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Machine learning based sensing of particle shape and size using passive artificial cilia 基于机器学习的被动人工纤毛粒子形状和大小感知
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-11-05 DOI: 10.1016/j.jfluidstructs.2025.104446
Divyaprakash, Amitabh Bhattacharya
Passive biological cilia function as sensory organelles in various animal cells and microorganisms. In this computational study, we demonstrate that tip and base perturbations in an array of flexible passive artificial cilia may be used to detect the size and aspect ratio of ellipse-shaped particles immersed in an oscillatory Couette flow setup. Two-dimensional numerical simulations of the system are carried out for varying particle shape and size, and the immersed boundary method is used to couple the fluid and structure solvers. Kirchhoff rod theory and finite element method are used to evolve the elastic forces in cilia and particle, respectively. A machine learning model, comprising a Long Short-Term Memory (LSTM) network coupled with a regression layer, is trained using the generated data, in which features such as cilia tip deflection and base angle at three time instances are used to sense the particle size and shape. Using unseen simulation data, we show that the trained model is capable of predicting the size and aspect ratio of the particle within an average prediction error of 6 percent over the entire dataset. The model using cilia base deflection appears to be less sensitive to particle aspect ratio compared to the model using cilia tip deflection, especially for smaller particles. This non-optical sensing technique is especially useful for detecting particle size and shape in opaque liquids.
被动生物纤毛是多种动物细胞和微生物的感觉细胞器。在这项计算研究中,我们证明了柔性被动人工纤毛阵列中的尖端和基部扰动可以用来检测浸入振荡库埃特流装置中的椭圆形状颗粒的大小和长径比。对不同颗粒形状和大小的系统进行了二维数值模拟,并采用浸入边界法对流体和结构求解器进行了耦合。采用Kirchhoff杆理论和有限元法分别对纤毛和颗粒的弹性力进行了演化。使用生成的数据训练由长短期记忆(LSTM)网络和回归层组成的机器学习模型,其中使用三个时间实例的纤毛尖端偏转和底角等特征来感知颗粒大小和形状。使用未见过的模拟数据,我们表明训练模型能够在整个数据集的平均预测误差为6%的范围内预测粒子的大小和纵横比。与使用纤毛尖端偏转的模型相比,使用纤毛基部偏转的模型对颗粒宽高比的敏感性较低,特别是对于较小的颗粒。这种非光学传感技术对于检测不透明液体中的颗粒大小和形状特别有用。
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引用次数: 0
Multiphysics analysis of a flexible oscillating water column wave energy converter with dielectric elastomer membrane 介电弹性体膜柔性振荡水柱波能转换器的多物理场分析
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-11-03 DOI: 10.1016/j.jfluidstructs.2025.104447
Yang Huang , Qing Xiao , Liu Yang , Saishuai Dai , Saeid Lotfian , Feargal Brennan
Flexible wave energy converters (FlexWECs) have emerged as a promising solution to address the limitations of conventional rigid devices in harsh marine environments. Among them, oscillating water column (OWC) systems integrated with dielectric elastomer generators (DEGs) offer simplified architectures, enhanced adaptability, and direct wave-to-electric energy conversion. However, the complex multiphysics interactions between fluid, structure, and electric fields remain poorly understood, hindering design optimization and performance prediction. This study develops a high-fidelity computational framework to simulate the coupled fluid-structure-electric behaviour of a flexible OWC wave energy converter (WEC) with a DEG membrane. The framework is first validated against experimental data, demonstrating good agreement in capturing the deformation of the flexible membrane induced by the coupled electrostatic and hydrodynamic forces. Subsequently, the model is applied to investigate how electric field influences the WEC system behaviour under regular wave excitation. Results show that applying an electric field reduces the effective stiffness of the membrane, leading to increased deformation. Additionally, it does raise overall structural stress levels, especially near the membrane centre and edge regions, where the maximum stresses are observed. Notably, electric excitation induces a secondary deformation mode in the membrane during the near-flat phase. These effects become more pronounced with increasing initial voltage, which also leads to an approximately quadratic increase in output power. The insights gained from this study provide a deeper understanding of fluid-structure-electricity (FSE) interactions in flexible OWC WECs and offer design guidance for enhancing energy harvesting efficiency in next-generation WEC devices.
