The near-field energetics and directional properties of internal gravity waves (IGWs) radiated from the turbulent wake of a sphere towed through a linearly stratified fluid are investigated using a series numerical experiments. Simulations have been performed for an initial Reynolds number $Re\equiv UD/\unicode[STIX]{x1D708}\in \{5\times 10^{3},10^{5},4\times 10^{5}\}$ and internal Froude number $Fr\equiv 2U/ND\in \{4,16,64\}$ , defined using body-based scales – $D$ , the sphere diameter; $U$ , the tow speed; and $N$ , the Brunt–Vaisala frequency. Snapshots of temporally evolving wake flow fields are sampled over the full wake evolution. The energy extracted from the wake through internal wave radiation is quantified by computing the total wave power emitted through a wake-following elliptic cylinder. The total time-integrated wave energy radiated is found to increase with $Re$ and decrease with $Fr$ . The peak radiated wave power occurs at early times, near to the onset of buoyancy control, and is found to be approximately unchanged in magnitude as $Re$ is increased. For the two higher $Re$ considered, at late times, IGWs continue to be emitted – accounting for a distinct increase in total radiated wave energy. The most powerful IGWs are radiated out of the wake at a wide range of angles for $Nt<10$ , at $20^{\circ }{-}70^{\circ }$ to the horizontal for $10\leqslant Nt\leqslant 25$ , and nearly parallel to the horizontal late in the non-equilibrium regime of wake evolution. Internal wave radiation is found to be an important sink for wake kinetic energy after $Nt=10$ , suggesting wave radiation cannot be neglected when modelling stratified turbulent wakes in geophysical and ocean engineering applications.

中文翻译：

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来自分层湍流尾流的内部重力波辐射

使用一系列数值实验研究了从通过线性分层流体拖曳的球体的湍流尾流辐射的内部重力波 (IGW) 的近场能量学和方向特性。对初始雷诺数 $Re\equiv UD/\unicode[STIX]{x1D708}\in \{5\times 10^{3},10^{5},4\times 10^{5} 进行了模拟\}$ 和内部弗劳德数 $Fr\equiv 2U/ND\in \{4,16,64\}$ ，使用基于身体的尺度定义 - $D$ ，球体直径；$U$ ，牵引速度；和 $N$ ，Brunt-Vaisala 频率。在整个尾流演化过程中对随时间演化的尾流流场的快照进行采样。通过内波辐射从尾流中提取的能量通过计算通过尾流跟随椭圆柱体发射的总波功率来量化。发现辐射的总时间积分波能随着 $Re$ 增加而随着 $Fr$ 减少。峰值辐射波功率出现在早期，接近浮力控制的开始，并且随着 $Re$ 的增加，其幅度几乎没有变化。对于考虑的两个较高的 $Re$，在后期，IGW 继续发射 - 占总辐射波能量的明显增加。最强大的 IGW 以大范围的角度从尾流中辐射出来，$Nt<10$，$20^{\circ }{-}70^{\circ }$ 到水平方向 $10\leqslant Nt\leqslant 25$ ，并且在尾流演化的非平衡状态后期几乎平行于水平线。发现内波辐射是 $Nt=10$ 后尾流动能的重要汇，