On the Mach reflection of a solitary wave: revisited
On the Mach reflection of a solitary wave: revisited
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关于孤立波的马赫反射：重温
DOI：
10.1017/s0022112010006014
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发表时间：
2011
影响因子：
3.7
通讯作者：
Y. Kodama
中科院分区：
文献类型：
--
作者：
Wenwen Li;H. Yeh;Y. Kodama
在实验室波浪水槽中，对斜入射孤立波在垂直壁面上的反射进行了实验研究。借助激光诱导荧光（LIF）技术实现了水面变化的精确测量，并捕获了马赫反射的详细特征。在反射过程的发展阶段，干波不是Korteweg-de弗里斯（KdV）孤子的形式，而是一个受迫波，其尾部是一个不断加宽的凹陷。干波放大的演化与Kadomtsev-Petviashvili（KP）理论符合得很好。渐近特性和行为也与Miles（J. Fluid Mech.，vol.79，1977 b，p.171），除了在马赫反射和规则反射之间的过渡附近的那些。在实验室环境中没有实现预测的干波的最大四倍放大。另一方面，实验室观测与Tanaka的高阶模型的先前数值结果非常一致（J. Fluid Mech.，第248卷，1993，第637页）。目前的实验室研究是第一个合理地分析验证的理论，注意到，从以前的（数值和实验室）实验研究存在很大的差异。实验和理论之间的协议可以部分归因于大距离测量的精密实验室设备是有能力的。更重要的是，为了将实验结果与理论进行比较，在考虑有限入射波角的情况下，通过对理论的适当解释推导出了修正的相互作用参数。我们的实验室数据表明，最大干波可以达到高于最大孤立波的高度。波浪在近壁处破碎，导致离壁处波高和坡度显著增大。
Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is not in the form of a Korteweg–de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression. Evolution of stem-wave amplification is in good agreement with the Kadomtsev–Petviashvili (KP) theory. The asymptotic characteristics and behaviours are also in agreement with the theory of Miles (J. Fluid Mech., vol. 79, 1977b, p. 171) except those in the neighbourhood of the transition between the Mach reflection and the regular reflection. The predicted maximum fourfold amplification of the stem wave is not realized in the laboratory environment. On the other hand, the laboratory observations are in excellent agreement with the previous numerical results of the higher-order model of Tanaka (J. Fluid Mech., vol. 248, 1993, p. 637). The present laboratory study is the first to sensibly analyse validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking near the wall results in the substantial increase in wave height and slope away from the wall.