[论文解读] Water Waves from General, Time-Dependent Surface Pressure Distribution in the Presence of a Shear Current

Yan Li, Simen Å. Ellingsen|arXiv (Cornell University)|Nov 9, 2015

Ocean Waves and Remote Sensing参考文献 18被引用 3

一句话总结

本文提出了一种在均匀涡度剪切流存在下，由随时间变化的表面压力分布激发的三维水波的解析解。研究表明，剪切流导致瞬态波形出现强烈不对称性，上游波的衰减显著慢于下游波，并表明瞬态波阻力随时间减弱，而稳态船波形态则持续存在，尤其在逆流航行时更为明显。

ABSTRACT

We obtain a general solution for the water waves resulting from a general, time-dependent surface pressure distribution, in the presence of a shear current of uniform vorticity beneath the surface, in three dimensions. Linearized governing equations and boundary conditions including the effects of gravity, a distributed external pressure disturbance, and constant finite depth, are solved analytically, and particular attention is paid to classic initial value problems: an initial pressure impulse and a steady pressure distribution which appears suddenly. In the present paper, good agreement with previous results is demonstrated. We subsequently show both analytically and numerically how transient waves from a suddenly appearing steady pressure distribution vanis for large times, and steady ship waves remain. The transient contribution to wave resistance was derived. The results show that a shear current has significant impact on the transient wave motions, resulting in asymmetry between upstream and downstream waves. The case of the suddenly appearing steady pressure is an intermediate case between ring waves and ship waves, starting out as the former and evolving gradually into the latter. The ship's direction of motion relative to the current is found to be crucial in determining how quickly effects of transient waves die out. Transient effects take much longer to doe out for a ship going against the shear flow than for one going downstream, when the two ships have the same velocity relative to the water surface. For ship motion against the shear current, thus, wave effects of transients, e.g., due to maneuvering could accumulate and be far more significant than on a uniform current.

研究动机与目标

• 推导在剪切流存在下，由任意随时间变化的表面压力分布激发的水波的一般解析解。
• 研究突然施加的稳态压力分布引起的瞬态波行为，连接环形波与船波动力学。
• 量化剪切流对波阻的影响，特别是瞬态贡献部分。
• 分析由于水流引起的色散效应导致的上游与下游波形之间的不对称性。
• 确定船体运动方向相对于剪切流如何影响瞬态波效应的衰减速率。

提出的方法

• 求解包含重力、恒定水深及分布外部压力扰动的线性化欧拉方程。
• 应用包含表面压力分布和均匀涡度剪切流存在的边界条件。
• 使用解析方法求解初值问题，特别是脉冲和突然施加压力的情形。
• 采用傅里叶变换与拉普拉斯变换处理时变激励并推导闭式解。
• 进行数值模拟以验证解析结果并可视化波的演化过程。
• 推导波阻表达式，分离瞬态与稳态贡献部分。

实验结果

研究问题

• RQ1 剪切流如何影响由突然施加的压力分布激发的瞬态波形？
• RQ2 在剪切流存在下，瞬态波的衰减行为如何？其在上游与下游传播中的差异是什么？
• RQ3 船体运动方向相对于剪切流在多大程度上影响瞬态波效应的持续时间？
• RQ4 在时变激励下，波阻如何分解为瞬态与稳态分量？
• RQ5 在突然施加稳态压力条件下，系统如何从环形波状行为过渡到船波状行为？

主要发现

• 由突然出现的稳态压力分布激发的瞬态波，随时间演化从环形波状形态转变为船波状形态。
• 瞬态波对波阻的贡献随时间衰减，但当船逆流航行时，其衰减显著慢于顺流航行时。
• 剪切流引起强烈不对称性：由于群速度和色散关系的改变，上游波比下游波持续时间长得多。
• 对于逆流航行的船只，瞬态波效应（如机动引起的波）可能累积并在长时间内保持显著。
• 解析解在涡度为零的极限下与先前结果高度一致，验证了模型的正确性。
• 稳态波形持续存在，而瞬态分量渐近趋于零，证实了稳态激励下永久波形特征的存在。