柔性波浪能转换器(FlexWECs)已成为解决传统刚性设备在恶劣海洋环境中的局限性的一种有前途的解决方案。其中,与介电弹性体发生器(DEGs)集成的振荡水柱(OWC)系统简化了结构,增强了适应性,并实现了直接的波电转换。然而,流体、结构和电场之间复杂的多物理场相互作用仍然知之甚少,这阻碍了设计优化和性能预测。本研究开发了一个高保真的计算框架来模拟带有DEG膜的柔性OWC波能转换器(WEC)的流-固-电耦合行为。该框架首先与实验数据进行了验证,证明了在捕捉由静电和水动力耦合引起的柔性膜变形方面的良好一致性。随后,应用该模型研究了电场在规则波激励下对WEC系统行为的影响。结果表明,施加电场降低了膜的有效刚度,导致变形增加。此外,它确实提高了整体结构应力水平,特别是在膜中心和边缘区域附近,在那里观察到最大应力。值得注意的是,在近平坦阶段,电激励在膜中诱导了二次变形模式。随着初始电压的增加,这些影响变得更加明显,这也导致输出功率大约二次增长。从这项研究中获得的见解提供了对柔性OWC WECs中流体-结构-电(FSE)相互作用的更深入理解,并为提高下一代WEC设备的能量收集效率提供了设计指导。
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引用次数: 0
Numerical simulation of ship hydroelastic responses in 3D realistic ocean waves with occurrence of freak waves 异形波发生时三维现实海浪中船舶水弹性响应的数值模拟
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-11-03 DOI: 10.1016/j.jfluidstructs.2025.104448
Jialong Jiao , Zhenwei Chen , Yuanming Chen , Shuai Chen , Caixia Jiang
Oceangoing ships may encounter rarely occurring waves like freak waves during their operational lifespan, which largely affects the safety of ships. In this paper a two-way CFD-FEM fluid-structure coupled method is adopted to simulate ship motions and wave load responses in three-dimensional (3D) freak waves. First, in-house code using MATLAB is developed to generate wave parameters which are used for generating short-crested waves and 3D freak waves in the CFD solver. The simulated freak waves are examined and the evolution of freak waves during propagation process is analyzed. Then, ship motions and wave loads considering hydroelastic response in 3D short-crested waves and in 3D freak waves are analyzed. The increase in motions and load responses when ship encountering freak waves is studied quantitatively. This study provides some insights into ship extreme dynamic responses in realistic seaways and in extreme freak waves.
远洋船舶在其使用寿命中可能会遇到罕见的异常浪,这在很大程度上影响了船舶的安全。本文采用双向CFD-FEM流固耦合方法,模拟了船舶在三维畸形波浪中的运动和波浪荷载响应。首先,利用MATLAB编写内部代码,生成CFD求解器中用于生成短峰波和三维畸形波的波参数。对模拟的畸形波进行了检验,分析了畸形波在传播过程中的演化。然后分析了三维短峰波和三维异形波中考虑水弹性响应的船舶运动和波浪荷载。定量研究了船舶遇异常浪时运动和载荷响应的增加。本文的研究为船舶在实际航道和极端异常浪中的极端动力响应提供了一些见解。
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引用次数: 0
Lift augmentation by incorporating bend twist coupled composites in flapping wing 在扑翼中加入弯曲扭转耦合复合材料的升力增强
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-24 DOI: 10.1016/j.jfluidstructs.2025.104439
Rahul Kumar, Devranjan Samanta, Srikant S. Padhee
Drawing inspiration from the adaptive wing shape of birds in flight, this study introduces a bio-inspired concept for shape adaptation utilizing bend-twist coupling (BTC) in composite laminates. The primary aim of the design optimization is to identify the optimal fibre orientation angles needed to produce the required bending and twisting deformations, which directly contribute to the design's goal of maximizing lift without relying on external mechanisms for twisting. This novel technique increases lift by up to five times compared to a curved bending wing. We have highlighted the vortex dynamics to provide insight into the underlying reasons for such a significant lift increment. In addition, the study presents the Von Mises stress experienced by the wing, offering a comprehensive understanding of the structural behavior. Furthermore, it highlights a significant improvement in efficiency, particularly within the optimal reduced frequency range of 0.25 to 0.4. These findings underscore the potential of this method for future applications in biomimetic drones, unmanned flapping wing vehicles (UFWVs), and other flapping wing-based systems, ultimately paving the way for new advancements in aerodynamics and structural optimization for next-generation aerial vehicle designs.
