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Keywords = wave dissipation

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23 pages, 3977 KB  
Article
Study on Waveform Superposition and Ultrasonic Gain During Nonlinear Propagation of Ultrasound in Fibrin Clots
by Linlin Zhang, Xiaomin Zhang, Fan Mo and Zhipeng Zhao
Appl. Sci. 2026, 16(2), 1137; https://doi.org/10.3390/app16021137 - 22 Jan 2026
Abstract
Fibrin clots with strain-hardening characteristics exhibit pronounced material nonlinearity and acoustic dispersion under ultrasound, leading to waveform distortion and shock formation during finite-amplitude wave propagation. However, peak-shock stress is limited by viscoelastic dissipation and dispersion, constraining the efficiency of ultrasound in applications such [...] Read more.
Fibrin clots with strain-hardening characteristics exhibit pronounced material nonlinearity and acoustic dispersion under ultrasound, leading to waveform distortion and shock formation during finite-amplitude wave propagation. However, peak-shock stress is limited by viscoelastic dissipation and dispersion, constraining the efficiency of ultrasound in applications such as thrombus ablation. To overcome this limitation, a shock wave amplification method using designed multi-wave-packet sequences is proposed. Based on a power-law model from quasi-static compression tests, shock generation under a single sinusoidal pulse was first simulated. The dual-wave-packet chasing strategy was then developed, in which the amplitude, frequency, and time delay of the second packet were tuned to achieve effective superposition with the precursor. The waveform superposition factor (WSF) was introduced for quantitative evaluation. Numerical results demonstrate that this strategy can significantly increase the peak-shock-wave stress, with a maximum gain of 22.7%. Parametric analysis further identified amplitude as the dominant factor influencing wavefront steepness and amplification effectiveness. This study provides a novel method and theoretical support for developing efficient and controllable ultrasonic sequences for thrombolysis. Full article
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21 pages, 4619 KB  
Article
Experimental Study on Suppression and Mechanism of Sloshing Impact Pressure by Vertical Slat Screens Under Broadband Horizontal and Vertical Excitation
by Liting Yu, Xiaoqian Luo, Jingcheng Lin, Jie Fan and Heng Jin
J. Mar. Sci. Eng. 2026, 14(2), 220; https://doi.org/10.3390/jmse14020220 - 21 Jan 2026
Abstract
Sloshing-induced impact pressure is a key damage factor for marine liquid tanks. While research aimed at overcoming screen failure in sloshing suppression under high-frequency excitation has focused on wave height, the dataset of impact pressure remains lacking. Moreover, the pattern of pressure suppression [...] Read more.
Sloshing-induced impact pressure is a key damage factor for marine liquid tanks. While research aimed at overcoming screen failure in sloshing suppression under high-frequency excitation has focused on wave height, the dataset of impact pressure remains lacking. Moreover, the pattern of pressure suppression under broadband excitation remains unclear. The primary contribution of this work is the first experimental dataset of impact pressure with vertical slat screens under broadband horizontal and vertical excitation. Second, it reveals pressure suppression patterns by screens across varying excitation frequencies and screen numbers. The results demonstrate that vertical slat screens can effectively suppress pressure. First, screen position matters more than number, proving that suppression is dominated by modal disturbance. Second, wave-height suppression does not reliably represent pressure suppression. Pressure suppression is systematically weaker. An exception occurs under vertical excitation, where pressure suppression can be stronger even when wave-height suppression fails. The results highlight the suppression mechanism dominated by modal disturbance and the instability inherent to parametric sloshing. Wave height, reflecting global potential energy, is effectively suppressed by modal disturbance. Pressure, originating from local kinetic energy, can be effectively suppressed by both modal disturbance and vortex dissipation. Full article
(This article belongs to the Special Issue Advances in Marine Engineering Hydrodynamics, 2nd Edition)
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23 pages, 13771 KB  
Article
Oblique Wave Scattering by a Floating Rectangular Porous Box with an Impermeable Bottom
by Yu-Chan Guo, Sarat Chandra Mohapatra and C. Guedes Soares
J. Mar. Sci. Eng. 2026, 14(2), 156; https://doi.org/10.3390/jmse14020156 - 11 Jan 2026
Viewed by 176
Abstract
Based on linear wave theory and potential flow theory, the wave scattering performance of a rectangular floating porous box with an impermeable bottom is investigated analytically. The mathematical formulation of the physical problem is well established and solved, and its analytical solutions are [...] Read more.
