0.

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27

Wiklund, K. "Wave interactions in a shallow-water model." Nonlinear Processes in Geophysics 5, no. 3 (1998): 137–44. http://dx.doi.org/10.5194/npg-5-137-1998.

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Abstract. By using a Hamiltonian method, non-linear three-wave interaction in a class of systems related to the shallow water model is considered and a general coupling coefficient is presented. In the special case where two inertial waves and one Rossby wave interact resonantly, it is found that even a very small shear of the background velocity can be important in the interaction process. The stability of the system is considered by using a pseudo-energy method. Some implications for the dynamics of atmospheric flows are pointed out.

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28

Yano, Jun-Ichi, James C. McWilliams, Mitchell W. Moncrieff, and Kerry A. Emanuel. "Hierarchical Tropical Cloud Systems in an Analog Shallow-Water Model." Journal of the Atmospheric Sciences 52, no. 10 (1995): 1723–42. http://dx.doi.org/10.1175/1520-0469(1995)052<1723:htcsia>2.0.co;2.

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29

Lobeiras, Jacobo, Moisés Viñas, Margarita Amor, et al. "Parallelization of shallow water simulations on current multi-threaded systems." International Journal of High Performance Computing Applications 27, no. 4 (2012): 493–512. http://dx.doi.org/10.1177/1094342012464800.

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30

Fu, Xiaoyu, and V. D. Sharma. "Cauchy problem for quasilinear hyperbolic systems of shallow water equations." Applicable Analysis 92, no. 11 (2013): 2309–19. http://dx.doi.org/10.1080/00036811.2012.734376.

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31

Yang, Zhuan Yun. "Feasibility Analysis and Status of Shallow Pipe-Jacking Technology in Urban Drainage Systems." Key Engineering Materials 480-481 (June 2011): 1278–82. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.1278.

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Considering the current domestic situation that there is no provision for shallow pipe-jacking (with overburden soil layer not thicker than 3 m and 1.5 times of the pipe external diameter) in the existing water supply and drainage pipeline engineering design and construction specifications, a comprehensive analysis and discussion, based on the actual domestic condition, is made on the feasibility of shallow pipe-jacking technology in urban drainage systems. The problems confronting the shallow pipe-jacking technology theory research are also analyzed and the research status of shallow curve pi

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32

Schneider, Kleiton A., José M. Gallardo, Dinshaw S. Balsara, Boniface Nkonga, and Carlos Parés. "Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems." Journal of Computational Physics 444 (November 2021): 110547. http://dx.doi.org/10.1016/j.jcp.2021.110547.

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33

Harlamova, Anna Eduardovna, Mikhail Nikolaevich Pokusaev, and Alexei Viktorovich Trifonov. "Analysis of ship accidents caused by unreliable operation of cooling systems of ship power plants." Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2023, no. 2 (2023): 30–40. http://dx.doi.org/10.24143/2073-1574-2023-2-30-40.

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The article considers transport accidents on watercrafts in inland waterways, sea and ocean waters caused by unreliable operation of the main systems during operation in ice and shallow water conditions difficult for naviga-tion and by the violations technical operation rules by the crew members. There are given the statistical data on the accidents and causes of accidents on the water. Frequent breakdowns due to unreliable operation of the open (two-circuit) cooling system of the ship’s power plants are stated. Open systems, in which fresh water circulating through cooled power equipment is c

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34

Cardoso-Ribeiro, Flávio Luiz, Denis Matignon, and Laurent Lefèvre. "Dissipative Shallow Water Equations: a port-Hamiltonian formulation." IFAC-PapersOnLine 54, no. 19 (2021): 167–72. http://dx.doi.org/10.1016/j.ifacol.2021.11.073.

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35

Kılıç, Tuğba, Onur Akyol, and Reha Metin Alkan. "Comparison of UAV-based digital elevation model with multi beam bathymetry for shallow water." International Journal of Engineering and Geosciences 10, no. 3 (2025): 303–12. https://doi.org/10.26833/ijeg.1582508.