从鸟类在飞行中的自适应翅膀形状中获得灵感,本研究引入了一种利用弯曲-扭转耦合(BTC)在复合材料层合板中进行形状自适应的仿生概念。设计优化的主要目的是确定产生所需弯曲和扭转变形所需的最佳纤维取向角度,这直接有助于实现在不依赖外部扭转机构的情况下最大化升力的设计目标。与弯曲的机翼相比,这种新技术将升力提高了5倍。我们强调了涡旋动力学,以深入了解如此显著升力增加的潜在原因。此外,该研究还展示了机翼所经历的冯米塞斯应力,提供了对结构行为的全面理解。此外,它还突出了效率的显著提高,特别是在0.25到0.4的最佳降低频率范围内。这些发现强调了该方法未来在仿生无人机、无人扑翼飞行器(UFWVs)和其他基于扑翼的系统中的应用潜力,最终为下一代飞行器设计的空气动力学和结构优化铺平了道路。
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引用次数: 0
Stability analysis of a twisting flexible plate immersed in an axial airflow 扭曲柔性板在轴向气流中的稳定性分析
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-23 DOI: 10.1016/j.jfluidstructs.2025.104444
D.A. Pulido-Caviedes , J.A. Licea-Salazar , A. Cros
We study the stability of a rectangular, flexible plate subject to twisting motions and immersed in a uniform, incompresible axial flow. The twisting motion is characterized by the angle ϕ(x,t) where x is the axial coordinate and t is time, in such a way that no spanwise curvature is allowed. The complex fluid–structure interaction is governed by the torque which comes from the pressure difference between both faces of the plate. By writting the boundary conditions in the Fourier space, the three-dimensional flow potential generated by the twisting flexible plate is calculated and the torque is estimated. Subsequently, the Galerkin method enables the estimation of the frequency and growth rate of each plate mode as a function of three nondimensional parameters: a reduced fluid velocity, the mass ratio M between the fluid and plate densities, and the aspect ratio of the plate. Three different boundary conditions are analyzed: clamped-free, clamped-clamped and free-free. We find that, in all three cases, mode 1 first destabilizes through divergence when the fluid velocity is increased. At higher speed values, fluttering develops as a combination of the first two modes in both the free-free and clamped-clamped configurations. Our findings also suggest that greater plate mass and reduced width contribute to improved plate stability and for a given aspect ratio, the critical velocities evolve as 1/M.
我们研究了一个矩形,柔性板受扭转运动和浸泡在均匀的,不可压缩的轴流的稳定性。扭转运动的特征是角φ (x,t),其中x是轴向坐标,t是时间,在这样一种方式,没有跨向曲率是允许的。复杂的流固相互作用是由板的两个面之间的压力差产生的扭矩控制的。通过在傅里叶空间中写出边界条件,计算了挠性板在扭转过程中产生的三维流势,并对其转矩进行了估计。随后,Galerkin方法可以将每个板块模式的频率和增长率作为三个非三维参数的函数进行估计:降低的流体速度,流体与板块密度之间的质量比M,以及板块的长径比。分析了三种不同的边界条件:无夹固、夹固-夹固和自由-自由。我们发现,在所有三种情况下,当流体速度增加时,模式1首先通过散度失稳。在较高的速度值下,颤振发展为自由-自由和夹紧-夹紧配置中前两种模式的组合。我们的研究结果还表明,更大的板块质量和更小的宽度有助于提高板块的稳定性,对于给定的纵横比,临界速度演变为1/M。
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引用次数: 0
Experimental study on modal characteristics of an underwater rotating disc in coupled nodal circle and diameter modes 水下旋转盘节点圆与直径耦合模态特性试验研究
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-23 DOI: 10.1016/j.jfluidstructs.2025.104443
Jiayun Zhang , Yongshun Zeng , Peijian Zhou , Wei Wang , Lingjiu Zhou , Zhifeng Yao
This paper investigates the modal characteristics of an underwater disc at different rotation speeds through modal testing. Modal testing was performed on the underwater disc within a rotation speed range of 0 to 720 rpm using a specially designed experimental setup. Modal analysis was conducted to extract the natural frequencies, damping ratios, and mode shapes of the disc. The study focuses on the characteristics of Coupled Nodal Circle and Diameter (CNCD) modes related to rotation speeds. The results show that: (1) the mode shapes and natural frequencies of the non-rotating underwater disc are consistent with the analytical predictions; (2) experiments show that CNCD mode frequencies agree with the analytical model’s forward-wave predictions, exhibit no splitting due to weak Coriolis force and circulatory forces effects, and that backward waves are overdamped due to higher shear; (3) for RC〈 0.43, CNCD mode damping ratios remain stable under hydrostatic viscous damping. When RC〉 0.43, the (2,1) mode exhibits a significant damping increase, indicating dominance of dynamic hydroelastic damping; (4) resonance was amplified when CNCD modes overlapped with nodal diameter modes, and these speeds should be avoided in engineering practice. The findings provide insights for the design of impellers in high-head pump turbines and the operational performance of such units.
