The Character Study on Shear Instability of Ocean Internal Waves in Strong Semi-Diurnal Tidal Currents
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摘要: 本文将定常垂向剪切流和正压半日潮流的叠加作为背景流，给出了在此背景流下无海底地形起伏的海洋内波非静力控制方程组，建立了一个二维海洋内波数值模型，用以研究内波的生成、发展和演变特性以及不稳定内波的结构和性质。主要研究结果为：当给定一个初始小扰动时，仅有潮流作为背景流的条件下，扰动不会发展。背景流为正压半日潮流与定常垂向剪切流叠加时，扰动出现剪切不稳定，其能量呈增长趋势。扰动能量出现与潮流同周期的波状变化。内波生成后，呈现与潮流大小同步的顺、逆剪切流方向的平移，顺向平移远较逆向平移快，总体上沿顺向剪切流方向移动，表明潮流对内波发展有调制作用。该内波流函数扰动呈现由多个闭合正负环流圈构成的波包形态，环流中心出现在水体中部。密度扰动主体均出现在跃层附近，为跃层所俘获。因潮流与扰动的相互作用，会使单一频率的简谐波变成包含很多频率的波包，即为潮流的变频作用，其会明显降低内波剪切不稳定的增长率，该作用具有维稳特性。内波的群速度总趋势沿剪切流方向。不稳定内波的水平尺度基本与扰动初值无关。该内波的性质属非平衡的重力（惯性）波。Abstract: A two-dimensional numerical model of ocean internal waves is established by using the non-static governing equations of the waves without seafloor topography to study the generation, development and evolution characteristics, as well as the structure and properties of internal waves under the background flow, which is the superposition of steady vertical shear flow and the strong barotropic semi-diurnal tidal currents. The main research results are as follows: When there is an initial disturbance and only the tidal currents is used as the background flow, the disturbance will not develop. When the barotropic semi-diurnal tidal currents and the steady vertical shear flows are superimposed as the background flow, the disturbance shows shear instability, and its energy shows an increasing trend and a wave-like change in the same phase as the tidal current. After the internal waves were generated, showing a moving in the direction of forward and reverse shear flow synchronized with the period of the tidal current. The forward moving was much faster than the reverse moving, and overall it moved along the direction of forward shear flow, indicating that the tidal current had a modulating effect on the development of internal waves. The flow function disturbance of the internal wave presents a wave packet shape composed of multiple closed positive and negative circles, with the circulation center appearing in the middle of the water body. The main body of density disturbance appears near the pycnocline and is captured by the pycnocline. Due to the interaction between tidal currents and disturbances, a single frequency harmonic wave can be transformed into a wave packet containing many frequencies, known as the frequency conversion effect of currents. This effect significantly reduces the growth rate of internal wave shear instability and has the characteristics of maintaining stability. The overall trend of the group velocity of internal waves is along the direction of shear flow. The horizontal scale of the unstable internal waves is basically independent of the initial disturbance value. The nature of this internal waves are non-equilibrium gravitational (inertial) waves.
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图 1
$ \sigma ' $ 初始场的空间分布（单位：10−4ms−2），Fig. 1 The
$ \sigma ' $ distribution at initial moment (units: 10−4 ms−2)
图 2 Ex1中ED (a), EN (b)以及潮流随时间的变化
Fig. 2 ED (a), EN (b) and the tidal current change with time in Ex1
图 3 Ex1中流函数的空间分布图（单位：m2s−1）
积分时间：（a）1 h，（b）12 h，（c）24 h，（d）72 h
Fig. 3 The distribution of stream functions in Ex1 (units: m2s−1)
Integration time: (a)1 h, (b)12 h, (c)24 h, (d)72 h
图 4 Ex1中
$ \sigma ' $ 的空间分布图（单位：10−4ms−2）积分时间：（a）1 h，（b）12 h，（c）24 h，（d）72 h
Fig. 4 The
$ \sigma ' $ distribution in Ex1 (units: 10−4 m s−2)Integration time: (a)1 h, (b)12 h, (c)24 h, (d)72 h
图 5 Ex2中 ED (a), EN (b)以及潮流随时间的变化
Fig. 5 ED (a), EN (b) and tidal current change with time in Ex2
图 6 Ex2中流函数的空间分布图（单位：m2s−1）
积分时间：（a）12 h，（b）72 h
Fig. 6 The distribution of stream functions in Ex2 (units: m2 s−1)
Integration time: (a)12 h, (b)72 h
图 8 Ex2 (a)及Ex1 (b)中群速度随积分时间的变化
Fig. 8 group velocity change with time in Ex2 (a) and Ex1 (b)
图 9 Ex1流函数(a)及
$ \sigma ' $ (b)的水平分布Fig. 9 horizontal distribution of stream functions (a) and
$ \sigma ' $ (b) in Ex1
图 10 Ex4 (a)及Ex3 (b)中流函数水平分布
Fig. 10 distribution of stream functions in Ex4 (a) and Ex3 (b)
表 1 Ex1～Ex5的数值试验方案
Tab. 1 Ex1～Ex5 numerical experiment schemes
试验
名称正压
潮流定常剪切流 平流项u'∂/∂x,
w'∂/∂z初始扰动水平
尺度（m）EX1 yes yes yes 320 EX2 yes yes no 320 EX3 no yes yes 320 EX4 no yes no 320 EX5 yes yes yes 640 
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表 2 Ex1、Ex2中ED(a)、EN(b) 值
Tab. 2 ED (a), EN (b) in Ex1, Ex2
试验 时间 0 h 1 h 12 h 24 h 36 h 48 h 60 h 72 h 84 h 96 h Ex1 Ed 0.0000E+00 0.6679E-02 0.7746E-02 0.7848E-02 0.9436E-02 0.9437E-02 0.9992E-02 0.1061E-01 0.1132E-01 0.1045E-01 En 0.2559E-05 0.6898E-05 0.7154E-05 0.6774E-05 0.1026E-04 0.8966E-05 0.9733E-05 0.1059E-04 0.1087E-04 0.1036E-04 Ex2 Ed 0.0000E+00 0.6936E-02 0.8670E-02 0.1103E-01 0.1289E-01 0.1328E-01 0.1522E-01 0.1659E-01 0.1646E-01 0.1549E-01 En 0.2559E-05 0.5748E-05 0.8115E-05 0.1012E-04 0.1289E-04 0.1281E-04 0.1499E-04 0.1609E-04 0.1617E-04 0.1532E-04 注：Ed单位：ms−1； En 单位：ms−2
下载: 导出CSV
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