Generation and evolution on symmetric ocean inner waves in unstable background flow
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摘要: 本文采用无海底地形但考虑海洋跃层和剪切背景流的二维非静力准不可压缩方程组的数值模式，开展失稳垂向剪切背景流下线性和非线性对称型海洋内波生成演变的数值实验，并对结果进行分析、比较和讨论。研究结果表明，线性内波强度随积分时间始终呈指数增长，并有内波的对称不稳定；而非线性内波强度则在发展期呈准线性增长，最终进入稳定期。线性增长比非线性增长要快得多，非线性效应具有维稳作用。对该线性和非线性对称型内波，在跃层附近位密度扰动均有大值中心，即其为跃层所俘获，这与实际观测相一致；流函数与位密度扰动两者均有很好配合，位密度扰动的正、负中心分别相应于流函数的上升、下沉运动，表明有从海底向上的斜对流发生，且以跃层为顶盖。对线性内波来说，随积分时间增加，其波形大体不变，其正、负振幅也大体相同，并有符号相反原地增长的两个倾斜环流圈，而在它们之间则有较强倾斜上升流。非线性内波波形随积分时间改变，倾斜环流圈数目也在增加，最终形成负环流强于正环流的结果，并导致流函数、位密度扰动水平梯度剧增，其可视为间断。Abstract: Using the two-dimensional non-static numerical model, which neglect the submarine topography but consider the pycnocline and background shear flow, the numerical experiment was made on the generation and evolution of linear and nonlinear symmetric ocean internal waves in the unstable downward shear background flow. After analyzing and comparing the results, the main conclusions are as follows: the linear internal wave strength is exponentially growing with integral time, and there’s symmetric instability of the wave, while nonlinear internal wave strength is growing quasi-linearly in the development stage, and finally enters the stabilization stage. The linear growing is much faster than the nonlinear growing and the latter has a stabilizing effect. For linear and nonlinear symmetric internal waves, there are maximum value of potential density perturbation, which is captured by the pycnocline. This is consistent with actual observations. The stream function and potential density perturbation are well coordinated, which is reflected in the positive and negative centers of the potential density perturbation corresponding to the rising and sinking movements of the stream function, respectively. This shows that there is a slantwise convection occurred from the bottom of the sea and the pycnocline is the top cover. For linear internal waves, with the increase of integral time, its waveform is basically the same and the positive and negative amplitude is also about the same. There are two slantwise circulations that grow in opposite signs and between them is a strong slantwise upwelling. The waveform of nonlinear internal wave changes with the integration time and the number of slantwise circulations is also increasing, resulting in the stronger negative circulations and a sharp increase in the horizontal gradient of stream function and potential density perturbation. The sharp increase can be regarded as an interruption.
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图 1 线性(a)和非线性(b)模式中E值随时间变化
Fig. 1 The variation of E values over time in linear (a) and nonlinear (b) models
图 2 线性模型中流函数的空间分布（等值线表示流函数，单位：m2/s）
水平格距为80 m，海洋层次第1层为海底，第24层为海面，层距为80 m
Fig. 2 The distribution of stream functions in linear models (isolines represent stream functions, unit: m2/s)
The horizontal grid distance is 80 m, the first layer is the sea floor, the 24th layer is the sea surface, the layer distance is 80 m
图 3 线性模型中位密度扰动场的空间分布（等值线表示位密度，单位：10−4 m/s2）
水平格距为80 m，海洋层次第1层为海底，第24层为海面，层距为80 m
Fig. 3 The distribution of potential density perturbation in linear models (isolines represent potential density, unit: 10−4 m/s2)
The horizontal grid distance is 80 m, the first layer is the sea floor, the 24th layer is the sea surface, the layer distance is 80 m
图 4 非线性模型中流函数的空间分布（等值线表示流函数，单位：m2/s）
水平格距为80 m，海洋层次第1层为海底，第24层为海面，层距为80 m
Fig. 4 The distribution of streamfunctions in nonlinear models (isolines represent stream function, unit: m2/s)
The horizontal grid distance is 80 m, the first layer is the sea floor, the 24th layer is the sea surface, the layer distance is 80 m
图 5 非线性模型中位密度场的空间分布（等值线表示位密度，单位10−4 m/s2）
水平格距为80 m，海洋层次第1层为海底，第24层为海面，层距为80 m
Fig. 5 The distribution of potential density perturbation fields in nonlinear models (isolines represent potential density, unit: 10−4 m/s2)
The horizontal grid distance is 80 m, the first layer is the sea floor, the 24th layer is the sea surface, the layer distance is 80 m
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