Shallow Water Research Articles

A Positivity-Preserving and Well-Balanced High Order Compact Finite Difference Scheme for Shallow Water Equations

A Positivity-Preserving and Well-Balanced High Order Compact Finite Difference Scheme for Shallow Water Equations

Potential effects of internal dam-break in Stare Miasto Reservoir in Poland

Study regionThe research object is located in Wielkopolska province (Poland), which is well-known for its rural character and scarcity of water. To prevent droughts, small reservoirs are installed in local watersheds. It enables control of water conditions for agriculture and improvement of local climate. The main challenge is prevention from the deposition of sediments in a reservoir. To minimize this threat, the specific constructions of the reservoir are applied, e.g. internal dams. Study focusThe Stare Miasto reservoir consists of an internal dam with the upper zone separated. The highway bridge split the main part. In 2014 a flood wave propagated through the reservoir. The crest of the internal dam was shifted generating a potential risk of internal dam failure. The consequences of such an event were analyzed using a two-dimensional hydrodynamic numerical tool that solves the shallow water equations with finite volume method on unstructured mesh. New hydrological insight for the regionThe results obtained prove that the dam break increases the risk of bridge instability. The shear stresses generated during break of internal dam may exceed 50 N/m2, what cause danger of deep scour generation under and below the construction. Unexpectedly, the existence of the bridge decreased the threat of the main dam overtopping. The study may be a valuable inspiration for the design of new reservoirs inevitable in controlling water resource conditions in the region.

Exact Solutions of the Shallow Water System with an Inclined Bottom

Exact Solutions of the Shallow Water System with an Inclined Bottom

Анализ работы современных водолазных судов, оснащенных системой динамического позиционирования (DP)

. The principle of operation of modern diving vessels equipped with dynamic positioning (DP) systems is analyzed. The classification of diving operations on such vessels is considered. To perform certain construction work or maintenance of underwater facilities, a diving team is needed – the most important component in an integral part of the most difficult work, where the ROV (remote-controlled uninhabited underwater vehicle) of the working class, equipped with tools for certain purposes, is not adapted for complex tasks. The topic of limiting the length of the hose cable (a technology that ensures the delivery of vital consumables, signals and energy via cable to the diver) for underwater work is touched upon. An assessment of the safe working distance of divers near the bow thrusters and propeller columns of the DP vessel is carried out using the example of the most modern vessel in the Caspian Sea to support diving operations, as well as for the installation of underwater structures of the deep-sea bases of the Khankendi. Conclusions are drawn about the widespread use of DP systems on modern ships, in particular those involved in the oil and gas industry, as well as other areas of the marine industry. A study has been conducted to assess the safety of diving operations of a DP vessel operating in shallow water. An assessment is given to limit the movement of the vessel during diving operations. The specifics of the universal vessel involved in connection with the risks of human life, the working environment of divers, various environmental conditions, the proximity of the vessel's propulsion systems and many other additional risks that pose a danger are indicated. The thesis on the need for careful planning and management of diving operations has been confirmed.

Measurement-based carbon intensity of US offshore oil and gas production

The United States (US) produces oil and gas from six offshore regions: the North Slope of Alaska, Cook Inlet in Alaska, offshore California, and three Gulf of Mexico (GOM) sub-regions: state shallow, federal shallow, and deep waters. Measurement-based assessment of direct greenhouse gas emissions from this production can provide real-world information on carbon emissions to inform decisions on current and future production. In evaluating the climate impact of production, the carbon intensity (CI, the ratio of greenhouse gases emitted compared to the energy of fuels produced) is often used, though it is rarely quantified with measurements. Here, we complete an observational evaluation of the US offshore sector and present the largest current set of measurement-based CIs. We collected airborne measurements of methane, carbon dioxide, and nitrogen oxides from the North Slope, Cook Inlet, and California and combined with prior GOM results. For Alaska and California, we found emissions agree with facility-level inventories, however, the inventories miss some facilities. The US offshore CI, on a 100 year GWP basis, is 5.7 g CO2e/MJ[4.5, 6.8, 95% confidence interval]. This is greater than double the CI based on the national US inventory, with the discrepancy attributed primarily to methane emissions from GOM shallow waters, with a methane dominated CI of 16[12, 22] for GOM federal shallow waters and 43[25–65] for state shallow waters. Regional intensities vary, with carbon dioxide emissions largely responsible for CI on the North Slope 11[7.5, 15], in Cook Inlet 22[13, 34], offshore California 7.2[3.2, 13], and in GOM deep waters 1.1[1.0, 1.1]. These observations indicate offshore operations outside of the GOM in the US have modest methane emissions, but the CI can still be elevated due to direct carbon dioxide emissions. Accurate assessment of different offshore basins, with differing characteristics and practices, is important for the climate considerations of expanded production.

