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Keywords = abrupt jumps

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17 pages, 1754 KiB  
Article
A Fuzzy Five-Region Membership Model for Continuous-Time Vehicle Flow Statistics in Underground Mines
by Hao Wang, Maoqua Wan, Hanjun Gong and Jie Hou
Processes 2025, 13(8), 2434; https://doi.org/10.3390/pr13082434 - 31 Jul 2025
Abstract
Accurate dynamic flow statistics for trackless vehicles are critical for efficiently scheduling trackless transportation systems in underground mining. However, traditional discrete time-point methods suffer from “time membership discontinuity” due to RFID timestamp sparsity. This study proposes a fuzzy five-region membership (FZFM) model to [...] Read more.
Accurate dynamic flow statistics for trackless vehicles are critical for efficiently scheduling trackless transportation systems in underground mining. However, traditional discrete time-point methods suffer from “time membership discontinuity” due to RFID timestamp sparsity. This study proposes a fuzzy five-region membership (FZFM) model to address this issue by subdividing time intervals into five characteristic regions and constructing a composite Gaussian–quadratic membership function. The model dynamically assigns weights to adjacent segments based on temporal distances, ensuring smooth transitions between time intervals while preserving flow conservation. When validated on a 29-day RFID dataset from a large coal mine, FZFM eliminated conservation bias, reduced the boundary mutation index by 11.1% compared with traditional absolute segmentation, and maintained high computational efficiency, proving suitable for real-time systems. The method effectively mitigates abrupt flow jumps at segment boundaries, providing continuous and robust flow distributions for intelligent scheduling algorithms in complex underground logistics systems. Full article
(This article belongs to the Special Issue Data-Driven Analysis and Simulation of Coal Mining)
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13 pages, 2983 KiB  
Article
Impact of Reset Pulse Width on Gradual Conductance Programming in Al2O3/TiOx-Based RRAM
by Hyeonseong Lim, Wonbo Shim and Tae-Hyeon Kim
Micromachines 2025, 16(6), 718; https://doi.org/10.3390/mi16060718 - 17 Jun 2025
Viewed by 486
Abstract
This work investigates the impact of reset pulse width on multilevel conductance programming in Al2O3/TiOx-based resistive random access memory. A 32 × 32 cross-point array of Ti (12 nm)/Pt (62 nm)/Al2O3 (3 nm)/TiOx [...] Read more.
This work investigates the impact of reset pulse width on multilevel conductance programming in Al2O3/TiOx-based resistive random access memory. A 32 × 32 cross-point array of Ti (12 nm)/Pt (62 nm)/Al2O3 (3 nm)/TiOx (32 nm)/Ti (14 nm)/Pt (60 nm) devices (2.5 µm × 2.5 µm active area) was fabricated via e-beam evaporation, atomic layer deposition, and reactive sputtering. Following an initial forming step and a stabilization phase of five DC reset–set cycles, devices were programmed using an incremental step pulse programming (ISPP) scheme. Reset pulses of fixed amplitude were applied with widths of 100 µs, 10 µs, 1 µs, and 100 ns, and the programming sequence was terminated when the read current at 0.2 V exceeded a 45 µA target. At a 100 µs reset pulse width, most cycles exhibited abrupt current jumps that exceeded the target current, whereas at a 100 ns width, the programmed current increased gradually in all cycles, enabling precise conductance tuning. Cycle-to-cycle variation decreased by more than 50% as the reset pulse width was reduced, indicating more uniform filament disruption and regrowth. These findings demonstrate that controlling reset pulse width offers a straightforward route to reliable, linear multilevel operation in Al2O3/TiOx-based RRAM. Full article
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18 pages, 644 KiB  
Article
From Jump-Start to Phase-Out—Transitioning Policy Making Towards a Primarily Market Driven Charging Infrastructure Rollout in Germany
by Johannes Martin Loehr and Maik Hanken
World Electr. Veh. J. 2025, 16(6), 300; https://doi.org/10.3390/wevj16060300 - 29 May 2025
Viewed by 500
Abstract
During the early phases of EV market penetration, German policy makers supported the roll-out of a nation-wide charging infrastructure network by extensive state activities, most notably voluminous funding schemes to provide subsidies for publicly owned as well as business-driven charge point operators. An [...] Read more.
