Propagation, Dissipation, and Mixing Effects of Wind-Generated Near-Inertial Internal Waves under the Nontraditional Approximation
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摘要: 本文采用数值模式MITgcm二维非静力模型，模拟了低纬度海区（2°−20°）风生近惯性内波在传统近似与非传统近似下的生成、传播与耗散过程，系统分析了非传统近似（即保留科氏参数水平分量）对近惯性内波传播路径、能量耗散以及海洋内部混合的影响。非传统近似拓宽了内波的频散关系，使近惯性内波能够产生亚惯性分量，从而穿越传统近似下的惯性纬度，向高纬及深海持续输送能量。极向传播的近惯性内波在非传统近似惯性纬度附近下传至海底，经海底反射后能量在近底层聚集，显著增强该区域的垂向剪切，触发剪切不稳定产生内波能量耗散。不稳定区域单位纬向宽度的平均耗散功率为0.25 W/m，由此增强的湍流混合进而驱动深海的跨等密度面体积输运可达1.2×10−4 Sv。基于模拟结果与全球近惯性内波能量耗散估算结果，本文粗略地估算了非传统近似下风生近惯性内波诱发的深海湍流混合在全球范围内可驱动～1 Sv量级的上升流。上述结果表明非传统近似对于准确评估风生近惯性内波能量耗散及其在全球经向翻转环流中的作用具有重要意义。Abstract: This study employs the MITgcm two-dimensional non-hydrostatic numerical model to simulate the generation, propagation, and dissipation processes of wind-generated near-inertial internal waves in the low-latitude ocean region (2°–20°) under both the traditional approximation and the nontraditional approximation. The effects of the nontraditional approximation (retention of the horizontal component of the Coriolis parameter) on the propagation pathways, energy dissipation, and ocean interior mixing of near-inertial internal waves are systematically analyzed. The nontraditional approximation broadens the dispersion relation of internal waves, enabling near-inertial internal waves to generate sub-inertial components. Consequently, these waves can cross the inertial latitudes defined under the traditional approximation and continuously transport energy toward higher latitudes and the deep ocean. Poleward-propagating near-inertial internal waves, under the nontraditional approximation, propagate downward to the seafloor in the vicinity of the inertial latitude. After bottom reflection, wave energy accumulates within the near-bottom layer, significantly enhancing vertical shear in this region and triggering shear instability, which leads to near-inertial internal waves energy dissipation. The mean dissipation power per unit zonal width in the Shear instability region is 0.25 W/m, and the associated enhanced turbulent mixing drives diapycnal volume transport in the deep ocean reaching 1.2 × 10−4 Sv. Based on the model results and a global estimate of near-inertial wave energy dissipation, this study roughly estimates that under the non-traditional approximation, wind-generated near-inertial internal waves induce deep-ocean turbulent mixing, which drives a global upwelling of approximately 1 Sv. These results indicate that the non-traditional approximation is essential for accurately quantifying near-inertial wave energy dissipation and its role in the global meridional overturning circulation.