本文通过模态试验研究了水下圆盘在不同转速下的模态特性。使用专门设计的实验装置,在0到720 rpm的转速范围内对水下圆盘进行模态测试。进行了模态分析,提取了圆盘的固有频率、阻尼比和模态振型。重点研究了节点圆径耦合模态与转速的关系。结果表明:(1)非旋转水下圆盘的模态振型和固有频率与解析预测一致;(2)实验表明,CNCD模态频率与解析模型的前向波预测一致,由于弱科里奥利力和循环力的影响,没有出现分裂,并且由于较高的剪切,后向波出现过阻尼;(3)当RC < 0.43时,cd模态阻尼比在静水粘性阻尼下保持稳定。当RC > 0.43时,(2,1)模态阻尼显著增加,表明动力水弹性阻尼占主导地位;(4)当模态与节点直径模态重叠时,共振被放大,在工程实践中应避免这种速度。研究结果为高扬程泵式水轮机叶轮的设计及其运行性能提供了参考。
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引用次数: 0
Low-order coupled model for vortex-induced vibrations mitigation by resonant piezoelectric shunt 谐振式压电分流器抑制涡激振动的低阶耦合模型
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-22 DOI: 10.1016/j.jfluidstructs.2025.104442
Arthur Haudeville , Xavier Amandolese , Boris Lossouarn , Christophe Giraud-Audine , Olivier Thomas
The present work investigates the ability of a reduced-order fluid–structure model to estimate the vortex-induced vibrations (VIV) of marine lifting surface under hydrodynamic flow, such as hydrofoils. A particular VIV area is scrutinized, for which a hydrodynamic excitation mechanism due to a Kármán-type vortex wake organization successively locks the first twisting and second bending mode of a cantilever truncated hydrofoil. Coupling two structural oscillators with a Van der Pol wake oscillator satisfactorily reproduces the amplitude response and the lock-in frequency. This work also investigates the ability of a piezo-elasto-hydrodynamic model to anticipate the vibration amplitude of the hydrofoil when mitigated thanks to a resonant piezoelectric shunt. Composed of an inductance in series with a resistance connected to a piezoelectric patch, the passive shunt was tuned to minimize the vibration amplitude in the frequency lock-in range. The proposed semi-empirical models are fitted to experimental results in order to reproduce the coupled system’s dynamic.