During the early phases of EV market penetration, German policy makers supported the roll-out of a nation-wide charging infrastructure network by extensive state activities, most notably voluminous funding schemes to provide subsidies for publicly owned as well as business-driven charge point operators. An increasing EV adoption rate and therefore an increasing demand has since shifted the focus of policy making towards enabling a privately funded, competitive market. More recently, budgetary constraints have led to abrupt restrictions on policy making and market disruptions. This paper aims to provide insight into policy making during this transitional period, give reason for why a state-funded jump start was necessary for developing the charging infrastructure, and explore how policy makers now intend to foster the development of a functioning market while phasing out detrimental interventionist measures. Full article
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15 pages, 6118 KiB  
Article
Wind Performance of New and Existing Continuous Beam Bridges During Construction Stages
by Fulin Yang, Xinmin Zhang, Zeen Xie and Jianming Hao
Buildings 2025, 15(5), 791; https://doi.org/10.3390/buildings15050791 - 28 Feb 2025
Viewed by 711
Abstract
This study assesses the wind resistance and vortex-induced vibration (VIV) risks of the Dongzhou River Bridge in China reconstruction during critical construction stages. Computational Fluid Dynamics (CFD) simulations analyzed wind effects when the twin main girders were maximally separated, revealing asymmetric vortex shedding [...] Read more.
This study assesses the wind resistance and vortex-induced vibration (VIV) risks of the Dongzhou River Bridge in China reconstruction during critical construction stages. Computational Fluid Dynamics (CFD) simulations analyzed wind effects when the twin main girders were maximally separated, revealing asymmetric vortex shedding patterns influenced by upstream–downstream aerodynamic interactions. The upstream girder’s wake generated complex flow fields, increasing turbulence on the downstream girder and indicating elevated VIV susceptibility. A 1:50 scale aeroelastic model validated these findings through wind tunnel tests, confirming that CFD-predicted critical VIV wind speeds aligned with experimental observations. Tests identified a distinct “jump-like” vibration mode at specific wind speeds (35–40 m/s full-scale equivalent), characterized by abrupt amplitude escalation rather than gradual growth—a signature of unstable VIV resonance. However, measured amplitudes remained below the 61.5 mm full-scale equivalent safety threshold, confirming that vibrations posed no critical risk. While aerodynamic coupling between girders requires monitoring during cantilever construction, the study concludes that existing control measures ensure safe construction and operation without structural modifications. These results provide actionable guidelines for wind risk mitigation through construction sequencing and real-time wind speed restrictions. Full article
(This article belongs to the Section Building Structures)
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12 pages, 2159 KiB  
Article
Dynamic Analysis of Support Bracket of the Oceanic Bridge Fabrication Machine (Movable Formwork)
by Zongshuai Zhou and Linjian Shangguan
J. Mar. Sci. Eng. 2025, 13(1), 31; https://doi.org/10.3390/jmse13010031 - 29 Dec 2024
Viewed by 861
Abstract
This study aims to evaluate the vibration and response performance of the core component support bracket in the DXZ32/900 oceanic bridge fabrication machine (movable formwork) to provide a foundation for its structural optimization. A finite element model of the support bracket is established, [...] Read more.
This study aims to evaluate the vibration and response performance of the core component support bracket in the DXZ32/900 oceanic bridge fabrication machine (movable formwork) to provide a foundation for its structural optimization. A finite element model of the support bracket is established, and three analyses are conducted: modal analysis to determine inherent frequencies and vibration modes, harmonic response analysis to evaluate steady-state behavior under sinusoidal loads, and transient dynamic analysis to assess displacement responses to dynamic loads. The frequency distribution indicates that the natural frequencies are densely packed without abrupt jumps, reflecting the complexity of the dynamic performance of the support bracket. Moreover, frequencies below the fourth order exhibit minimal deformation and limited impact on the overall dynamics. Sensitivity analysis is conducted to evaluate the impact of sectional parameter optimization on material efficiency and dynamic performance, ensuring robust design improvements. In summary, the findings reveal key vibration characteristics and response patterns, providing theoretical insights to guide the improvement of the support bracket and ensure the safety and efficiency of the bridge fabrication machine. Full article
(This article belongs to the Section Ocean Engineering)
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20 pages, 788 KiB  
Article
Fuzzy Resilient Control of DC Microgrids with Constant Power Loads Based on Markov Jump Models
by Wei Hu, Yu Shen, Fan Yang, Zhen Chang and Shanglin Zhao
Mathematics 2024, 12(17), 2656; https://doi.org/10.3390/math12172656 - 27 Aug 2024
Cited by 2 | Viewed by 828
Abstract
This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics [...] Read more.