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Accurate bathymetric data is essential for marine and coastal applications, particularly in shallow water regions. Unmanned Aerial Vehicle (UAV)-based systems are recognized for their cost-effectiveness and flexibility, making them a promising alternative in shallow-water environments where Multi Beam Echosounder (MBES) systems often face limitations due to high operational costs or logistical challenges. However, the UAV-based method is influenced by refraction effects, which result in underwater objects being perceived as shallower than their actual depth, leading to a decrease in the accura

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36

Umar, Emi Prasetyawati, Alfian Nawir, Hariani M. Pakka, Jamaluddin Jamaluddin, Nurfadhilah Sam Tappa, and Watcharin Joemsittiprasert. "Analysis of Shallow Groundwater Quality as Consumable Water in Maros Baru District Aquifer Systems, South Sulawesi, Indonesia." International Journal of Hydrological and Environmental for Sustainability 1, no. 1 (2022): 33–40. http://dx.doi.org/10.58524/ijhes.v1i1.55.

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Water is a source of necessity for humans. Water quality is very important to be considered as the source of clean water. Some people in Maros Baru District use ground wells as the source of water needs. Therefore it is important to know the physical quality and pH level of shallow wells and to know the worthiness of shallow wells in Maros Baru District with reference to Permenkes No.492/ 2010. This study examined the feasibility of water based on the physical quality and the pH level of water taken from shallow wells. The research was carried out directly in field with 14 sampling points scat

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37

Park, Eungyu, and Hongbin Zhan. "Hydraulics of horizontal wells in fractured shallow aquifer systems." Journal of Hydrology 281, no. 1-2 (2003): 147–58. http://dx.doi.org/10.1016/s0022-1694(03)00206-3.

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38

Al-Khaled, Kamel, and M. K. Al-Safeen. "Homotopy Perturbation Method For Fractional Shallow Water Equations." Sultan Qaboos University Journal for Science [SQUJS] 19, no. 1 (2014): 74. http://dx.doi.org/10.24200/squjs.vol19iss1pp74-86.

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In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The results obtained reveal that these methods are both very effective and simple for finding approximate solutions. Some numerical examples and plots are prese

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39

Ferencz, Beata, and Jarosław Dawidek. "Water exchange of three shallow Łęczna-Włodawa Lakes." Limnological Review 12, no. 2 (2012): 65–72. http://dx.doi.org/10.2478/v10194-011-0045-x.

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AbstractThe research was carried out in three Łęczna-Włodawa lake-catchment systems, during the hydrological years 2007-2009. The observed lakes varied in terms of basin morphometry and catchment features. The hydrological functioning of the lakes resulted from three main factors: 1) storage capacity of the lake basin, 2) catchment area and relief, 3) human impact on water distribution. The vertical water exchange ratio in Lake Sumin was almost four-times higher than flushing time. In Lakes Rotcze and Syczyńskie horizontal water exchange, presented as flushing time was significantly higher tha

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40

CASTRO, MANUEL J., ALBERTO PARDO MILANÉS, and CARLOS PARÉS. "WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE." Mathematical Models and Methods in Applied Sciences 17, no. 12 (2007): 2055–113. http://dx.doi.org/10.1142/s021820250700256x.

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The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in Ref. 2 for the shallow water system to more general hyperbolic systems with source term. The key idea is to interpret the numerical scheme obtained with this technique as a path-conservative method, as defined in Ref. 35. This generalization allows us, on the one hand, to construct well-balanced numerical schemes for new problems, as the two-layer shallow water system. On the other hand, we construct numerical schemes for the shallow water system with better well-balanced properties. In particular we

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41

Sandrini, Giovanni, Arco Wagenvoort, Roland van Asperen, Bas Hofs, Dirk Mathijssen, and Albert van der Wal. "Illuminating the Impact of a Floating Photovoltaic System on a Shallow Drinking Water Reservoir: The Emergence of Benthic Cyanobacteria." Water 17, no. 8 (2025): 1178. https://doi.org/10.3390/w17081178.