Based on linear wave theory and potential flow theory, the wave scattering performance of a rectangular floating porous box with an impermeable bottom is investigated analytically. The mathematical formulation of the physical problem is well established and solved, and its analytical solutions are appropriately obtained using the matched eigenfunction expansion method. The convergency and accuracy of the analytical solutions are carefully verified and thoroughly validated. It is found that the present analytical solutions converge up to three decimal places and agree well with the numerical results published in the previous literature. Furthermore, important numerical results are calculated to thoroughly analyze the oblique wave scattering performance of the proposed rectangular floating porous box with an impermeable bottom and its efficiency in preventing incident waves when used as a floating breakwater. It is concluded that the dimensionless width (L/h), submergence depth (d/h), and frictional coefficient (f) have a significant influence on the scattering performance and the transmission coefficient of the proposed porous box. This work is beneficial for the design and future development of floating rectangular porous box breakwaters. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 4520 KB  
Article
Quasi-2D Axisymmetric Modelling of Smooth–Turbulent Transient Flow: Comparison with 1D and 3D-CFD Models
by Pedro Ferreira and Dídia Covas
Water 2026, 18(2), 141; https://doi.org/10.3390/w18020141 - 6 Jan 2026
Viewed by 315
Abstract
This study compares the numerical results obtained with an axisymmetric quasi two-dimensional (Q2D) model with those from two different types of dimensional models for smooth–turbulent transient flows generated by an instantaneous valve closure. The first is a high-accuracy three-dimensional computational fluid dynamics (3D-CFD) [...] Read more.
This study compares the numerical results obtained with an axisymmetric quasi two-dimensional (Q2D) model with those from two different types of dimensional models for smooth–turbulent transient flows generated by an instantaneous valve closure. The first is a high-accuracy three-dimensional computational fluid dynamics (3D-CFD) model. The second type is the one-dimensional (1D) model, analysing results from five unsteady friction formulations, namely four convolution integral-based (CIB) formulations and one instantaneous acceleration-based (IAB) formulation. The Q2D and 1D models are also compared with experimental data collected under laboratory conditions for a fast but non-instantaneous valve closure. The differences between the 1D, Q2D and 3D-CFD modelling approaches are quantified and discussed, focusing on the ability of each model to reproduce the different features of the transient flow phenomenon and the associated computation–accuracy trade-offs. The 3D-CFD model exhibits a more pronounced front-wave rounding, as it more accurately represents the valve conditions, where its closure induces highly turbulent flow with a strongly heterogeneous velocity profile. The Q2D model provides an accurate estimation of unsteady energy dissipation, when fully developed flow conditions are ensured with the advantage of requiring less computational effort than the 3D-CFD. These conclusions also apply to full convolution-based 1D models, whereas approximate 1D formulations can significantly reduce accuracy and limit their range of applicability. The comparison with experimental data corroborates the excellent results of the Q2D model. The Q2D model demonstrates to be an efficient alternative in terms of accuracy and computational time to 3D-CFD and 1D full convolution models. Full article
(This article belongs to the Special Issue Hydrodynamics in Pressurized Pipe Systems)
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33 pages, 21972 KB  
Article
Wave Attenuation Performance of a Floating Breakwater Integrated with Flexible Wave-Dissipating Structures
by Xianlin Jia, Su Guo, Kangjie Wang, Sai Fu, Xintong Yu and Wei Peng
J. Mar. Sci. Eng. 2026, 14(1), 97; https://doi.org/10.3390/jmse14010097 - 4 Jan 2026
Viewed by 255
Abstract
This study develops a two-dimensional numerical model to investigate the hydrodynamic performance of a floating breakwater coupled with flexible wave-dissipating structures (FWDS). The model integrates the immersed boundary method with a finite element structural solver, enabling accurate simulation of fluid–structure interactions under wave [...] Read more.