本文研究了一种降阶流固模型在水动力流(如水翼)作用下海洋升力表面涡激振动(VIV)的估计能力。研究了一个特殊的涡激区域,在该区域内,由于Kármán-type涡尾迹组织的水动力激励机制连续锁定了悬臂截尾水翼的第一扭转和第二弯曲模式。耦合两个结构振荡器与一个范德波尔尾迹振荡器令人满意地再现振幅响应和锁定频率。这项工作还研究了压电弹性水动力模型预测由于谐振压电分流而减轻的水翼振动幅度的能力。该无源分流器由一个电感和一个连接在压电片上的电阻串联而成,在频率锁定范围内被调谐到最小的振动幅度。所提出的半经验模型与实验结果拟合,以再现耦合系统的动态。
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引用次数: 0
Flow-induced vibration of twin-pipe model with varying mass and damping: A study using virtual physical framework 基于虚拟物理框架的变质量变阻尼双管模型流激振动研究
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-22 DOI: 10.1016/j.jfluidstructs.2025.104438
Jiawei Shen , Shixiao Fu , Xuepeng Fu , Torgeir Moan , Svein Sævik
Flow-induced vibration (FIV) commonly occurs in rigidly coupled twin-pipe structures. However, the limited understanding of their FIV responses and hydrodynamic features presents a major challenge to the development of reliable engineering designs. To bridge this gap, the present study experimentally investigates the FIV characteristics of a rigidly coupled twin-pipe model with elastic support using a virtual physical framework (VPF), which enables flexible control of structural parameters during physical testing. A distinctive feature of twin-pipe structures is the presence of in-line hydrodynamic interactions and torsional moments arising from the rigid coupling. The in-line interaction is primarily compressive and becomes more pronounced as the mass ratio increases. The torsional moment coefficient exhibits a rise–fall trend with increasing reduced velocity UR and stabilizes around 0.46 at low mass ratios. In addition, an “amplitude drop” phenomenon is observed near UR=6, attributed to energy dissipation from the downstream pipe. The mass ratio significantly affects FIV amplitude, frequency, and hydrodynamic coefficients. As the mass ratio decreases, the synchronization region broadens and the hydrodynamic coefficients become more stable. Meanwhile, at mass ratio of 1.0, a “resonance forever” behavior is observed. Damping primarily suppresses FIV amplitude, with minimal impact on dominant frequency and hydrodynamic coefficients. These findings provide valuable insights into twin-pipe FIV mechanisms and support a scientific basis for future structural design optimization.
流激振动(FIV)通常发生在刚性耦合的双管结构中。然而,对其FIV响应和水动力特性的有限理解对可靠工程设计的发展提出了重大挑战。为了弥补这一差距,本研究利用虚拟物理框架(VPF)实验研究了具有弹性支撑的刚性耦合双管模型的FIV特性,该模型可以在物理测试期间灵活控制结构参数。双管结构的一个显著特征是存在在线流体动力相互作用和刚性耦合引起的扭转力矩。这种在线相互作用主要是压缩的,并且随着质量比的增加而变得更加明显。扭转矩系数随减小速度UR的增加呈上升-下降趋势,在低质量比时稳定在0.46左右。此外,在UR=6附近还观察到“振幅下降”现象,这是由于下游管道的能量耗散。质量比显著影响FIV振幅、频率和水动力系数。随着质量比的减小,同步区变宽,水动力系数趋于稳定。同时,在质量比为1.0时,观察到“永远共振”行为。阻尼主要抑制FIV振幅,对主频率和水动力系数的影响最小。这些发现为双管FIV机制提供了有价值的见解,并为未来的结构设计优化提供了科学依据。
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引用次数: 0
A time-domain computational method for the assessment of the dynamic response of long-span submerged floating tunnels under coupled action of multiple loads in marine environments 海洋环境下多荷载耦合作用下大跨水下浮式隧道动力响应的时域计算方法
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-18 DOI: 10.1016/j.jfluidstructs.2025.104440
Wenlong Luo , Bo Huang , Lihua Wang , Jing Chen , Hongbo Su , Jianting Zhou , Hao Ding , Ke Li , Liang Cheng , Dan Zhong
The submerged floating tunnel (SFT) is a new type of transportation structure used to cross water areas. In complex marine environments, the long-span SFT is subjected to nonlinear coupled effects of multiple loads, resulting in extremely complex dynamic responses. At present, the calculation methods for the dynamic response of the long-span SFT in marine environments have the following main deficiencies: (1) When different cable models, tube-end boundary conditions, and load patterns are adopted, the resulting mathematical models of the SFT often exhibit different expressions, with complex governing equations. The models lack flexibility and generality when considering different cable arrangements and load combinations. Existing studies are typically limited to fixed structural configurations under single-load effects. (2) Restricted by computational costs, the Morison equation is commonly used to calculate fluid loads on long-span SFTs. This equation can only account for one-way fluid-structure interaction (FSI) effects, fails to compute the torque exerted by fluids on the SFT tube, and ignores the influence of seabed topography on the flow field. Addressing the current research gaps in the analysis of dynamic characteristics of the long-span SFT under marine conditions, particularly the challenges in two-way FSI computation for long-span configurations, this paper proposes a time-domain computational method for dynamic response analysis of the long-span SFT under coupled action of multiple loads, which provides a general computational framework for dealing with the multi-load action problems of SFTs. The computational framework incorporates a two-way FSI calculation model based on a system of two-dimensional potential flow wave flumes, which overcomes the limitations in computational efficiency in bidirectional coupling analysis of the long-span SFT, and addresses the challenges in the applicability of the Morison equation under complex working conditions. This paper verifies the correctness of the proposed method for calculating structural dynamic responses by comparing the calculation results of finite element mode. The accuracy of the potential flow flume in calculating wave loads is also verified by comparing with the calculation results of the viscous fluid model. Finally, by comparing with the results of the frequency-domain calculation of dynamic responses of the SFT, it demonstrates the reliability of the FSI calculation.
