Vortex generation by deep-water breaking waves
Vortex generation by deep-water breaking waves
复制标题
深水破碎波产生涡流
DOI：
10.1017/jfm.2013.453
复制
发表时间：
2013
影响因子：
3.7
通讯作者：
W. Melville
中科院分区：
文献类型：
--
作者：
N. Pizzo;W. Melville
深水表面重力波破碎引起的波浪耗散与由此产生的湍流和混合之间的联系对于提高对海气相互作用过程的认识至关重要。从控制平均流演化的整体平均欧拉方程开始，我们模拟了与断裂诱导的雷诺兹剪切应力相关的强迫，作为描述断裂深水表面重力波对水柱的整体规模效应的体力。由此，我们导出了一个方程，描述了由于物体力而产生的整体平均速度场的循环$\Gamma $。通过研究破碎波和脉冲强迫流体之间的关系，我们提出了一种体力的函数形式，使我们能够建立在经典的涡环现象的基础上，既量化了破碎波产生的循环，又描述了诱导运动的涡结构。使用缩放参数，我们表明$\Gamma = \alpha {(hk)}^{3/ 2} {c}^{3} / g$，其中（$c, h, k$）分别表示破碎波的特征速度，高度和波数，$g$是由于重力引起的加速度，$\alpha $是常数。这样，我们就可以找到环流和由于破裂造成的单位波峰长度的波浪能量耗散率之间的直接关系，${\epsilon }_{l} $。最后，将模型与已有的实验数据进行了比较。
Abstract The connection between wave dissipation by breaking deep-water surface gravity waves and the resulting turbulence and mixing is crucial for an improved understanding of air–sea interaction processes. Starting with the ensemble-averaged Euler equations, governing the evolution of the mean flow, we model the forcing, associated with the breaking-induced Reynolds shear stresses, as a body force describing the bulk scale effects of a breaking deep-water surface gravity wave on the water column. From this, we derive an equation describing the generation of circulation, $\Gamma $ , of the ensemble-average velocity field, due to the body force. By examining the relationship between a breaking wave and an impulsively forced fluid, we propose a functional form for the body force, allowing us to build upon the classical work on vortex ring phenomena to both quantify the circulation generated by a breaking wave and describe the vortex structure of the induced motion. Using scaling arguments, we show that $\Gamma = \alpha {(hk)}^{3/ 2} {c}^{3} / g$ , where ( $c, h, k$ ) represent a characteristic speed, height and wavenumber of the breaking wave, respectively, $g$ is the acceleration due to gravity and $\alpha $ is a constant. This then allows us to find a direct relationship between the circulation and the wave energy dissipation rate per unit crest length due to breaking, ${\epsilon }_{l} $ . Finally, we compare our model and the available experimental data.