This study develops a two-dimensional numerical model to investigate the hydrodynamic performance of a floating breakwater coupled with flexible wave-dissipating structures (FWDS). The model integrates the immersed boundary method with a finite element structural solver, enabling accurate simulation of fluid–structure interactions under wave excitation. Validation against benchmark cases, including cantilever beam deflection and flexible vegetation under waves, confirms the model’s reliability. Parametric analyses were conducted to examine the influence of the elastic modulus and height of the FWDS on wave attenuation efficiency. Results show that structural flexibility plays a crucial role in modifying wave reflection, transmission, and dissipation characteristics. A lower elastic modulus enhances energy dissipation through large deformation and vortex generation, while higher stiffness promotes reflection with reduced dissipation. Increasing the height of the FWDS improves overall wave attenuation but exhibits diminishing returns for long-period waves. The findings highlight that optimized flexibility and geometry can effectively enhance the energy-dissipating capacity of floating breakwaters. This study provides a theoretical basis for the design and optimization of hybrid floating breakwaters integrating flexible elements for coastal and offshore wave energy mitigation. Full article
(This article belongs to the Special Issue Numerical Analysis and Modeling of Floating Structures)
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17 pages, 19521 KB  
Article
Experimental Comparisons of the Wave Attenuation Characteristics Among Different Flexible-Membrane Breakwaters
by Ming-Liang Cai, Jing-Ping Wu, Shao-Min Wang and Xi Yi
J. Mar. Sci. Eng. 2026, 14(1), 78; https://doi.org/10.3390/jmse14010078 - 31 Dec 2025
Viewed by 188
Abstract
In this paper, physical experiments were conducted to analyze the wave attenuation characteristics of a combinational breakwater in a 2D piston-type wave flume. The proposed breakwater consisted of a box and double flexible membranes, one of which was fixed on both sides of [...] Read more.
In this paper, physical experiments were conducted to analyze the wave attenuation characteristics of a combinational breakwater in a 2D piston-type wave flume. The proposed breakwater consisted of a box and double flexible membranes, one of which was fixed on both sides of the box, while the other was positioned at a specific distance from the box sides. The flexible membranes dropped down naturally and formed a U shape. Optimal configuration parameters of the proposed breakwater were determined separately through a series of comparison experiments among mooring breakwaters in regular waves; the box draft d was determined by a box-type breakwater and the membrane spacings Lu and Ld from the box sides were determined by a U-shaped flexible-membrane breakwater, where the wave attenuation coefficients versus kh and B/λ were provided. Then, using the literature, the present box–membrane breakwater with membrane spacings was compared to two similar flexible-membrane breakwaters. One was the above-mentioned U-shaped flexible-membrane breakwater, the other was a box–membrane breakwater in which the flexible membranes were directly fastened on the box sides. The results indicate that with optimal configuration parameters, the wave attenuation performance of the proposed breakwater had been enhanced due to the increase in both dissipating and reflecting wave energy. Full article
(This article belongs to the Section Ocean Engineering)
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25 pages, 6501 KB  
Article
Automated Detection of Submerged Sandbar Crest Using Sentinel-2 Imagery
by Benjamí Calvillo, Eva Pavo-Fernández, Manel Grifoll and Vicente Gracia
Remote Sens. 2026, 18(1), 132; https://doi.org/10.3390/rs18010132 - 30 Dec 2025
Viewed by 432
Abstract
Coastal sandbars play a crucial role in shoreline protection, yet monitoring their dynamics remains challenging due to the cost and limited temporal coverage of traditional surveys. This study assesses the feasibility of using Sentinel-2 multispectral imagery combined with the logarithmic band ratio method [...] Read more.