沉浮隧道是一种用于跨水域的新型运输结构。在复杂的海洋环境中,大跨度SFT结构受到多种荷载的非线性耦合作用,产生极其复杂的动力响应。目前,海洋环境下大跨度SFT动力响应的计算方法存在以下主要不足:(1)当采用不同的索模型、管端边界条件和荷载模式时,得到的SFT数学模型往往表现出不同的表达式,控制方程复杂。在考虑不同的电缆布置和荷载组合时,模型缺乏灵活性和通用性。现有的研究通常局限于单荷载作用下的固定结构构型。(2)受计算成本的限制,morrison方程通常用于计算大跨度SFTs的流体荷载。该方程只能考虑单向流固耦合效应,不能计算流体作用在SFT管上的扭矩,忽略了海底地形对流场的影响。针对目前海洋条件下大跨度桥架动力特性分析研究的空白,特别是大跨度结构双向FSI计算的挑战,本文提出了多载荷耦合作用下大跨度桥架动力响应分析的时域计算方法,为处理桥架多载荷作用问题提供了一个通用的计算框架。该计算框架引入了基于二维势流波流槽系统的双向流固耦合计算模型,克服了大跨度SFT双向耦合分析计算效率的局限性,解决了morrison方程在复杂工况下适用性的挑战。通过比较有限元模型的计算结果,验证了所提出的结构动力响应计算方法的正确性。通过与粘性流体模型计算结果的对比,验证了势流水槽计算波浪荷载的准确性。最后,通过与SFT动力响应频域计算结果的比较,验证了FSI计算的可靠性。
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引用次数: 0
Exact and explicit wavenumbers and closed-form solutions of the Ye equation for water wave propagation over L-type bed terrains 水波在l型河床上传播的Ye方程的精确和显式波数和封闭解
IF 3.5 2区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2025-10-18 DOI: 10.1016/j.jfluidstructs.2025.104441
Huan-Wen Liu
The differential equations governing water surface gravity wave motion over uneven seabeds are generally difficult to be solved analytically. For the original Laplace equation together with appropriate boundary and radiation conditions, there appears to be only one closed-form solution, called Roseau’s solution. For the depth-averaged equations such as the mild-slope type equation, the Ye equation, and the Boussinesq equation, the closed-form solutions are rare because the wavenumber has never been solved exactly from the Airy dispersion equation since it was derived by Airy in 1841. In this paper, Airy dispersion equation is exactly solved for linear surface gravity waves propagating over a cluster of special terrains, called the L-type seabeds. Furthermore, based on the explicit Airy wavenumbers, closed-form solutions to the Ye equation for wave reflection by a trapezoidal hump/trench with the two slopes being the L-type terrains are successfully constructed. To this author’s knowledge, this is the first group of closed-form solutions to depth-averaged wave equations in the whole wave range from shallow-water waves to deep-water waves.
不均匀海床上水面重力波运动的微分方程一般难以解析求解。对于原始拉普拉斯方程,在适当的边界和辐射条件下,似乎只有一个闭型解,称为罗索解。对于深度平均方程,如缓坡型方程、Ye方程和Boussinesq方程,由于Airy色散方程自1841年由Airy导出以来从未精确地解出波数,因此闭型解很少。本文精确求解了线性表面重力波在l型海床上传播时的Airy频散方程。此外,基于显式Airy波数,成功地构造了两坡为l型地形的梯形驼峰/沟槽反射Ye方程的闭型解。据笔者所知,这是在从浅水波到深水波的整个波浪范围内,深度平均波动方程的第一组闭型解。
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引用次数: 0
期刊
Journal of Fluids and Structures
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