This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics which are characterized by a T-S fuzzy model. According to the parallel distributed compensation principle, mode-dependent fuzzy resilient controllers are designed to stabilize the resultant T-S fuzzy Markov jump DC microgrid. The “resilient” means the controller could cope with the uncertainty caused by the inaccurate execution of the control laws. This uncertainty is governed by a Bernoulli distributed random variable and thus may not occur. Then, the mean square exponential stability is analyzed for the closed-loop system by using the mode-dependent Lyapunov function. Since the stability conditions are not convex, a design algorithm is further derived to calculate the fuzzy resilient controller gains. Finally, simulations are provided to test the effectiveness of the proposed results. Full article
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24 pages, 14057 KiB  
Article
Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions
by Sergei Aliukov
Mathematics 2024, 12(1), 138; https://doi.org/10.3390/math12010138 - 31 Dec 2023
Cited by 1 | Viewed by 1225
Abstract
In recent years, the economies of many countries around the world have been in a situation of intense, rapidly changing, abrupt processes. The current situation urgently requires a change in the economic paradigm in the near future, which leads to the need to [...] Read more.
In recent years, the economies of many countries around the world have been in a situation of intense, rapidly changing, abrupt processes. The current situation urgently requires a change in the economic paradigm in the near future, which leads to the need to develop new conceptual models. The purpose of the article is to develop basic theoretical principles and practical approaches to modeling macroeconomic processes based on the analysis of jump and generalized functions. The objectives of the study are the following: (1) describe the main types of impulse and jump functions using examples from economic theory and practice; (2) perform an analytical representation of impulse and jump functions; (3) select macroeconomic characteristics to analyze rapidly changing processes in the economy; and (4) create models and mechanisms for forecasting impulsive and abrupt changes in the macroeconomy. The approaches to the development of macroeconomic theory and its methods proposed in the article are not associated with the use of evolutionary continuous functions; for example, power functions, which is typical for many canonical macroeconomic models. These approaches do not include management decisions to achieve optimal values of given target functions, which is typical for recursive macroeconomic models of dynamic programming. This article is about formulating the main provisions of macroeconomic theory and its methods, which, with varying degrees of accuracy, could give a forecast about the upcoming possibility of sudden changes (impulse, shock, spasmodic, and others) in the macroeconomic situation. The research methodology is statistical analysis, special methods developed by the author for studying impulse, and jump processes. As a result of this study, the basic principles of modeling macroeconomic theory based on rapid impulse and abrupt changes were formulated, approaches to constructing the tools of this theory were outlined, and problems and tasks for further research were identified. Full article
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20 pages, 8476 KiB  
Article
Modeling and Comparative Analysis of Atmospheric Pressure Anodic Carbon Arc Discharge in Argon and Helium–Producing Carbon Nanostructures
by Almaz Saifutdinov and Boris Timerkaev
Nanomaterials 2023, 13(13), 1966; https://doi.org/10.3390/nano13131966 - 28 Jun 2023
Cited by 18 | Viewed by 2596
Abstract
In this work, within the framework of a unified model for the discharge gap and electrodes, a comparative numerical analysis was carried out on the effect of evaporation of graphite anode material on the characteristics of the arc discharge in helium and argon. [...] Read more.