Coastal sandbars play a crucial role in shoreline protection, yet monitoring their dynamics remains challenging due to the cost and limited temporal coverage of traditional surveys. This study assesses the feasibility of using Sentinel-2 multispectral imagery combined with the logarithmic band ratio method to automatically detect submerged sandbar crests along three morphologically distinct beaches on the northwestern Mediterranean coast. Pseudo-bathymetry was derived from log-transformed band ratios of blue-green and blue-red reflectance used to extract the sandbar crest and validated against high-resolution in situ bathymetry. The blue-green band ratio achieved higher accuracy than the blue-red band ratio, which performed slightly better in very shallow waters. Its application across single, single/double, and double shore-parallel bar systems demonstrated the robustness and transferability of the approach. However, the method requires relatively clear or calm water conditions, and breaking-wave foam, sunglint, or cloud cover conditions limit the number of usable satellite images. A temporal analysis at a dissipative beach further revealed coherent bar migration patterns associated with storm events, consistent with observed hydrodynamic forcing. The proposed method is cost-free, computationally efficient, and broadly applicable for large-scale and long-term sandbar monitoring where optical water clarity permits. Its simplicity enables integration into coastal management frameworks, supporting sediment-budget assessment and resilience evaluation in data-limited regions. Full article
(This article belongs to the Section Ocean Remote Sensing)
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17 pages, 3068 KB  
Article
Magnetoresponsive Fiber-Reinforced Periodic Impedance-Gradient Absorber: Design and Microwave Absorption Performance
by Yuan Liang, Wei Chen, Shude Gu, Xu Ding and Yuping Duan
Nanomaterials 2026, 16(1), 42; https://doi.org/10.3390/nano16010042 - 29 Dec 2025
Viewed by 382
Abstract
In recent years, achieving ultra-wideband electromagnetic absorption has emerged as a critical challenge in confronting advanced broadband electromagnetic detection technologies. This capability is essential for effectively countering sophisticated radar systems. In this study, we present a novel multilayer metamaterial absorber that integrates an [...] Read more.
In recent years, achieving ultra-wideband electromagnetic absorption has emerged as a critical challenge in confronting advanced broadband electromagnetic detection technologies. This capability is essential for effectively countering sophisticated radar systems. In this study, we present a novel multilayer metamaterial absorber that integrates an FR4 transmission layer, a periodic gradient dielectric structure designed for resonant impedance matching, and a magnetic skin layer for enhanced energy dissipation. By employing asymptotic gradients in both structure and composition, this design achieves dual-gradient electromagnetic parameter modulation, enabling efficient absorption across the X, Ku, and K bands (8.6–26.4 GHz) with a total thickness of 3.5 mm (effective thickness: 2 mm) and a density that is one-third that of conventional magnetic metamaterials. The proposed absorber demonstrates polarization insensitivity, stability across wide incident angles (up to 60°), and an absorption efficiency of 94%, as confirmed by full-wave simulations and experimental validation. Moreover, the fiber-reinforced hierarchical structure addresses the traditional trade-off between broadband absorption performance and mechanical load-bearing capacity. Full article
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22 pages, 1677 KB  
Article
Wave Scattering by Inverse T-Type Compound Breakwater with Ocean Currents: An Analytical and Numerical Study
by Aman Kumar Kushwaha, Harekrushna Behera and Vinay Kumar Gupta
Mathematics 2026, 14(1), 22; https://doi.org/10.3390/math14010022 - 21 Dec 2025
Viewed by 242
Abstract
The present work focuses on wave scattering generated by an inverse T-type compound breakwater in the presence of the ocean current. The boundary value problem (BVP) is investigated using two distinct strategies: an exact formulation derived from the eigenfunction expansion method (EEM) and [...] Read more.
