类马赫毛细-重力尾迹
Mach-like capillary-gravity wakes
摘要：
我们确定实验的角度$α$的最大波振幅在远场尾流后面的垂直表面穿孔圆柱体平移在恒定速度$U$的邦德数$\mathrm{Bo}_D = D / λ_c$范围在0.1和4.2之间，其中$D$是圆柱体直径和$λ_c$的毛细管长度。在所有情况下，尾流角被发现遵循马赫-类法律在大的速度，$α\sim U^{-1}$，但不同的前因子取决于值的$\mathrm{Bo}_D$。对于小的$\mathrm{Bo}_D$（大的毛细管效应），尾流角近似遵循$α\simeq c_{\rm g,min} / U$定律，其中$c_{\rm g,min}$是毛细管重力波的最小群速度。对于较大的$\mathrm{Bo}_D$（弱毛细管效应），我们恢复了一个与大速度下船舶尾流相似的规律$α\sim \sqrt{gD}/U$ [Rabaud和Moisy，Phys. Rev. Lett. { \bf 110}，214503（2013）]。利用色散波的一般性质，即由扰动发出的波包的特征波长是扰动大小的顺序，我们提出了一个简单的模型，描述了这两个马赫制度之间的过渡作为邦德数是不同的。我们发现，新的毛细管法$α\simeq c_{\rm g,min} / U$起源于毛细管尖角（不同于通常的重力尖角）的存在下，沿该能量辐射的扰动积累的债券数量的统一的顺序。该模型，补充由移动高斯压力扰动引起的表面高程的数值模拟，是在定性与实验测量。
英文摘要：
We determine experimentally the angle $α$ of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity $U$ for Bond numbers $\mathrm{Bo}_D = D / λ_c$ ranging between 0.1 and 4.2, where $D$ is the cylinder diameter and $λ_c$ the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, $α\sim U^{-1}$, but with different prefactors depending on the value of $\mathrm{Bo}_D$. For small $\mathrm{Bo}_D$ (large capillary effects), the wake angle approximately follows the law $α\simeq c_{\rm g,min} / U$, where $c_{\rm g,min}$ is the minimum group velocity of capillary-gravity waves. For larger $\mathrm{Bo}_D$ (weak capillary effects), we recover a law $α\sim \sqrt{gD}/U$ similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. {\bf 110}, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wavepacket emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law $α\simeq c_{\rm g,min} / U$ originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
