The characteristics of the wave coherent stress and its parameterization under swell condition
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摘要: 动量通量的准确参数化是海洋和大气灾害预报、气候变化的核心问题。涌浪诱导的浪致雷诺(Wave Coherent,WC)应力是引起参数化不确定性的主要问题之一。基于2012年春季南海北部博贺海洋气象观测平台的大气湍流及海浪观测数据,本文使用协谱法提取WC应力。观测显示风向和涌浪方向垂直时,WC应力贡献接近零;当风向和浪向相近或者反向时,WC应力贡献可占总动量通量的20~25%。为刻画WC应力,本文对比了Janssen(1991,J91方案)和Zou等(2024,Z24方案),发现源自剪切不稳定的J91方案给定的WC应力比观测小1−2个量级;而Z24方案与观测吻合较好;对比还显示J91方案给定的WC应力廓线随着高度单调递减,而Z24方案随着高度先增大后减小。两种WC应力参数化对湍流应力的影响反映在风廓线的差异上,J91方案给定的风廓线与基于传统Monin-Obukhov相似理论(Monin-Obukhov Similarity Theory,MOST)一致,而Z24方案的显示涌浪排放能量时,由于WC应力最大值所在位置高度受大气稳定度影响,导致稳定(不稳定)时靠近(远离)海面的风速比J91方案大。本研究还给定了包含WC应力的参数化方案,并与COARE 3.5进行对比,结果显示本研究的参数化方案在风速区间3−7 m/s的相关系数上高于COARE 3.5,而整体样本偏差比COARE 3.5小。
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关键词:
- 涌浪 /
- 浪致雷诺(WC)应力 /
- 动量通量 /
- 剪切不稳定理论
Abstract: Accurate parameterization of the momentum flux plays a decisive role in ocean and atmospheric hazards and climate change. However, the Wave Coherent (WC) stress, as one of the uncertainties factors, modulates the momentum flux severely. In this paper, the WC stress is extracted from the observation obtained from the South China Sea in 2012. The observation shows that the contribution of WC stress to total wind stress relies on the angle difference between wind and wave direction: it approaches zero when the angle difference is 90° and accounts for 20~25% when the angle is ~180°. To describe the WC stress, the scheme of Janssen (J91) and Zou et al. (2024) (Z24) is compared. The result shows that J91 can underestimate the WC stress by about 1~2 orders of magnitude, while Z24 behaves better. The WC stress given by J91 decreases with height, leading to a non-effect on wind profile; while WC stress given by Z24 first increases then decreases, with the height of its maximum being influenced by atmospheric stability, which leads to higher wind speeds near (or away from) the sea surface under stable (or unstable) conditions compared to the J91 scheme when swell exerted upward momentum flux. A new method to parameterize the momentum flux is also given by including the WC stress in this paper; the result shows that it has a high correlation coefficient in the wind speed range of 3–7 m/s and a smaller overall sample bias than the Coupled Ocean-Atmosphere Response Experiment (COARE) 3.5.-
Key words:
- swell wave /
- Wave Coherent (WC) stress /
- momentum flux /
- shear instability
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图 3 顺风向观测高度的WC应力占总应力贡献比(τwavex/τ)随风向、浪向的夹角差的变化示意图(a),以及贡献比随湍流应力、WC应力的夹角差的变化示意图(b),其中(a,b)协谱法
Fig. 3 The contribution ratio of the along-wind WC stress (τwavex/τ) to total stress changing with the angle difference between wind and wave (a), and angle difference between turbulent stress and WC stress (b), where (a, b) are derived from the cospectral method
图 4 侧风向观测高度的WC应力占总应力贡献比(τwavex/τ)随风向、浪向的夹角差的变化示意图(a),以及贡献比随湍流应力、WC应力的夹角差的变化示意图(b),其中(a,b)协谱法
Fig. 4 The contribution ratio of the across-wind WC stress (τwavey/τ) to total stress changing with the angle difference between wind and wave (a), and angle difference between turbulent stress and WC stress (b), where (a, b) are derived from the cospectral method
图 6 顺风向WC应力占总应力贡献比随风向、浪向的夹角差的变化示意图(a),以及贡献比随湍流应力、WC应力的夹角差的变化示意图(b)。(a,b)绿色折线代表Z24方案,由公式(13)给出
Fig. 6 The contribution of along-wind WC stress to total stress computed from the Z24 scheme changing with the angle difference between wind and wave (a), between turbulent stress and WC stress (b). In (a) and (b), the green dashed lines represent the results obtained by the Z24 scheme, while the blue dashed lines denote the observational results
图 7 风速为10 m/s、波龄为1.2时的海浪产生的WC应力。图(a)黑线为海浪谱Swave,菱形为海浪成长率
$ \gamma $ 。图(b)为WC应力廓线。剪切不稳定给定的WC应力在临界层(风速和海浪相速度相等的高度)内为常数,之外为零,因此某个频率的WC应力廓线表现为柱状Fig. 7 The WC stress over the wave spectra (the solid black line in Figure a), here the wave spectra are computed from Donelan et al. by using U10 = 10 m/s and cp/U10 = 1.2. The diamonds are the wave growth rate. Figure b shows the WC profiles computed from shear instability. The WC stress does not change with height within the critical height and becomes zero above the cirtical height
图 9 2012年03月21日07时波龄cp/u* = 74.56的涌浪激发的WC 应力随高度变化。图中
$H = z{\omega _p}$ ,Hmax代表WC应力完全衰减至0的高度。紫实线、黑虚线、红实线和蓝色实线分别为公式(9)、(13)、Cao and Shen大涡模拟[31]和Buckley and Veron[29]实验室结果Fig. 9 The profile of WC stress at 21 07 03 2012, here
$H = z{\omega _p}$ and Hmax is the height where WC stress decay to zero. The purple line, dashed line, red line and blue line are the result from Eqs. (9), (13), Cao and Shen and Buckley and Veron图 10 (a,c,e,g) 涌浪下WC应力(蓝实线)、湍流应力(红实线)、总应力(黑实线)随高度的变化,橙色虚线为有效波高所在高度,棕色虚线为8m观测面;(b,d,f,h) 涌浪下近海面大气风廓线随高度的变化。(b,d,f,h) 红实线代表Z24方案下风廓线、黑虚线代表传统MOST下大气风廓线、绿实线代表基于Miles剪切不稳定的J91方案下风廓线。(a,b) 2012年02月21日23时(case5);(c,d) 2012年02月21日11时(case3);(e,f) 2012年02月20日09时(case5);(g,h) 2012年04月09日06时30分(case3)
Fig. 10 The profile of WC, turbulent stress and total stress changing with height (a,c,e,g). The orange dashed line and brown line represent the significant wave height and observed height. The wind profiles influencd by waves. The red line, black line, green line represent the result from Z24, MOST and J91. Figures a and b correspond to case 5 under stable conditions, Figures c and d correspond to case 3 under stable conditions, Figures e and f correspond to case 5 under unstable conditions, and Figures g and h correspond to case 3 under unstable conditions
表 1 各case的湍流应力、WC应力的方向分布
Tab. 1 The directional distribution of τturb and τwave for different cases
τturbx τturby τwavex τwavey case 1 > 0 > 0 < 0 < 0 case 2 > 0 < 0 < 0 < 0 case 3 > 0 > 0 > 0 > 0 case 4 > 0 < 0 > 0 > 0 case 5 > 0 > 0 < 0 > 0 case 6 > 0 < 0 < 0 > 0 注:大气极端稳定情形下的case4后续不在本文予以讨论 -
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