Search Results (255)

The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the $(G^{\prime }/G)$ expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article

In this study, we focus on solving the nonlinear time-fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations, using the Yang transform iterative method (YTIM). This method combines the Yang transform with a new iterative scheme to construct reliable and efficient solutions. Readers can understand the procedures clearly, since the implementation of Yang transform directly transforms fractional derivative sections into algebraic terms in the given problems. The new iterative scheme is applied to generate series solutions for the provided problems. The fractional derivatives are considered in the Caputo sense. To validate the proposed approach, two numerical examples are analysed and compared with exact solutions, as well as with the results obtained from the fractional reduced differential transform method (FRDTM) and the q-homotopy analysis transform method (q-HATM). The comparisons, presented through both tables and graphical illustrations, confirm the enhanced accuracy and reliability of the proposed method. Moreover, the effect of varying the fractional order is explored, demonstrating convergence of the solution as the order approaches an integer value. Importantly, the time-fractional Hirota–Satsuma coupled KdV and modified Korteweg–de Vries (MKdV) equations investigated in this work are not only of theoretical and computational interest but also possess significant implications for achieving global sustainability goals. Specifically, these equations contribute to the Sustainable Development Goal (SDG) “Life Below Water” by offering advanced modelling capabilities for understanding wave propagation and ocean dynamics, thus supporting marine ecosystem research and management. It is also relevant to SDG “Climate Action” as it aids in the simulation of environmental phenomena crucial to climate change analysis and mitigation. Additionally, the development and application of innovative mathematical modelling techniques align with “Industry, Innovation, and Infrastructure” promoting advanced computational tools for use in ocean engineering, environmental monitoring, and other infrastructure-related domains. Therefore, the proposed method not only advances mathematical and numerical analysis but also fosters interdisciplinary contributions toward sustainable development. Full article

Recent advances in passive acoustic monitoring (PAM) have markedly improved the ability to study marine soundscapes by enabling long-term, non-invasive monitoring of biological sounds across large spatial and temporal scales. Among aquatic organisms, fish are primary contributors to biophony, producing sounds associated with feeding, reproduction, and social behavior. However, the majority of previous research has focused on individual vocalizations, with limited attention to collective acoustic phenomena such as fish choruses. This study quantitatively analyzes choruses produced by the small yellow croaker (Larimichthys polyactis), an ecologically and commercially important species in the Northwest Pacific Ocean. Using power spectral density (PSD) analysis, we examined long-term underwater recordings from a sea cage containing approximately 2000 adult small yellow croakers. The choruses were centered around ~600 Hz and exhibited sound pressure levels 15–20 dB higher at night than during the day. These findings highlight the ecological relevance of fish choruses and support their potential use as indicators of biological activity. This study lays the foundation for incorporating fish choruses into soundscape-based PAM frameworks to enhance biodiversity and habitat monitoring. Full article

Stylolites are a common mineral dissolution feature in rocks that develop during compression and form distinct tooth structures. On a tectonic plate scale, mid-ocean ridges (MORs) and transform faults are a significant feature of the Earth’s surface that develop due to accretion of new material in an extensional regime. We present a comparison between the two features and argue that transform faults in MOR are similar to the sides of stylolite teeth, with both features representing kinematic faults (KFs). First, we present a numerical model of both stylolite and MOR growth and show that in both cases, KFs nucleate and grow spontaneously. In addition, we use a well-established technique (Family–Vicsek scaling) of describing fractal self-affine interfaces, which has been used for stylolites, to characterize the pattern of MOR systems in both simulations and natural examples. Our results show that stylolites and MOR have self-affine scaling characteristics with similar scaling regimes. They both show a larger roughness exponent at the small scale, a smaller exponent at the intermediate scale, followed by a flattening of the system at the largest scale. For stylolites, the physical forces behind the scaling are the surface energy at the small mineral scale, the elastic energy at the intermediate scale, followed by the system reaching the correlation length where growth stops. For MORs, the physical forces behind the scaling are not yet clear; however, the self-affine scaling shows that transform faults at MORs do not have a preferred spacing, but that the spacing is fractal. Our study offers a new perspective on the study of natural roughening phenomena on various scales, from minerals to tectonic plates, and a new view on the development of MORs. Full article