The present work focuses on wave scattering generated by an inverse T-type compound breakwater in the presence of the ocean current. The boundary value problem (BVP) is investigated using two distinct strategies: an exact formulation derived from the eigenfunction expansion method (EEM) and a computational framework developed with the boundary element method (BEM). A comparison of outcomes from both techniques with established studies confirms the consistency and accuracy of the present formulations. Reflection and transmission coefficients, along with the time-domain simulations of the free surface, are evaluated under different wave conditions and structural configurations. In the long-wave region, the reflection coefficient exhibits strong dependence on the wavenumber, with higher values observed as the height and width of the porous section increase. Increasing the friction coefficient within the porous layer considerably reduces wave transmission to the leeside, demonstrating the important role of friction in energy dissipation. Furthermore, greater ocean current velocity leads to an increase in the reflection curve, highlighting the significant effect of hydrodynamic conditions on wave–structure interaction. The time-domain simulations of the free surface are also presented to provide a clear visualization of the wave behavior on the surface, both with and without the presence of an ocean current. The findings shed light on the combined influence of breakwaters and ocean currents, enabling the development of coastal protection measures that enhance resilience, sustainability, and safety from erosion and damage. Full article
(This article belongs to the Section C: Mathematical Analysis)
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22 pages, 24804 KB  
Article
Numerical Simulation and Verification of Free-Surface Flow Through a Porous Medium
by Perizat Omarova, Alexandr Neftissov, Ilyas Kazambayev, Lalita Kirichenko, Aliya Aubakirova and Aliya Borsikbayeva
Water 2025, 17(24), 3505; https://doi.org/10.3390/w17243505 - 11 Dec 2025
Viewed by 571
Abstract
Managing hydraulic behaviour and water quality in semi-arid, transboundary rivers such as the Talas River in Kazakhstan requires reliable numerical tools for predicting free-surface flow through porous hydraulic structures. This study develops and verifies a two-dimensional computational fluid dynamics (CFD) framework for simulating [...] Read more.
Managing hydraulic behaviour and water quality in semi-arid, transboundary rivers such as the Talas River in Kazakhstan requires reliable numerical tools for predicting free-surface flow through porous hydraulic structures. This study develops and verifies a two-dimensional computational fluid dynamics (CFD) framework for simulating free-surface water flow through porous media and demonstrates its applicability to a real river reach of the Talas in the Zhambyl region. The model combines the Volume of Fluid (VOF) method with the Darcy–Forchheimer formulation to represent porous resistance, while turbulence is described by the RNG kε model, and pressure–velocity coupling is handled by the PISO algorithm. Model verification is conducted against a classic dam-break experiment involving a rectangular porous barrier across a laboratory channel. The simulations successfully reproduce the main experimental observations, including rapid drawdown after gate opening, formation and attenuation of the free-surface wave, localized depression above the porous insert, and the subsequent approach to a quasi-steady state. Time histories of water levels at control points and the spatial progression of the wet front show close agreement with measurements. Using the validated setup, a site-specific two-dimensional domain for the Talas River is constructed to analyse the hydraulic influence of a porous bar. The model quantifies velocity redistribution and energy dissipation across the porous patch and provides physically consistent flow fields suitable for engineering assessments under various discharge conditions. Full article
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15 pages, 2237 KB  
Article
First Full-Scale 2D Field Experiment on Semi-Embedded Rubber Column Metamaterials: Enhanced Attenuation of Love Waves and Mechanistic Insights
by Xinchao Zhang, Ning Zheng, Changyin Ji, Yulin Lu and Qingfan Shi
Materials 2025, 18(24), 5517; https://doi.org/10.3390/ma18245517 - 8 Dec 2025
Viewed by 340
Abstract
Despite recent numerical simulations and limited laboratory studies highlighting the potential of semi-embedded seismic metamaterials (SEM) in attenuating Rayleigh waves, their real-world effectiveness remains unverified, particularly for Love waves. Love waves pose significant destructive risks to slender structures but have rarely been the [...] Read more.