Towards autonomous inland shipping: a manoeuvring model in confined waterways

ABSTRACT Autonomous inland water vessels are essential for promoting intelligent and sustainable waterborne transport. An accurate ship manoeuvring model ensures reliable control strategies and enhances navigation safety. Although ship manoeuvrability models have existed for decades, few studies address shallow and restricted waters. This study introduces a manoeuvring model for inland water vessels, accounting for confinement effects on ship motion. The Manoeuvring Modelling Group (MMG) model in open water serves as the baseline, incorporating empirical methods for shallow water and bank effects. This approach aims to provide a fast and accurate prediction of vessel motion response. The model was validated with free-running experimental data of a pusher-barge model from turning tests at three water depths. Additional case studies highlight shallow water impact compared to infinite water performance under bank effects. Finally, course-keeping case studies are presented, integrating a Proportional-Derivative controller with combined river current and bank-induced forces..

Space–time statistics of 2D soliton gas in shallow water studied by stereoscopic surface mapping

Space–time statistics of 2D soliton gas in shallow water studied by stereoscopic surface mapping

Sponge-associated microbes in the twilight zone of Curaçao

AbstractMesophotic reefs, located in the "Twilight Zone" of the ocean, are coral reefs that exist in relatively deep waters ranging from approximately 30 to 150 m below the surface. These reefs are situated just beyond the reach of conventional SCUBA diving and are typically explored using advanced diving techniques or with the aid of submersibles. In the present study, we used a state-of-the-art submersible to sample 26 sponge specimens belonging to 11 species. High (HMA) or low (LMA) microbial abundance status was assigned to species based on TEM imagery. Prokaryotic communities associated with these sponges were, furthermore, assessed using high-throughput sequencing. Proteobacteria, Chloroflexi, Actinobacteriota, and Acidobacteriota were the most abundant phyla overall. HMA/LMA status proved to be a highly significant predictor of prokaryotic composition. HMA sponges also tended to be more diverse in terms of richness and evenness than LMA sponges. 14 predictor-classes were identified using an exploratory technique based on machine learning including classes within the phyla Chloroflexi (e.g., Dehalococcoidia and JG30-KF-CM66) and Acidobacteriota (Thermoanaerobaculia and Subgroups 11 and 21). Previous studies have demonstrated the prevalence of the HMA/LMA dichotomy in shallow waters and, recently, the deep sea. Our results demonstrate its prevalence in the mesophotic realm.

Numerical study of nonlinear time-fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising in propagation of waves

In this manuscript, the numerical approximation of the solution for time-fractional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) nonlinear partial differential equation is described involving the Caputo fractional derivative with the help of two novel techniques namely, Sumudu Residual Power Series (SRPS) method and Homotopy Perturbation Sumudu Transform (HPST) method. CDGSK equation describe the propagation of capillary waves and shallow water waves. The results obtained through numerical approximation shows that both SRPS and HPST under consideration are reliable and efficient. The present framework precisely reflects the behavior of the obtained result for various fractional orders. Additionally, we conduct a comparison between the exact solution and an approximate series solution to affirm the efficacy of the proposed techniques. This analysis highlights the efficiency and precision of both techniques in solving nonlinear fractional differential equations. All the numerical simulations are demonstrated graphically using Maple and Matlab.

Numerical Investigation on a High-Speed Transom Stern Ship Advancing in Shallow Water

A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed displacement ship with a transom stern moving in shallow water. The nonlinear free surface condition is satisfied by adopting an iterative algorithm on the real free surface. The transom condition is considered by implementing a modified transom condition. Computations of wave-making resistance, sinkage and trim in deep water are first performed, and satisfactory agreement is achieved by comparing with the experimental results; the simulations are then extended to the shallow water case. It indicates that the present method can provide a suitable balance of practicability and robustness, which can be considered as an efficient tool for the guidance in ship design stage.

Fractional view analytical analysis of generalized regularized long wave equation

Abstract In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxiliary function method and the Laplace iterative transform method, we approximate these equations. These formulas are used to characterize plasma waves in oceans and ion acoustic waves in shallow water. The results discovered have important ramifications for our comprehension of many physical events. Our results show that both methods are robust, easy to use, and successful. Both methods yield results that are satisfactory to each other. With the use of tables and graphs, we compared the two suggested approaches. The findings suggest that the suggested methods can be widely applied to explore other real-world problems.