Underwater vehicles serve as critical assets for global ocean exploration and naval capability enhancement. The marine environment exhibits intricate hydrodynamic phenomena that significantly threaten underwater vehicle navigation safety, particularly in four prevalent complex conditions: surface waves, oceanic currents, stratified fluids, and internal waves. This comprehensive review systematically examines the impacts of these four marine environments on underwater vehicles through critical analysis and synthesis of contemporary advances in theoretical frameworks, experimental methodologies, and numerical simulation approaches. The identified influences are categorized into five primary aspects: hydrodynamic characteristics, dynamic response patterns, load distribution mechanisms, navigation trajectory optimization, and stealth performance. Particular emphasis is placed on internal wave interactions, with rigorous analysis derived from experimental investigations and numerical modeling of internal wave dynamics and their coupling effects with underwater vehicles. In addition, this review points out and analyzes the shortcomings of the current research in various aspects and puts forward some thoughts and suggestions for future research directions that are worth further exploration, including enriching the research objects, upgrading the experimental techniques, and introducing artificial intelligence methods. Full article

Fluid effects are important in films and advertisements, where their realism and aesthetic quality directly impact the visual experience. With the rapid advancement of digital technology and computer-aided design (CAD), modern visual effects are used to simulate various water-related phenomena, such as flowing water, ocean waves, and raindrops. However, creating these realistic effects is not solely dependent on advanced software and hardware; it also requires an understanding of the technical and artistic aspects of visual effects artists. In the creation process, the artist must possess a keen aesthetic sense and innovative thinking to craft stunning visual effects to overcome technological constraints. Whether depicting the grandeur of turbulent ocean scenes or the romance of gentle rain, the artist needs to transform fluid effects into expressive visual language to enhance emotional impact, aligning with the storyline and the director’s vision. The production process of fluid effects typically involves the following critical steps. First, the visual effects artist utilizes CAD-based tools, particle systems, or fluid simulation software to model the dynamic behavior of water. This process demands a solid foundation in physics and the ability to adjust parameters flexibly according to the specific needs of the scene, ensuring that the fluid motion appears natural and smooth. Next, in the rendering stage, the simulated fluid is transformed into realistic imagery, requiring significant computational power and precise handling of lighting effects. Finally, in the compositing stage, the fluid effects are seamlessly integrated with live-action footage, making the visual effects appear as though they are parts of the actual scene. In this study, the technical details of creating fluid effects using free software such as Blender were explored. How advanced CAD tools are utilized to achieve complex water effects was also elucidated. Additionally, case studies were conducted to illustrate the creative processes involved in visual effects production to understand how to seamlessly blend technology with artistry to create unforgettable visual spectacles. Full article

The time-fractional generalized Burger–Fisher equation (TF-GBFE) is utilized in many physical applications and applied sciences, including nonlinear phenomena in plasma physics, gas dynamics, ocean engineering, fluid mechanics, and the simulation of financial mathematics. This mathematical expression explains the idea of dissipation and shows how advection and reaction systems can work together. We compare the homotopy perturbation transform method and the new iterative method in the current study. The suggested approaches are evaluated on nonlinear TF-GBFE. Two-dimensional (2D) and three-dimensional (3D) figures are displayed to show the dynamics and physical properties of some of the derived solutions. A comparison was made between the approximate and accurate solutions of the TF-GBFE. Simple tables are also given to compare the integer-order and fractional-order findings. It has been verified that the solution generated by the techniques given converges to the precise solution at an appropriate rate. In terms of absolute errors, the results obtained have been compared with those of alternative methods, including the Haar wavelet, OHAM, and q-HATM. The fundamental benefit of the offered approaches is the minimal amount of calculations required. In this research, we focus on managing the recurrence relation that yields the series solutions after a limited number of repetitions. The comparison table shows how well the methods work for different fractional orders, with results getting closer to precision as the fractional-order numbers get closer to integer values. The accuracy of the suggested techniques is greatly increased by obtaining numerical results in the form of a fast-convergent series. Maple is used to derive the approximate series solution’s behavior, which is graphically displayed for a number of fractional orders. The computational stability and versatility of the suggested approaches for examining a variety of phenomena in a broad range of physical science and engineering fields are highlighted in this work. Full article