Despite recent numerical simulations and limited laboratory studies highlighting the potential of semi-embedded seismic metamaterials (SEM) in attenuating Rayleigh waves, their real-world effectiveness remains unverified, particularly for Love waves. Love waves pose significant destructive risks to slender structures but have rarely been the focus of research. To address this gap, we present the first full-scale 2D field experiment on an SEM composed of an array of semi-embedded rubber column resonators. The experimental results reveal a global bandgap spanning 25–37 Hz and a localized bandgap at 37–42 Hz. At the central frequency of the global bandgap (f0 = 31 Hz), the attenuation reaches −9.3 dB for Love waves and −5.3 dB for Rayleigh waves, with the mitigation of Love waves being notably pronounced. Furthermore, our theoretical and experimental analyses provide novel mechanistic insights: the primary energy dissipation in flexible rubber resonators arises from the resonance of their exposed above-ground sections, while the underground buried parts introduce damping that moderately reduces the efficiency of surface wave attenuation. This pioneering full-scale on-site validation bridges the critical gap between simulation-based predictions and practical seismic protection systems, providing valuable reference for the engineering application of SEM, especially for mitigating destructive waves. Full article
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22 pages, 8864 KB  
Article
Enhanced Sound Absorption of Aluminum Foam Composites by Introducing Pore-Penetrating Fibers
by Bei Huang, Shuang Xiong, Xin Wang, Longyue Qin, Xiaoqing Zuo and Hui Wang
Materials 2025, 18(24), 5515; https://doi.org/10.3390/ma18245515 - 8 Dec 2025
Viewed by 401
Abstract
To address the issue of sound absorption valleys in open-cell aluminum foam and enhance mid-to-high frequency (800–6300 Hz) performance, we developed a novel pore-penetrating 316L stainless steel fiber–aluminum foam (PPFCAF) composite using an infiltration method. The formation mechanism of the pore-penetrating fibers, the [...] Read more.
To address the issue of sound absorption valleys in open-cell aluminum foam and enhance mid-to-high frequency (800–6300 Hz) performance, we developed a novel pore-penetrating 316L stainless steel fiber–aluminum foam (PPFCAF) composite using an infiltration method. The formation mechanism of the pore-penetrating fibers, the resultant pore-structure, and the accompanying sound absorption properties were investigated systematically. The PPFCAF was fabricated using 316L stainless steel fiber–NaCl composites created by an evaporation crystallization process, which ensured the full embedding of fibers within the pore-forming agent, resulting in a three-dimensional fiber-pore interpenetrating network after infiltration and desalination. Experimental results demonstrate that the PPFCAF with a porosity of 82.8% and a main pore size of 0.5 mm achieves a sound absorption valley value of 0.861. An average sound absorption coefficient is 0.880 in the target frequency range, representing significant improvements of 9.8% and 9.9%, respectively, higher than that of the conventional infiltration aluminum foam (CIAF). Acoustic impedance reveal that the incorporated fibers improve the impedance matching between the composite material and air, thereby reducing sound reflection. Finite element simulations further elucidate the underlying mechanisms: the pore-penetrating fibers influence the paths followed by air particles and the internal surface area, thereby increasing the interaction between sound waves and the solid framework. A reduction in the main pore size intensifies the interaction between sound waves and pore walls, resulting in a lower overall reflection coefficient and a decreased reflected sound pressure amplitude (0.502 Pa). In terms of energy dissipation, the combined effects of the fibers and refinement increase the specific surface area, thereby strengthening viscous effects (instantaneous sound velocity up to 46.1 m/s) and thermal effects (temperature field increases to 0.735 K). This synergy leads to a notable rise in the total plane wave power dissipation density, reaching 0.0609 W/m3. Our work provides an effective strategy for designing high-performance composite metal foams for noise control applications. Full article
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17 pages, 12479 KB  
Article
A Study of Sediment Behavior for Dam-Break Flow over Granular Bed
by Kyung Sung Kim
Mathematics 2025, 13(24), 3919; https://doi.org/10.3390/math13243919 - 8 Dec 2025
Viewed by 263
Abstract
Dam-break flows involve strong non-linearity and complex fluid–solid interactions, often causing severe flooding and structural damage. Particle-based CFD methods, such as the Moving Particle Semi-implicit (MPS) method, are effective in modeling such flows due to their mesh-free, Lagrangian nature. This study presents an [...] Read more.