Restoration Strategies in the Heidaigou Open-Pit Mine Dump Based on Water Sources and Plant Water Utilization

In this study, three typical plants capable of restoring in the Heidaigou open-pit mine dump, namely, Pinus sylvestris var. mongolica, Caragana korshinskii, and Medicago sativa, were taken as the research objects. The δ2H and δ18O values of atmospheric precipitation, soil water, stem water, and leaf water were measured using the stable isotope technique, and the distribution characteristics of the δ2H and δ18O values of different water sources were identified. The IsoSource model (version1.3.1) was used to calculate the contribution rate of different water sources to the plants, and the differences and dynamic changes in the water sources for P. sylvestris var. mongolica, C. korshinskii, and M. sativa during the rainy season were examined. Results showed that the water source of the three plants was found to be mainly soil water, and the utilization of each potential water source varied in different periods of the rainy season. In June, when SWC was sufficient, P. sylvestris var. mongolica and M. sativa primarily absorbed and utilized shallow and middle soil water, with relative utilization ratios of 55.5% and 59%, respectively, while C. korshinskii has a more balanced utilization ratio of soil water in each layer, with shallow soil water utilization at 33.7%, middle soil water at 34.2%, and deep soil water at 32.2%. In August, when SWC decreased, P. sylvestris var. mongolica, C. korshinskii, and M. sativa were all transferred to deep soil water, with utilization ratios of 75.8%, 78.8%, and 71.1%, respectively. The values showed that these three typical plants are capable of restoring can respond to external water changes through the plastic transformation of water absorption sources. Among them, C. korshinskii can flexibly use soil water in each layer, has stronger survival competitiveness in drought, and can better adapt to the fragile ecological environment of a mining dump.

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

This article investigates the non-linear generalized geophysical KdV equation, which describes shallow water waves in an ocean. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include U-shaped, W-shaped, singular, periodic, bright, dark, kink-type, breather soliton, multi-singular soliton, singular soliton with high amplitude, multiple periodic, multiple lump wave soliton, and flat kink-type soliton solutions. The travelling wave patterns of the model are graphically presented with suitable parameter values using the modern software Maple and Wolfram Mathematica. The visual representation of the solutions in 3D, 2D, and contour surfaces enhances understanding of parameter impact. Sensitivity and modulation instability analyses were performed to offer insights into the dynamics of the examined model. The observed dynamics of the proposed model were presented, revealing quasi-periodic chaotic, periodic systems, and quasi-periodic behaviour. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.

NONLINEARITY AND MEMORY EFFECTS: THE INTERPLAY BETWEEN THESE TWO CRUCIAL FACTORS IN THE HARRY DYM MODEL

This study investigates the nonlinear time-fractional Harry Dym ([Formula: see text]) equation, a model with significant applications in soliton theory and connections to various other nonlinear evolution equations. The Harry Dym ([Formula: see text]) equation describes the propagation of nonlinear waves in various physical contexts, including shallow water waves, nonlinear optics, and plasma physics. The fractional-order derivative introduces a memory effect, allowing the model to capture nonlocal interactions and long-range dependencies in the wave dynamics. The primary objective of this research is to obtain accurate analytical solutions to the [Formula: see text] equation and explore its physical characteristics. We employ the Khater III method as the primary analytical technique and utilize the He’s variational iteration ([Formula: see text]) method as a numerical scheme to validate the obtained solutions. The close agreement between analytical and numerical results enhances the applicability of the solutions in practical applications of the model. This research contributes to a deeper understanding of the [Formula: see text] equation’s behavior, particularly in the presence of fractional-order dynamics. The obtained solutions provide valuable insights into the complex interplay between nonlinearity and memory effects in the wave propagation phenomena described by the model. By shedding light on the physical characteristics of the [Formula: see text] equation, this study paves the way for further investigations into its potential applications in diverse physical settings.

Well-Balanced conservative central upwind scheme for solving the dam-break flow problem over erodible bed

This work deals with the numerical solution of dam-break flow over an erodible bed. The mathematical model is a combination of the shallow water, the transport diffusion and the bed morphology change equations. The system is solved by a well-Balanced central upwind scheme with conservative property. Several tests are illustrated in order to validate the accuracy and the performance of the model. A comparison of central upwind scheme and Roe scheme is presented.

A Fundamental Study on Inter-Array Cabling Methods Between Two Floating Offshore Wind Turbines in Shallow Waters

As the transition to renewable energy accelerates, interest in wind farms is heightening. There is a need to safely and economically transport energy produced from Floating Offshore Wind Turbines (FOWTs) to the shore. Consequently, this study conducted an analysis of inter-array cabling methods between two FOWTs in shallow waters, targeting the southwestern sea of South Korea. This research targeted four shapes of dynamic power cables: free hanging catenary, lazy wave shape, suspended and W-configuration type. To verify the economy of the dynamic power cable, the total lengths were compared, and to check safety, curvature and tension were examined. Insights obtained through this study indicate that among the four shapes of dynamic power cables, the lazy wave shape has substantial advantages in shallow waters.

Nitrogen migration and transformation during re-suspension and photo-induction in landscape water replenished by reclaimed water.