As the core components of geophysical dynamic system, oceans and atmospheres are dominated by the Coriolis force, which governs complex dynamic phenomena such as internal waves, gravity currents, vortices, and others involving multi-scale spatiotemporal coupling. Due to the limitations of in situ observations, large-scale rotating tanks have emerged as critical experimental platforms for simulating Earth’s rotational effects. This review summarizes recent advancements in rotating tank applications for studying oceanic flow phenomena, including mesoscale eddies, internal waves, Ekman flows, Rossby waves, gravity currents, and bottom boundary layer dynamics. Advanced measurement techniques, such as particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), have enabled quantitative analyses of internal wave breaking-induced mixing and refined investigations of vortex merging dynamics. The findings demonstrate that large-scale rotating tanks provide a controllable experimental framework for unraveling the physical essence of geophysical fluid motions. Such laboratory experimental endeavors in a rotating tank can be applied to more extensive scientific topics, in which the rotation and stratification play important roles, offering crucial support for climate model parameterization and coupled ocean–land–atmosphere mechanisms. Full article

Blocking anticyclones are important atmospheric phenomena generally associated with extreme weather (e.g., droughts and cold air surges). Blockings also constitute large-scale indicators of climate change. The study of blockings in the Southern Hemisphere (SH) has been traditionally carried out utilizing reanalysis products. This paper is aimed at presenting an updated, comprehensive climatology of blockings in the SH as extracted from the ERA5 and the NCEP/NCAR reanalysis datasets in the 1940–2022 and 1948–2022 periods, respectively. Blockings were located by means of a unidimensional index at 500 hPa. The results were stratified by season, longitude, region, persistence, and intensity, and the climatology from both datasets was compared. The primary location of blockings was close to the Date Line in every season. Additionally, depending on the season, up to fourth-rank maxima could be located. Generally, the secondary maxima were found in the south Atlantic; lower-order maxima were located in the south-eastern Pacific, west of South America, and in the south-western Indian Ocean east of South Africa. The most intense blockings were concentrated in the Pacific and in the south Atlantic in both datasets, and they were also located in the Indian Ocean, but in the ERA5 reanalysis only. The longest-lived blockings occurred in the south Pacific and in the south Atlantic during southern winter. Full article

The objective of this study is to detect the locations of submarine groundwater discharge (SGD) in the coastal area of the El Jebha region, located in northwestern Morocco. It is hypothesized that this zone is fed by one of the most rain-rich karstic aquifers in Morocco (the Dorsale Calcaire). The region’s geology is complex, characterized by multiple faults and fractures. Thermal remote sensing is used in this study to locate potential SGD zones, as groundwater emerging from karst systems is typically cooler than surrounding ocean water. Landsat satellite imagery was used to assess temperature variations and detect anomalies associated with the presence of freshwater in the marine environment. El Jebha’s geographical location, with a direct interface between limestone and sea, makes it an ideal site for the appearance of submarine groundwater discharges. This study constitutes the first use of Landsat-8/9 thermal-infrared imagery, processed with a multi-temporal fuzzy-overlay method, to detect SGD. Out of 107 Landsat scenes reviewed, 16 cloud-free images were selected. The workflow identified 18 persistent cold anomalies, of which three were classified as high-probability SGD zones based on recurrence and spatial consistency. The results highlight several potential SGD zones, confirming the cost-effectiveness of thermal remote sensing in mapping thermal anomalies and opening up new perspectives for the study of SGD in Morocco, where these phenomena remain rarely documented. Full article

The internal growth patterns and surface micromorphology of diamonds provide a record of their multi-stage evolution, from initial formation within the mantle to their eventual ascent to the Earth’s surface via deeply derived kimberlite magmas. In this study, gemological microscopic examination, Diamond View^TM, Raman spectroscopy, and electron probe analysis were employed to analyze the surface features, internal patterns, and inclusions of the Tancheng alluvial diamonds in Shandong Province, China. The results show that surface features of octahedra with triangular and sharp edges, thick steps with irregular contours or rounded edges, and thin triangular or serrated layers are developed on diamonds during deep-mantle storage, as well as during the growth process of diamonds, when they are not subjected to intense dissolution. The rounding of octahedral and cubic diamond edges and their transformation into tetrahedral (THH) shapes are attributed to resorption in kimberlitic magma. These characteristics indicate that the Tancheng diamonds were commonly resorbed by carbonate–silicate melts during mantle storage. Abnormal birefringence phenomena, including irregular extinction patterns, petaloid and radial extinction patterns, and banded birefringence, were formed during the diamond growth stage. In contrast, fine grid extinction patterns and composite superimposed extinction patterns are related to later plastic deformation. The studied diamonds mainly contain P-type inclusions of olivine and graphite, with a minority of E-type inclusions, including coesite and omphacite. The pressure of entrapment of olivine inclusions within the Tancheng diamonds ranges from 4.3 to 5.9 GPa, which is consistent with that of coesite inclusions, which yield pressure ranging from 5.2 to 5.5 GPa, and a temperature range of 1083–1264 °C. Overall, the evidence suggests that Tancheng diamonds probably originated from hybrid mantle sources metasomatized by the subduction of ancient oceanic lithosphere. Full article