In this work, within the framework of a unified model for the discharge gap and electrodes, a comparative numerical analysis was carried out on the effect of evaporation of graphite anode material on the characteristics of the arc discharge in helium and argon. The effect of changing the plasma-forming ion, in which the ion of evaporated atomic carbon becomes the dominant ion, is demonstrated. For an arc discharge in helium, this effect is accompanied by a jump-like change in the dependence of the current density on voltage (CVC), and smoothly for a discharge in argon. With regard to the dynamics of the ignition of an arc discharge, it is shown that during the transition from glow discharge to arc in helium, the discharge parameters are also accompanied by an abrupt change, while in argon, this transition is smooth. This is due to the fact that the ionization potentials, as well as the ionization cross sections, differ significantly for helium and carbon, and are close in value for helium and argon. For various points on the CVC, the density distributions of the charged and neutral particles of an inert gas and evaporated gases are presented. Full article
(This article belongs to the Special Issue Synthesis of Nanostructures in Gas-Discharge Plasma)
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19 pages, 1821 KiB  
Article
Markovian-Jump Reinforcement Learning for Autonomous Underwater Vehicles under Disturbances with Abrupt Changes
by Wenjie Lu, Yongquan Huang and Manman Hu
J. Mar. Sci. Eng. 2023, 11(2), 285; https://doi.org/10.3390/jmse11020285 - 27 Jan 2023
Cited by 1 | Viewed by 1990
Abstract
This paper studies the position regulation problems of an Autonomous Underwater Vehicle (AUV) subject to external disturbances that may have abrupt variations due to some events, e.g., water flow hitting nearby underwater structures. The disturbing forces may frequently exceed the actuator capacities, necessitating [...] Read more.
This paper studies the position regulation problems of an Autonomous Underwater Vehicle (AUV) subject to external disturbances that may have abrupt variations due to some events, e.g., water flow hitting nearby underwater structures. The disturbing forces may frequently exceed the actuator capacities, necessitating a constrained optimization of control inputs over a future time horizon. However, the AUV dynamics and the parameters of the disturbance models are unknown. Estimating the Markovian processes of the disturbances is challenging since it is entangled with uncertainties from AUV dynamics. As opposed to a single-Markovian description, this paper formulates the disturbed AUV as an unknown Markovian-Jump Linear System (MJLS) by augmenting the AUV state with the unknown disturbance state. Based on an observer network and an embedded solver, this paper proposes a reinforcement learning approach, Disturbance-Attenuation-net (MDA–net), for attenuating Markovian-jump disturbances and stabilizing the disturbed AUV. MDA–net is trained based on the sensitivity analysis of the optimality conditions and is able to estimate the disturbance and its transition dynamics based on observations of AUV states and control inputs online. Extensive numerical simulations of position regulation problems and preliminary experiments in a tank testbed have shown that the proposed MDA–net outperforms the existing DOB–net and a classical approach, Robust Integral of Sign of Error (RISE). Full article
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15 pages, 3212 KiB  
Article
PN Codes Estimation of Binary Phase Shift Keying Signal Based on Sparse Recovery for Radar Jammer
by Bo Peng and Qile Chen
Sensors 2023, 23(1), 554; https://doi.org/10.3390/s23010554 - 3 Jan 2023
Cited by 4 | Viewed by 3012
Abstract
Parameter estimation is extremely important for a radar jammer. With binary phase shift keying (BPSK) signals widely applied in radar systems, estimating the parameters of BPSK signals has attracted increasing attention. However, the BPSK signal is difficult to be processed by traditional time [...] Read more.
Parameter estimation is extremely important for a radar jammer. With binary phase shift keying (BPSK) signals widely applied in radar systems, estimating the parameters of BPSK signals has attracted increasing attention. However, the BPSK signal is difficult to be processed by traditional time frequency analysis methods due to its phase jumping and abrupt discontinuity features which makes it difficult to extract PN (PN) codes of the BPSK signal. To solve this problem, a two-step PN codes estimation method based on sparse recovery is introduced in this paper. The proposed method first pretreats the BPSK signal by estimating its center frequency and converting it to zero intermediate frequency (ZIF). The pretreatment transforms phase jumps of the BPSK signal into the level jumps of the ZIF signal. By nonconvex sparsity promoting regularization, the level jumps of the ZIF signal are extracted through an iterative algorithm. Its effectiveness is verified by numeric simulations and semiphysical tests. The corresponding results demonstrate that the proposed method is able to estimate PN codes from the BPSK signal in serious electromagnetic environments. Full article
(This article belongs to the Special Issue Advances in Radar Sensors)
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12 pages, 5345 KiB  
Article
Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed
by Marzieh Naem Hasani, Kouros Nekoufar, Morteza Biklarian, Morteza Jamshidi, Quoc Bao Pham and Duong Tran Anh
Water 2023, 15(1), 80; https://doi.org/10.3390/w15010080 - 26 Dec 2022
Cited by 6 | Viewed by 2730
Abstract
Stilling basins with sudden expansions are one of the energy dissipation structures. In the hydraulic jump, pressure fluctuations cause significant damages in stilling basins by cavity formation, erosion, and vibration. Roughness can also lead to changes of the behavior of stream lines and [...] Read more.
