Observations of turbulent mixing in the Bohai Sea during weakly stratified period
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摘要: 利用2017年9月在渤海共享航次中取得的湍流混合直接观测数据，本文研究了渤海海域湍流混合的空间分布特征及有关的影响因素。9月观测海区水体垂向层结较弱，莱州湾受黄河冲淡水影响出现高温低盐结构，位于渤海中央浅滩南北两侧洼地的双中心冷水结构依旧存在。湍流观测结果表明湍动能耗散率在10−9～10−5 W/kg之间变化，统计上满足对数正态分布。耗散率强值区出现在辽东湾及渤海湾湾口近岸处，相应的垂向湍扩散系数约为10−6～10−2 m2/s。垂向上，水体表、底层混合较强，进一步研究发现弱层化水体的平均湍动能耗散率〈ε〉与风速和正压潮流速的大小存在正相关关系。另一方面，耗散率ε与浮性频率N近似满足
$\varepsilon = 2.0 \times {10^{ - 8}} + 3.0 \times {10^{ - 7}}{({N^2}/N_0^2)^{ - 5}}$ 的拟合函数关系，反映了层化对水体垂向混合的抑制作用。Abstract: Based on the direct turbulence observations in the Bohai Sea during September 2017, this study investigates the spatial distribution of turbulent mixing in the Bohai Sea and the associated influencing factors. The water column was weakly stratified during the observation period. As influenced by the freshwater input from Yellow River, relatively warm and fresh water was found in the Laizhou Bay. The typical south-north dual-core cold bottom water structure still exited in the central Bohai Sea during the observation period. The observed turbulent kinetic energy (TKE) dissipation rate ε ranged from 10−9 to 10−5 W/kg and statistically satisfied the lognormal distribution. Intensified mixing was found at the nearshore region of the Liaodong Bay and the Bohai Bay. The corresponding vertical eddy diffusivity was about 10−6～10−2 m2/s. In the vertical direct direction, strong mixing occurred near the sea surface and bottom layers. Further analysis shows that the station-averaged TKE dissipation rate are positively related to the wind speed and barotropic tidal velocity. On the other hand, the dissipation rate and buoyancy frequency N satisfied the power function relationship of$\varepsilon = 2.0 \times {10^{ - 8}} + 3.0 \times {10^{ - 7}}{({N^2}/N_0^2)^{ - 5}}$ indicating that inhibition effect of stratification on turbulent mixing. -
图 1 渤海观测站位分布
红色圆圈为同时包含VMP与CTD观测的站位，绿色方块为只进行CTD观测的站位，背景颜色代表水深，根据前人研究[20]，用虚线框将中央海盆与莱州湾、渤海湾以及辽东湾区别开来
Fig. 1 Distribution of observation stations in the Bohai Sea
Location of the stations that have both VMP and CTD measurements are denoted by the red circles. Other stations with only CTD measurements are denoted by green squares. Consistent with the previous study[20], the dashed lines separate the Laizhou Bay, Bohai Bay, Liaodong Bay from the central region
图 2 B54站位原始剪切剖面（a）；不同深度范围的实测剪切波数谱（蓝色虚线）与对应的理论Nasmyth谱（红色虚线），红色三角表示剪切谱的积分上限（b～e）；耗散率
$\varepsilon $ （橘黄实线）与位势密度${\sigma _\theta }$ （灰线）剖面（f）Fig. 2 The profile of the raw shear at Station B54 (a); the shear spectra at wavenumber space (blue dashed lines) and the corresponding Nasmyth spectra (red dotted lines) calculated within different depth ranges, the red triangles indicate the upper limits of integration (b−e); the profiles of the calculated dissipation rate
$\varepsilon $ (orange line) and potential density${\sigma _\theta }$ (gray line) (f)
图 3 温度（a）、盐度（b）、位势密度（c）以及浮性频率平方N2（d）三维空间分布
Fig. 3 Spatial distribution of temperature (a), salinity(b), potential density (c) and squared buoyancy frequency N2 (d) in a 3D view
图 4 湍动能耗散率
$\varepsilon $ （a）和垂向湍扩散系数${K_\rho }$ （b）空间分布Fig. 4 Spatial distribution of turbulent kinetic energy dissipation rate
$\varepsilon $ (a) and vertical eddy diffusivity${K_\rho }$ (b) in a 3D view
图 5 从左列至右列分别代表断面位置、浮性频率平方（N2）、流速剪切平方（S2）、湍动能耗散率（
$\varepsilon $ ）（黑线：等温线）以及垂向湍扩散系数（${K_\rho }$ ）（灰线：等密线）的断面分布Fig. 5 From left to right are locations of the transects, cross-sectional distributions of squared buoyancy frequency N2, squared shear S2, TKE dissipation rate
$\varepsilon $ (black contours：isotherms) and vertical eddy diffusivity${K_\rho }$ (gray contours: isopycnals)
图 6 对数湍动能耗散率（
${\log _{10}}\varepsilon $ ）（a）与对数湍扩散系数（${\log _{10}}{K_\rho }$ ）（b）累积概率（CDF）分布红色点划线为对应的对数正态分布，黑色虚线对应对数正态分布模型的中位数
Fig. 6 The cumulative distribution functions (CDF) of
${\log _{10}}\varepsilon $ (a) and${\log _{10}}{K_\rho }$ (b)Red dot dash line is lognormal distribution，black dash lines denote the medians of the corresponding lognormal distribution
图 7 各站位平均耗散率的对数
${\log _{10}} $ 〈ε〉与海面以上10 m处风速（黑色三角）（a）和OTIS模型得到的正压潮流速（黑色实心圆）（b）的对应关系黑色实线表示最小二乘法线性拟合
Fig. 7 Station-averaged dissipation
${\log _{10}} $ 〈ε〉 versus the averaged wind speed at 10 m height during the observation period (black filled triangles) (a) and the barotropic current speed from OTIS (black filled circles) (b)The black solid lines represent the best linear least squares fit
图 8 湍动能耗散率
$\varepsilon $ 与1 m平均的归一化浮性频率平方N2（a）与2 m分辨率的归一化剪切平方S2（b）的散点分布（灰色圆点）灰色圆点为散点分布，黑点为网格中位数结果，最小二乘拟合直线用黑色实线表示，阴影表示95%置信区间
Fig. 8 The turbulent kinetic energy dissipation rate
$\varepsilon $ versus the normalized squared buoyancy frequency N2 (averaged into 1 m) (a) and the normalized squared shear S2 (averaged into 2 m) (b)The gray and black dots represent the raw and bin-median data, respectively. The best fitted lines are shown by dark solid lines with the 95% confidence intervals indicated by the gray shading
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