Ocean color remote sensing technology has proven to be an indispensable tool for monitoring ocean conditions, as it has consistently provided critical data on global ocean optical properties, color, and biogeochemical parameters over several decades. With the rapid advancement of artificial intelligence, the integration of machine learning (ML) models into ocean color remote sensing has become a significant focus within the scientific community. This article provides a comprehensive review of the current status and challenges associated with ML models in ocean color remote sensing, assessing their applications in atmospheric correction, color inversion, carbon cycle analysis, and data reconstruction. This review highlights the advancements made in applying ML techniques, such as neural networks and deep learning, to improve data accuracy, enhance resolution, and enable more precise predictions of oceanic phenomena. Despite challenges such as model generalization and computational complexity, ML has significant potential for enhancing our understanding of marine ecosystems, facilitating real-time monitoring, and supporting global climate models. Full article

The air–sea transfer of gases is important within climate physics, biogeochemistry and the control of pollutants. A two-layer model of transfer directly across the sea surface underpins most discourse, but an expanding literature also features transfer mediated by “suspended fragments”, either bubbles in the upper ocean or drops and aerosol in the lower atmosphere. In this study, we describe a categorization of process that elucidates departures from two-layer theory and is a starting point for quantification. On counting the distinct phenomena and their application to gases of various solubility, a total of eight categories are identified. Each category has a distinct scaling with respect to the properties of the gas and this is key to the relative importance of different categories and processes. Transfer through sea spray can be an exchange process, but the evaporation of sea spray is more effective and is an ejection process. The reactivity of carbon dioxide in aqueous solution enhances the effect of spray. Exceptional levels of sea spray generation and evaporation are required to be significant for most gases, but moderate levels are sufficient for carbon dioxide and the most soluble pollutants. Full article

Gravity water waves in the shallow-ocean scenario described by generalized Boussinesq–Broer–Kaup–Whitham (gBBKW) equations are discussed. The residual symmetry and Bäcklund transformation associated with the gBBKW equations are systematically constructed. The time and space evolution of wave velocity and height are explored. Additionally, it is demonstrated that the gBBKW equations are solvable through the consistent Riccati expansion method. Leveraging this property, a novel Bäcklund transformation, solitary wave solution, and soliton–cnoidal wave solution are derived. Furthermore, miscellaneous novel solutions of gBBKW equations are obtained using the modified Sardar sub-equation method. The impact of variations in the diffusion power parameter on wave velocity and height is quantitatively analyzed. The exact solutions of gBBKW equations provide precise description of propagation characteristics for a deeper understanding and the prediction of some ocean wave phenomena. Full article

The increasing pollution of polystyrene (PS) and polymethyl methacrylate (PMMA) microplastics (MPs) has become a global marine environmental problem. Diatoms contribute nearly 40% of marine primary productivity and shape the nitrogen cycle in the oceans. However, the persistence of the phytotoxicity of MPs on diatoms, especially nitrogen assimilation, remains largely unknown. To examine the persistence of PS and PMMA toxicity in diatoms, two subexperiments (a 96 h exposure followed by a recovery phase) were conducted on Thalassiosira pseudonana at concentrations ranging from 0.001 to 1 mg/L. The results showed that PS and PMMA inhibited algal growth by 3.76–6.49% and 4.44–8.37%; increased oxidative stress by 10.06–30.51% and 30.46–38.12%; and caused ultrastructural damage by 14.24–25.56% and 12.28–20%, respectively, consistent with the downregulation of glyoxylate, dicarboxylate metabolism, and glutathione metabolism. At the recovery stage, the algal density induced by PS was significantly recoverable at 0.001 and 0.01 mg/L, consistent with the enhanced carbohydrate metabolisms. After recovery, the cell permeability and reactive oxygen species (ROS) levels induced by PS and PMMA were significantly decreased at 1 mg/L, respectively, which was closely related to the downregulation of glycine, serine, and threonine metabolism and the upregulation of pantothenate and coenzyme A biosynthesis. Moreover, the inhibition of nitrogen assimilation enzymic activities induced by PS and PMMA was significantly recovered at 1 mg/L despite the downregulation of nitrogen metabolism. This study highlights the phenomena and mechanisms of phytotoxicity and recovery, and provides new insights for comprehensive understanding and evaluation of environmental risks of MPs. Full article