Turbulence during the reflection of internal gravity waves at critical and near-critical slopes
Turbulence during the reflection of internal gravity waves at critical and near-critical slopes
复制标题
临界和近临界坡度处内部重力波反射期间的湍流
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
S. Sarkar
中科院分区：
文献类型：
--
作者：
V. Chalamalla;B. Gayen;A. Scotti;S. Sarkar
摘要对平面内波在倾斜海底反射过程中的非线性动力学特性进行了直接数值模拟。通过改变入射弗劳德数$Fr$来评估入射波振幅的影响，并通过在近临界值范围内改变倾斜角来评估非临界状态的影响。在低$\mathit{Fr}$时，数值结果与近临界内波反射的线性无粘理论吻合较好。随着$\mathit{Fr}$的增加，反射过程变得非线性，形成高次谐波，并在反射波的演化过程中引发细尺度湍流。稍后，波响应变得准稳定，湍流系统地依赖于时间和空间相位。对流不稳定性被发现在每个周期中湍流的形成中起着至关重要的作用。详细研究了流量统计的周期演化，并确定了非临界和临界反射之间的定性差异。计算了湍流度与弗劳德数和倾斜角的参数关系。有趣的是，在给定的$\mathit{Fr}$的值，湍流动能（TKE）可以更高的一些非临界反射相比，正是临界反射。对于固定的斜坡角，随着弗劳德数的增加，在模拟的情况下，输入波能转化为湍流动能的份额和输入波功率的份额也增加湍流耗散。
Abstract Direct numerical simulation is performed with a focus on the characterization of nonlinear dynamics during reflection of a plane internal wave at a sloping bottom. The effect of incoming wave amplitude is assessed by varying the incoming Froude number, $Fr$ , and the effect of off-criticality is assessed by varying the slope angle in a range of near-critical values. At low $\mathit{Fr}$ , the numerical results agree well with linear inviscid theory of near-critical internal wave reflection. With increasing $\mathit{Fr}$ , the reflection process becomes nonlinear with the formation of higher harmonics and the initiation of fine-scale turbulence during the evolution of the reflected wave. Later in time, the wave response becomes quasi-steady with a systematic dependence of turbulence on the temporal and spatial phase. Convective instabilities are found to play a crucial role in the formation of turbulence during each cycle. The cycle evolution of flow statistics is studied in detail and qualitative differences between off-critical and critical reflection are identified. The parametric dependence of turbulence levels on Froude number and slope angle is calculated. Interestingly, at a given value of $\mathit{Fr}$ , the turbulent kinetic energy (TKE) can be higher for somewhat off-critical reflection compared to exactly critical reflection. For a fixed slope angle, as the Froude number increases in the simulated cases, the fraction of the input wave energy converted into the turbulent kinetic energy and the fraction of the input wave power dissipated by turbulence also increase.