Dam-break flows involve strong non-linearity and complex fluid–solid interactions, often causing severe flooding and structural damage. Particle-based CFD methods, such as the Moving Particle Semi-implicit (MPS) method, are effective in modeling such flows due to their mesh-free, Lagrangian nature. This study presents an improved MPS method with a novel friction model and enhanced fluid–solid interaction scheme to simulate dam-break-induced flows over fixed and mobile beds. The model is validated using experimental and analytical benchmarks, demonstrating improved accuracy and stability. Simulation results show that mobile beds significantly influence wave attenuation, energy dissipation, and sediment transport. In particular, step-down bed conditions promote sediment motion and modify wave behavior. These findings emphasize the importance of accounting for mobile seabed dynamics in numerical modeling of coastal and dam-break scenarios. The proposed MPS model offers a reliable and efficient tool for capturing key phenomena associated with fluid–solid interactions in naval and ocean engineering applications. Full article
(This article belongs to the Special Issue High-Order Numerical Methods and Computational Fluid Dynamics)
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28 pages, 1410 KB  
Entry
From Airy’s Equation to the Non-Dissipative Lorenz Model: Turning Points, Quantum Tunneling, and Solitary Waves
by Bo-Wen Shen
Encyclopedia 2025, 5(4), 208; https://doi.org/10.3390/encyclopedia5040208 - 5 Dec 2025
Viewed by 1021
Definition
This report bridges fundamental ideas from introductory calculus to advanced concepts in quantum mechanics and nonlinear dynamics. Beginning with the behavior of second derivatives in oscillatory and exponential functions, it introduces the Airy equation and the WKB approximation as mathematical tools for describing [...] Read more.
This report bridges fundamental ideas from introductory calculus to advanced concepts in quantum mechanics and nonlinear dynamics. Beginning with the behavior of second derivatives in oscillatory and exponential functions, it introduces the Airy equation and the WKB approximation as mathematical tools for describing wave propagation and quantum tunneling near turning points—locations where transitions between oscillatory and exponential components occur. The analysis then extends to the non-dissipative Lorenz model, whose double-well potential and solitary-wave (sech-type) solutions reveal a deep mathematical connection with the nonlinear Schrödinger equation. Together, these examples highlight the universality of second-order differential equations in describing turning-point dynamics, encompassing physical phenomena ranging from quantum tunneling to coherent solitary-wave structures in fluid and atmospheric systems. Full article
(This article belongs to the Section Physical Sciences)
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12 pages, 1616 KB  
Article
Observation of Horizontal Gravity Wave Activity in the Upper Stratosphere Using Monostatic Rayleigh Lidar
by Xueming Li, Xuanyu Zheng, Shaohua Gong and Qihai Chang
Atmosphere 2025, 16(12), 1376; https://doi.org/10.3390/atmos16121376 - 5 Dec 2025
Viewed by 283
Abstract
The prediction accuracy of the General Circulation Model (GCM) is influenced by the effectiveness of gravity wave activity parameterization. Although research focuses on small-scale horizontal gravity wave activity as a carrier for energy and momentum coupling between atmospheric layers, routine observations of horizontal [...] Read more.
The prediction accuracy of the General Circulation Model (GCM) is influenced by the effectiveness of gravity wave activity parameterization. Although research focuses on small-scale horizontal gravity wave activity as a carrier for energy and momentum coupling between atmospheric layers, routine observations of horizontal gravity wave activity on scales less than a dozen kilometers are scarce due to limitations in observational instruments. This paper presents a method for observing small-scale horizontal gravity waves using monostatic Rayleigh lidar, along with the associated data processing workflow. The data processing results indicate that the observed gravity waves generally exhibit wavelengths less than 3 km and phase velocities less than 0.5 m/s. Furthermore, the annual variation in small-scale horizontal gravity waves displays a semi-annual oscillation (SAO), like that observed in medium- and large-scale waves. This suggests that the observed gravity waves originate from secondary gravity waves resulting from saturation dissipation or breaking. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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