Stilling basins with sudden expansions are one of the energy dissipation structures. In the hydraulic jump, pressure fluctuations cause significant damages in stilling basins by cavity formation, erosion, and vibration. Roughness can also lead to changes of the behavior of stream lines and vortices. Despite the large number of works on the topic, the role of roughness in spatial hydraulic jumps is not yet fully understood. Present research aimed to study the influence of rough bed on pressure fluctuations of S-jump in abrupt expanding stilling basin. Experiments were conducted in a 0.8 m width and 12 m length flume. Channel expansions ratios were 0.33, 0.5, 0.67, and 1 within the range of Froude numbers, 2 to 9.5. The results showed that roughness decreases intensity of pressure fluctuations in an abrupt expansion stilling basin. Additionally, in sudden expanding sections, the energy loss increases, and the intensity of pressure fluctuations decrease due to the formation of lateral vortices. The reduction rate of maximum pressure fluctuation was 27%, 46%, and 58% for expansion ratio of 0.67, 0.5, and 0.33, respectively. The results revealed the clear dependence of these variables on the Froude number and the distance to the hydraulic jump toe. The maximum values of extreme pressure fluctuations occur in the range 0.609 < X < 3.385, where X is dimensionless distance from the toe of the hydraulic jump, which makes it highly advisable to reinforce the bed of stilling basins in this range. Full article
(This article belongs to the Special Issue Advances in Hydraulic Engineering Management)
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19 pages, 984 KiB  
Article
Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method
by Stanley S. Coelho, Lucas Queiroz and Danilo T. Alves
Entropy 2022, 24(12), 1851; https://doi.org/10.3390/e24121851 - 19 Dec 2022
Cited by 10 | Viewed by 5259
Abstract
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency [...] Read more.
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency ω1 and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis–Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when ω1<ω0. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state. Full article
(This article belongs to the Special Issue Quantum Nonstationary Systems)
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22 pages, 5397 KiB  
Article
Spatial-Temporal Variations of Active Accumulated Temperature and Its Impact on Vegetation NDVI in the Source Region of China’s Yellow River
by Henan Gu, Jian Luo, Guofang Li, Yueling Yao, Yan Huang and Dongjing Huang
Water 2022, 14(21), 3458; https://doi.org/10.3390/w14213458 - 29 Oct 2022
Cited by 3 | Viewed by 1960
Abstract
Global climate change has greatly influenced the ecosystems in the Tibetan Plateau. Many studies focused on the direct effects of climate warming on the headwater regions by mean temperature, while less investigating its implication for the eco-environment. To address this, the study discussed [...] Read more.
