Study of the near-inertial motions induced by Typhoon “Cempaka” (2021) in the continental shelf of western Guangdong
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摘要: 近惯性运动是海洋中广泛存在的一种频率接近局地惯性频率的海水运动，热带气旋是产生近惯性运动的主要动力之一。本文基于COAWST（Coupled Ocean-Atmosphere-Wave-Sediment Transport）数值模型系统，构建了一个覆盖南海北部陆架的波浪−海流耦合三维水动力模型，并对模型进行了充分验证。利用该模型模拟了2021年第7号台风“查帕卡”在粤西近海陆架上激发的近惯性运动。结果表明，近惯性动能在水平分布上有两个能量高值中心，一个在台风风速最大的近岸区域，另一个在离岸约130 km处，且第二个能量高值中心持续时间更久。在水深40 m以浅的近岸区域，近惯性运动以正压模态为主，表底层流速的相位相同，能量从表层向底层递减。随着水深逐渐增加，在水深70 m到100 m的区域，近惯性运动呈明显的两层结构，表底层近惯性运动的流速方向相反，垂向上出现两个能量高值中心，呈明显的一阶斜压模态特征。通过动力模态分解，发现部分两层结构明显的区域由一阶斜压模态和二阶斜压模态共同主导。随着水深继续增加，更高模态的近惯性运动在总的近惯性动能中占据越来越大的比重。动量平衡分析表明，在水深较浅、风速较大的近岸区域，整个水层内的动量平衡都是由垂向湍流黏性力和压强梯度力主导。而在水深较深、风速较小的离岸区域，垂向湍流黏性力集中在表层和底层，水体内部的动量平衡主要由压强梯度力、科氏力和局地加速度主导。这些结果说明近岸区域主要是风应力驱动的正压波动，而陆架区域，上混合层内的近惯性运动由风应力驱动，混合层以下的近惯性运动则是由正压的压强梯度力驱动的。Abstract: Near-inertial motion is a type of motion in the ocean that is ubiquitous and has a frequency close to the local inertial frequency. Tropical cyclones are one of the mainmechanisms that generate near-inertial motion. This study established a three-dimensional hydrodynamic model based on COAWST (Coupled Ocean-Atmosphere-Wave-Sediment Transport) numerical model system, which couples waves and currents, covers the northern shelf of the South China Sea, and was fully verified. The model was used to simulate the near-inertial motion triggered by Typhoon “Cempaka”, the No.7 typhoon of 2021, on the shelf of western Guangdong. The results indicate that there are spatially two peaks of near-inertial kinetic energy, one in the coastal area with the highest typhoon wind speed, and the other at 130 km offshore, with the second energy peak lasting longer. In the coastal area with water depth shallower than 40 m, the near-inertial motion is mainly in a barotropic mode. As the water depth gradually increases offshore, we found that the near-inertial motions exhibit a clear two-layer structure inthe regions with depths ranging from 70−100 m, with opposite directions of near-inertial flow in the surface and bottom layers, and two energy peaks in the vertical direction, showing the characteristics of the first baroclinic mode. Through dynamic modedecomposition, we found that some areas with obvious two-layer structures are composed of the first and secondbaroclinic modes. As the water depth continues to increase, higher modes of near-inertial flow account for an increasing proportion of the total near-inertial kinetic energy. Momentum balance analysis shows that in the coastal area with shallow water depth and high wind speed, the balance of momentum equation in the entire water layer is dominated by the vertical turbulent viscous force and pressure gradient force. In offshore areas with deeper water depths and lower wind speeds, vertical turbulent viscous forces are concentrated in the surface and bottom layers, and the balance of momentum equation in the intermediate water body is mainly dominated by the pressure gradient forces, Coriolis forces, and local acceleration. This indicates that the near-inertialmotion in the coastal area is mainly driven by barotropicwave caused bywind stress, while in the continental shelf area, the near-inertial motion in the uppermixed layer is driven by wind stress, and the near-inertial motion below the mixed layeris driven by barotropic pressure gradient force.