Sediment re-suspension plays a crucial role in releasing endogenous nitrogen and greenhouse gases in shallow urban waters. However, the impacts of repeated re-suspension and photo-induced processes on migration and transformation from endogenous nitrogen, as well as the emission of greenhouse gases, remain unclear. This study simulated three conditions: re-suspension (Rs), re-suspension combined with ultravioletirradiation (Rs + UV), and ultraviolet irradiation (UV). The findings revealed that both repeated sediment re-suspension and exposure to UV light altered the characteristics of surface sediments. Decrease of convertible nitrogen in sediments, leading to the release of ion-exchangeable nitrogen (IEF-N) into NH4+-N and NO3--N, influenced greenhouse gas production differently under various conditions. The study observed the highest concentration of dissolved N2O in under UV irradiation, positively correlated with NO2--N and NO3--N. Re-suspension increased the turbidity of the overlying water and accelerated nitrification, resulting in the highest NO3--N concentration and the lowest dissolved N2O concentration. Additionally, in the Rs + UV dissolved N2O maintained the higher concentrations than in Rs, with greatest amount of N conversion in surface sediments, and a 59.45% reduction in IEF-N. The production of N2O during re-suspension was mainly positively correlated with NH4+-N in the overlying water. Therefore, this study suggest that repeated re-suspension and light exposure significantly influence nitrogen migration and transformation processes in sediment, providing a theoretical explanation for the eutrophication of water and greenhouse gas emissions.

Rans investigation on the hydrodynamic performance of a ship moving obliquely in shallow and narrow channel

ABSTRACT The ship traveling in restricted waterways often experiences larger hydrodynamic forces and moments, together with larger sinkage, trim and heel, compared with that in open water. The hydrodynamic performance of an oil tanker moving obliquely in a shallow and narrow channel is investigated by using a RANS (Reynolds-Averaged Navier-Stokes) method in this work. The effects of ship-bank distance, water depth, etc. on hydrodynamic performance are analysed. When the ship gets closer to the channel bank or the inclination of the channel bank becomes steeper, the blockage effects due to the channel become more considerable. The effects of shallow water and ship drift motion will augment bank effects. The captive model test for a ship moving obliquely in a shallow and narrow channel are numerically carried out in both Circulating Water Channel (CWC) and Towing Tank (TT). The bank effects showed by TT are more considerable than that by CWC.

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves. Approximate long wave equation with a distinct dispersion relation offers the most accurate description of shallow water wave properties. Various methods, including the Adomian decomposition technique, the variational iteration method, the optimum homotopy asymptotic method, and the new iterative technique, have been employed and compared to those obtained using the fractional-order approximate long wave equation. The results of our study indicate that the optimal auxiliary function method is highly successful and practically simple, achieving better and more rapid convergence after just one repetition. This method is recognized as an efficient approach, demonstrating high precision in solving intriguing and intricate problems. Furthermore, it proves to be more time and resource efficient than other relevant analytical techniques, leading to significant savings in both volume and time. Compared to the Adomian decomposition technique, the new iterative technique, the variational iteration method, and the optimum homotopy asymptotic method, the suggested technique is extremely accurate computationally. It is also easy to analyze and solve fractionally linked nonlinear complex phenomena that arise in science and technology. We present the numerical and graphical findings that support these conclusions.

Niche structure and habitat shifts for coastal sharks of the US Southeast Atlantic and Gulf of Mexico

AbstractUnderstanding spatial ecology and predicting animal movements in response to environmental changes, such as anthropogenic climate change and multidecadal variability, is critical for effective conservation strategies. Niche structuring is key to some coastal shark species and size classes coexisting in the US Atlantic and Gulf of Mexico to limit interspecific and intraspecific interaction. Data from four fishery‐independent bottom longline surveys were used to evaluate the abiotic ecological niches of eight species of small and large coastal sharks. Gaussian mixture models separated length composition data into 14 size categories for ecological niche analysis. Generalized additive mixed effect models were fit and coupled with output from dynamic high‐resolution ocean models to predict suitable abiotic habitats, evaluate potential shifts in distribution, and explore the impacts of large‐scale climatological trends on abiotic habitats from 1994 to 2019. The abiotic niche for small coastal sharks generally tended toward warmer, high salinity, shallow bottom waters close to shore. No overarching niche was found for large coastal sharks, but appreciable ontogenetic differences were seen. Most taxa analyzed exhibited declining annual trends in higher quality habitats, particularly during fall months. The analysis provided evidence of shifts north along the Atlantic, to deeper offshore waters in the Atlantic and Gulf of Mexico, and the potential to redistribute in response to multidecadal climate variability for multiple species. The analytical framework described could aid in developing various spatiotemporal management measures, and results provide insight into the habitat characteristics of several species over broad spatiotemporal ranges and through ontogeny.