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Floating photovoltaic (FPV) systems can play an important role in energy transition. Yet, so far, not much is known about the effects of FPV systems on water quality and ecology. A sun-tracking FPV system (24% coverage) was installed on a shallow drinking water reservoir. We observed for the first time that benthic cyanobacteria (blue-green algae), which can deteriorate water quality, developed massively under the FPV system, while macrophytes and benthic algae, such as Chara (stonewort), mostly disappeared. Calculations of light availability explain this shift. The natural mixing of the water

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42

Turbal, Yuriy, Mariana Turbal, and Andrii Bomba. "Modeling of the solitary waves trajectories in “shallow water” environme." Modeling Control and Information Technologies, no. 6 (November 22, 2023): 96–101. http://dx.doi.org/10.31713/mcit.2023.027.

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Solitary waves in the “shallow water” environment are considered and approximate approach to calculation and prediction of trajectories of these waves is proposed. We use an approach which was developed in recent years and was called the T-representations method. This method allows to move away from the exact solutions of the corresponding systems of differential equations and construct the trajectory approximately, in fact estimating only the point of maximum of the wave amplitude and its displacement. An appropriate mathematical simplification makes efficient computer simulations possible. I

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43

Tarasov, Sergei, Zhu Jianjun, Petr Pivnev, and Mikhail Gubko. "Low-frequency parametric systems in the shallow sea." E3S Web of Conferences 196 (2020): 02017. http://dx.doi.org/10.1051/e3sconf/202019602017.

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The theoretical model of acoustic wave propagation in the ice-water layer is developed, with, taking into account the velocity dispersion. New opportunities for monitoring the marine environment on long routes, including those covered with ice, are discussed when using parametric sonar antennas. The results of research demonstrating single-mode excitation of a waveguide by a parametric array in a wide frequency band are presented. The possibility of compression of a broadband signal during its propagation, as a result of waveguide dispersion, which leads to an increasing of signal intensity, i

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44

Ilin, Konstantin. "Shallow-water models for a vibrating fluid." Journal of Fluid Mechanics 833 (November 2, 2017): 1–28. http://dx.doi.org/10.1017/jfm.2017.687.

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We consider a layer of an inviscid fluid with a free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency) free-surface waves. The first set of equations is obtained without assuming that the waves are long. These equations are as difficult to solve as the exact equations for irrotational water waves in a non-vibrating fluid. The other two models describe long waves. These models are obtained under two different assumptions about the amplitude of the vibration. S

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45

Niroumand-Jadidi, Milad, Nima Pahlevan, and Alfonso Vitti. "Mapping Substrate Types and Compositions in Shallow Streams." Remote Sensing 11, no. 3 (2019): 262. http://dx.doi.org/10.3390/rs11030262.

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Remote sensing of riverbed compositions could enable advances in hydro-morphological and habitat modeling. Substrate mapping in fluvial systems has not received as much attention as in nearshore, optically shallow inland, and coastal waters. As finer spatial-resolution image data become more available, a need emerges to expand research on the remote sensing of riverbed composition. For instance, research to date has primarily been based on spectral reflectance data from above the water surface without accounting for attenuation by the water-column. This study analyzes the impacts of water-colu

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46

Ion, Stelian, Dorin Marinescu, and Stefan-Gicu Cruceanu. "Riemann Problem for Shallow Water Equation with Vegetation." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 2 (2018): 145–73. http://dx.doi.org/10.2478/auom-2018-0023.

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Abstract We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems, it is necessary to introduce a family of paths that connects the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical

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47

Bresch, Didier, Benoît Desjardins, and Chi-Kun Lin. "On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems." Communications in Partial Differential Equations 28, no. 3-4 (2003): 843–68. http://dx.doi.org/10.1081/pde-120020499.

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Bellafiore, D., L. Zaggia, R. Broglia, et al. "Modeling ship-induced waves in shallow water systems: The Venice experiment." Ocean Engineering 155 (May 2018): 227–39. http://dx.doi.org/10.1016/j.oceaneng.2018.02.039.

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Bouarfa, S., and D. Zimmer. "Water-table shapes and drain flow rates in shallow drainage systems." Journal of Hydrology 235, no. 3-4 (2000): 264–75. http://dx.doi.org/10.1016/s0022-1694(00)00280-8.

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Eskilsson, C., and S. J. Sherwin. "Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems." Journal of Scientific Computing 22-23, no. 1-3 (2005): 269–88. http://dx.doi.org/10.1007/s10915-004-4140-x.

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