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图 2 南海北部陆架模型范围内的水深（a）和网格（b）
Fig. 2 The bathymetry (a) and grid (b) of the model domain
图 3 近惯性能量的水平分布
第一至第三列分别为台风前、台风期间、台风后的近惯性动能。黑色线为台风中心移动路径，绿色点为台风中心所在位置
Fig. 3 The near-inertial energy horizontal distribution
The first to third columns represent the near inertial kinetic energy before, during, and after the typhoon, respectively. The black line represents the movement path of the typhoon center, and the green dots indicate the location of the typhoon center
图 4 分析站位空间分布
黑线和黑点分别代表台风移动路径和台风中心位置，红色点为分析点位置
Fig. 4 The locations of the chosen study stations along the typhoon track
The black line and black dot represent the movement path and center position of the typhoon respectively, while the red dot represents the study stations
图 5 S1-1至S1-5站位的表（第15层）、中（第8层）、底层（第1层）流速的旋转谱
其中蓝色线表示顺时针旋转（CW）的成分，红色线表示逆时针旋转（CCW）的成分；阴影区表示近惯性频段
Fig. 5 The rotary velocity spectrum for the surface (Layer 15), middle (Layer 8) and bottom layer (Layer 1) of stations S1-1 to S1-5
blue line shows the clockwise component (CW), and the dashed red line denotes the counter-clockwise component (CCW), the shaded region shows the band of near-inertial
图 6 S2-1至S2-5站位的表（第15层）、中（第8层）、底层（第1层）流速的旋转谱
其中蓝色线表示顺时针旋转（CW）的成分，红色线表示逆时针旋转（CCW）的成分；阴影区表示近惯性频段
Fig. 6 The rotary velocity spectrum for the surface,middle and bottom layer of Stations S2-1 to S2-5
blue line shows the clockwise component (CW), and the dashed red line denotes the counter-clockwise component (CCW), the shaded region shows the band of near-inertial
图 7 S1断面的近惯性流速
第1行为风速矢量，第2行为东向流速u，第3行为北向流速v，黑色线为浮力频率N最大值所在深度
Fig. 7 Timeseries of wind, near inertial current of u and v at the Transect S1
The first row is the wind speed vector, the second row is the eastward flow velocity u, and the third row is the northward flow velocity v. The black solid line is the depth with maximum buoyancy frequency
图 8 S2断面的近惯性流速
第1行为风速矢量，第2行为东向流速u，第3行为北向流速v，黑色线为浮力频率N最大值所在深度
Fig. 8 Timeseries of wind, near inertial current of u and v at the Transect S2
The first row is the wind speed vector, the second row is the eastward flow velocity u, and the third row is the northward flow velocity v. The black solid line is the depth with maximum buoyancy frequency
图 9 S1和S2断面的风速和近惯性动能的时间变化
Fig. 9 Timeseries of wind speed and near inertial energy of sections S1 and S2
图 10 7月17日至8月31日各站位的平均浮力频率（N）剖面
Fig. 10 The vertical profiles of mean buoyancy frequency (N) from July 17 to August 31
图 11 各模态动能占总近惯性动能的比例
模态0表示正压模态，白线表示浮力频率N最大的位置
Fig. 11 The vertical profiles of percentage of near inertial energy to the total kinetic energy at different stations
Mode 0 represents the barotropic mode. The white lines denote the position of maximum N
图 12 各模态的垂向结构
图例1～4表示第一至第四斜压模态，0表示正压模态
Fig. 12 Vertical structure of each mode
Legends 1 to 4 represent the first to the fourth baroclinic mode, and 0 represents the barotropic mode.
图 13 各模态的特征流速
图例1～4表示第一至第四斜压模态，0表示正压模态
Fig. 13 Characteristic flow speed of each mode
Legends 1 to 4 represent the first to fourth baroclinic modes and 0 represents the barotropic modes
图 15 S1-1站位处的动量平衡分析
从上到下依次为水深0、0.38H、0.68H和0.98H的水层；图中各项意义：acc（加速度项）；cor（科氏力项）；hadv（水平对流项）；prsgrd（压强梯度项）；vvisc（垂向湍流黏性项）
Fig. 15 The time evolution of momentum terms at Station S1-1
from top to bottom the water layers at depths of 0, 0.38H, 0.68H, and 0.98H; acc is the local acceleration, cor is the Coriolis force, hadv is the horizontal advection, prsgrd is the pressure gradient force, and vvisc is the vertical friction
图 16 S1-3站位处的动量平衡分析
从上到下依次为水深0、0.38H、0.68H和0.98H的水层；图中各项意义：acc（加速度项）；cor（科氏力项）；hadv（水平对流项）；prsgrd（压强梯度项）；vvisc（垂向湍流黏性项）
Fig. 16 The time evolution of momentum terms at Station S1-3
from top to bottom the Water layers at depths of 0, 0.38H, 0.68H, and 0.98H; acc is the local acceleration, cor is the Coriolis force, hadv is the horizontal advection, prsgrd is the pressure gradient force, and vvisc is the vertical friction
图 17 S2-1站位处的动量平衡分析
从上到下依次为水深0、0.38H、0.68H和0.98H的水层；图中各项意义：acc（加速度项）；cor（科氏力项）；hadv（水平对流项）；prsgrd（压强梯度项）；vvisc（垂向湍流黏性项）
Fig. 17 The time evolution of momentum terms at Station S2-1
from top to bottom the Water layers at depths of 0, 0.38H, 0.68H, and 0.98H; acc is the local acceleration, cor is the Coriolis force, hadv is the horizontal advection, prsgrd is the pressure gradient force, and vvisc is the vertical friction
图 18 S2-3站位处的动量平衡分析
从上到下依次为水深0、0.38H、0.68H和0.98H的水层；图中各项意义：acc（加速度项）；cor（科氏力项）；hadv（水平对流项）；prsgrd（压强梯度项）；vvisc（垂向湍流黏性项）
Fig. 18 The time evolution of momentum terms at Station S2-3
from top to bottom the Water layers at depths of 0, 0.38H, 0.68H, and 0.98H; acc is the local acceleration, cor is the Coriolis force, hadv is the horizontal advection, prsgrd is the pressure gradient force, and vvisc is the vertical friction
表 1 各站位水层深度
Tab. 1 The depth of surface, middle, bottom layers of each station
站位 表层/m 中层/m 底层/m S1-1 0.05 10.05 25.96 S1-2 0.08 17.40 44.96 S1-3 0.15 32.21 83.21 S1-4 0.25 53.61 138.46 S1-5 0.80 173.96 449.33 S2-1 0.03 6.32 16.33 S2-2 0.07 15.54 40.13 S2-3 0.14 29.62 76.52 S2-4 0.18 38.68 99.90 S2-5 0.59 129.50 334.49 
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表 2 近惯性动能衰减时间尺度（单位：惯性周期，IP）
Tab. 2 The timescale of the decay of near inertial energy(unit: Inertia Period, IP)
S1-1 S1-2 S1-3 S1-4 S1-5 S2-1 S2-2 S2-3 S2-4 S2-5 上层 1.61 1.19 1.04 2.91 2.37 1.69 0.85 3.97 2.26 2.23 下层 1.75 1.20 1.60 2.34 4.58 1.55 1.97 3.05 5.62 2.57
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