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图 1 模式初始场
（a）温度分布（b）风应力大小和位置分布，风应力作用区域为40km（c）风应力大小随时间变化分布
Fig. 1 Initial fields of the numerical model
(a) Temperature distribution (b) Magnitude and spatial distribution of wind stress， the wind forcing region spans 40 km (c) Temporal evolution of wind stress magnitude
图 2 模式运行第70天的散度场
（a）传统近似和（b）非传统近似。（c）绿色方框区域叠加波射线的放大图。黑色虚线为传统近似、非传统近似的转折纬度线。品红色虚线内为风应力作用区域。绿色方框区域内为非传统近似下内波极向传播的影响区域
Fig. 2 Divergence field on day 70 of the model simulation
(a) Traditional approximation and (b) Non-traditional approximation. (c) Magnified superimposed internal wave rays within the green box. The black dashed lines denote the turning latitudes under the traditional and non-traditional approximations. The magenta dashed lines indicate the wind forcing region. The green box marks the region influenced by the poleward propagation of near-inertial waves under the nontraditional approximation
图 3 近惯性内波射线追踪模型结果
（a）传统近似和（b）非传统近似。黑色虚线为传统近似、非传统近似的转折纬度
Fig. 3 The ray-tracing model results of near-inertial waves
(a) Traditional approximation and (b) Non-traditional approximation. The black dashed lines denote the turning latitudes
图 4 模式运行第70天的理查德森数（Ri）分布
（a）传统近似和（b）非传统近似。黑色方框内为海底发生剪切不稳定的区域
Fig. 4 Distribution of the Richardson number (Ri) on day 70
(a)Traditional approximation and (b)Non-traditional approximation. The black box marks the seafloor region where shear instability occurs
图 5 Ri小于0.25的经向范围在剪切不稳定区域经向长度（图4黑色方框）中所占比例的深度-时间变化分布
Fig. 5 Depth-time variation of the proportion of the meridional extent with Ri < 0.25 to the meridional length of the shear instability region (black box in Fig. 4)
图 6 第70天浮力频率（N2）分布
（a）传统近似和（b）非传统近似下第70天N2对数分布
Fig. 6 Distribution of the buoyancy frequency N2 on day 70
(a) Traditional approximation and (b) non-traditional approximation: log(N2) distribution on day 70
图 7 非传统近似下纬度12.6°–16.2°区域（图2绿色方框内区域）近惯性内波累计能量变化的深度–时间分布
（a）能量通量散度项的时间积分$\displaystyle \int_{{t}_{0}}^{t}\nabla \cdot Fdt $；（b）t0时刻到t时刻内波总能量密度的差值$ \mathit{\Delta }E=E\left(t\right)-E\left({t}_{0}\right) $；（c）能量耗散项的时间积分$ \displaystyle\int_{{t}_{0}}^{t}\varepsilon dt $
Fig. 7 Depth–time distribution of the cumulative near-inertial wave energy variation in the latitude band 12.6°–16.2° (corresponding to the green box in Fig. 2) under the non-traditional approximation
(a)Time integral of the divergence of the energy flux term: $\displaystyle \int_{{t}_{0}}^{t}\nabla \cdot Fdt $; (b)The change in total wave energy density from time t0 to time t: $ {\varDelta }E=E\left(t\right)-E\left({t}_{0}\right) $; (c) Time integral of the energy dissipation term: $\displaystyle \int_{{t}_{0}}^{t}\varepsilon dt $
图 8 非传统近似下纬度12.6°–16.2°区域（图2绿色方框内区域）累计能量收支三项的时间序列
Fig. 8 Temporal variations of various cumulative energy components in the latitude band 12.6°–16.2° (corresponding to the green box in Fig. 2) under the non-traditional approximation
图 9 非传统近似下海底发生剪切不稳定区域（图4黑色方框内区域）KPP方案垂向湍流扩散率（Kz）深度–时间变化分布
Fig. 9 Depth-time distribution of vertical turbulent diffusivity (Kz) from the KPP scheme in the seafloor shear instability region under the non-traditional approximation (corresponding to the black box in Fig. 4)
图 10 非传统近似下海底发生剪切不稳定区域（图4黑色方框内区域）由内波破碎伴随的能量耗散所驱动的跨等密度面体积输运时间变化分布
（a）跨等密度面体积输运的霍夫莫勒图（b）子图a垂向积分后的净体积输运，黑色虚线处为平均值1.2×10−4 Sv5 总结和讨论
Fig. 10 Temporal evolution of diapycnal volume transport driven by energy dissipation associated with internal wave breaking in the near-bottom shear instability region under the non-traditional approximation (the black box in Fig. 4)
(a) Hovmöller diagram of diapycnal volume transport (b) Vertically integrated net volume transport from subpanel (a), with the black dashed line indicating the time-mean value of 1.2 × 10−4 Sv
表 1 不同层化强度与风应力强迫下深海的体积输运
Tab. 1 Volume transport in the deep ocean under different stratification intensities and wind stress forcing
1 500 m以深平均浮力频率平方/s -2 风应力/ N m-2 平均体积输运/ Sv 7.92×10-9 0.4 1.20×10−4 0.5 1.23×10−4 1 1.71×10−4 1.50×10-8 0.4 6.80×10−5 0.5 1.07×10−4 1 1.42×10−4 
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