Global climate change has greatly influenced the ecosystems in the Tibetan Plateau. Many studies focused on the direct effects of climate warming on the headwater regions by mean temperature, while less investigating its implication for the eco-environment. To address this, the study discussed the spatial-temporal variations of the bio-related climate indicators ≥0 °C annual accumulated temperature AAT0 and its lasting days LDT0, and corresponding ≥5 °C indicators AAT5 and LDT5 on the source region of the Yellow River (SRYR). The stationarity of indicators during 1979–2018 were tested by Pettitt test, and trends checked by linear regression analysis and Mann-Kendall test. Normalized difference vegetation index NDVI (2001–2016) was adopted to detect the correlation between vegetation activities and indicators. Results show that the AAT and LDT0 exhibited significant increasing trend over the SRYR, while the LDT5 significantly increased mainly under 4000 m. Most LDT extended due to the combined efforts of the early onset and late termination of the given temperature. 1997 was detected in the abrupt change analysis of AAT0 both on the basin scale and most area, and was adopted to divide the period into two stages. The regional mean AAT0 linearly grew at a rate of 96 °C decade−1 during the entire period, and 104 °C decade−1 during the second stage. Except for a drastic jump in the areal mean values, there was a distinct upward-shift of isoline in elevation between stages. NDVI showed strong correlativity with ≥0 °C indicators on the basin scale, according to the Pearson, Spearman and Kendall correlation coefficients, ranging from 0.5 to 0.7. Spatially, the overlap area between Pearson’s γ ≥ 0.5 and linearly rising AAT0 reached 50%, which was fully covered with significantly increasing AAT0 during the recent stage. Thus the rapid growth of ≥0 °C indicators would effectively accelerate NDVI over this major alpine grasslands, especially around the eastern low regions, where indicators are higher and grow faster. Full article
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27 pages, 10337 KiB  
Article
Implementation and Critical Analysis of the Active Phase Jump with Positive Feedback Anti-Islanding Algorithm
by Ênio Costa Resende, Henrique Tannús de Moura Carvalho and Luiz Carlos Gomes Freitas
Energies 2022, 15(13), 4609; https://doi.org/10.3390/en15134609 - 23 Jun 2022
Cited by 3 | Viewed by 2492
Abstract
The protection against the unintentional islanding of Grid-Tied inverters is an important electrical security issue addressed by the main Standards. This concern is justified in face of the fact that unintentional islanding can lead to abrupt variations of voltage and frequency, electrical damages, [...] Read more.
The protection against the unintentional islanding of Grid-Tied inverters is an important electrical security issue addressed by the main Standards. This concern is justified in face of the fact that unintentional islanding can lead to abrupt variations of voltage and frequency, electrical damages, professional accidents, power quality degradation, and out-of-phase reclosure. In response to the islanding concern, the literature has proposed several Anti-Islanding Protection (AIP) schemes that can be divided in passive and active methods. Many of the active AIP is based on the insertion of some disturbance in the inverter current in order to deviate the frequency out of the allowed thresholds, tripping the inverter internal disconnection system. Thus, the main objective of this paper is to analyze the performance of the Active Phase Jump with Positive Feedback (APJPF) algorithm compared to other well-known frequency drift-based solutions. More than that, this work covers the Non-Detection Zone (NDZ) problem, analyzing its main mapping methodologies and the normative requirements, exposing the minimum normative recommendations a given AIP must reach to be considered functional. The last contributions of this paper are the proposal of a parametrization criterion for the Active Frequency Drift with Pulsating Chopping Factor (AFDPCF) and for the APJPF. Full article
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33 pages, 7522 KiB  
Article
Supercritical Flow over a Submerged Vertical Negative Step
by Eugene Retsinis and Panos Papanicolaou
Hydrology 2022, 9(5), 74; https://doi.org/10.3390/hydrology9050074 - 28 Apr 2022
Cited by 2 | Viewed by 3367
Abstract
The transition from supercritical to subcritical flow around a fully submerged abrupt negative step in a horizontal rectangular open channel has been investigated. In a laboratory experiment the one-dimensional energy and the momentum conservation equations were studied by means of depth and pressure [...] Read more.
The transition from supercritical to subcritical flow around a fully submerged abrupt negative step in a horizontal rectangular open channel has been investigated. In a laboratory experiment the one-dimensional energy and the momentum conservation equations were studied by means of depth and pressure measurements by piezometers installed along the bottom and the step face. Froude number varied in the range 1.9 to 5.8 while the step height to critical depth ratio was in the range 1.34 to 2.56. The results are presented in dimensionless form using mainly a characteristic length scale that is the sum of critical depth and step height and the Froude number of the supercritical flow upstream. Five different types of rapidly varying flow are observed when the subcritical downstream tailwater depth varied. The supercritical water jet at the top of the step either strikes the bottom downstream of the step when the maximum pressure head is greater, or moves to the surface of the flow when it is lower than tailwater depth, and the separation of the two flow regimes occurs when the tailwater depth to the characteristic length scale is around 1.05. The normalized energy loss and a closure parameter for the momentum equation are presented in dimensionless diagrams for practical use by the design engineer. Finally, the one-dimensional equations of motion including Boussinesq terms are solved numerically and the results found are congruent to the experimental findings. Full article
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