水平海床运动产生的完全非线性波下的粒子轨迹

中文摘要 AI 辅助

我们研究了由具有规定时变速度的海床障碍物水平运动所产生的完全非线性水波和流体粒子动力学。控制方程是完整的欧拉方程，在时间依赖的共形域中表述，该域同时将移动的自由表面和海床映射到固定边界。本工作的主要贡献是在所得的真实非定常共形域中计算粒子轨迹的拉格朗日公式。我们在规范域中推导出一个闭式轨迹系统，其中共形映射的时间依赖性完全由解析函数的实部和虚部表示，该函数可以从表面通过谱方法求值。我们将该公式应用于水平海底滑坡运动产生的波浪，并将整个流体中的粒子位移表征为初始粒子位置和弗劳德数的函数。我们的发现确定了不同的区域，其中粒子运动主要与移动的海床、产生的波浪或两者的联合作用相关。结果揭示了驱动粒子运动的主导机制的转变：在低弗劳德数下，粒子位移主要与移动的海床相关，而在高弗劳德数下，产生的波浪变得越来越占主导地位，特别是在自由表面附近和远离障碍物的地方。数值预测与文献中可用的实验室数据进行了基准比较，显示出良好的一致性，并提供了模型精度的定量评估。此外，通过埃尔米特插值程序，可以轻松地将超出此处考虑的实验室地形纳入数值框架。

英文摘要

We investigate fully nonlinear water waves and fluid-particle dynamics generated by the horizontal motion of a seabed obstacle with prescribed time-dependent velocity. The governing equations are the full Euler equations, formulated in a time-dependent conformal domain that simultaneously maps the moving free surface and seabed onto fixed boundaries. The main contribution of this work is a Lagrangian formulation for computing particle trajectories in the resulting genuinely unsteady conformal domain. We derive a closed-form trajectory system in the canonical domain in which the time dependence of the conformal map is entirely represented by the real and imaginary parts of an analytic function that can be evaluated spectrally from the surface. We apply the formulation to waves generated by horizontal submarine landslide motion and characterize particle displacements throughout the fluid as functions of the initial particle position and Froude number. Our findings identify distinct regions in which particle motion is predominantly associated with the moving seabed, the generated wave, or the combined action of both. The results reveal a transition in the dominant mechanism driving particle motion: at low Froude numbers, particle displacements are primarily associated with the moving seabed, whereas at high Froude numbers the generated wave becomes increasingly dominant, particularly near the free surface and away from the obstacle path.The numerical predictions are benchmarked against laboratory data available in the literature, showing good agreement and providing a quantitative assessment of the model accuracy. Moreover, laboratory topographies beyond those considered here can be readily incorporated into the numerical framework through a Hermite interpolation procedure.

发表机构

• UFPR/Federal University of Paraná（巴拉那联邦大学）
• School of Sciences and Engineering, Universidad del Rosario（罗萨里奥大学理学院）
• Sección Matemáticas, Departamento Académico Ciencias, Pontificia Universidad Católica del Perú（秘鲁天主教大学科学学术部数学组）

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