Journal of Tropical Oceanography >
An application of nonlinear stream function in analysis of experimental wind-wave field
Received date: 2018-04-11
Request revised date: 2018-06-22
Online published: 2019-01-16
Supported by
National Natural Science Foundation of China (51239001)
Copyright
The wind on the water surface can create wind waves. The exchange mechanism of momentum and energy due to the turbulence of wave current is a complicated process. Wind stress is generally used to describe this energy exchange, and can be divided into three components: shear stress, wave induced stress and turbulent stress. An effective nonlinear wave current separation method, namely, the Nonlinear Stream Function Method (NSFM), is used to qualitatively describe the momentum and energy transports between wave and current. An analytical stream function is constructed, which can effectively express nonlinear waves and satisfies the Laplace equation, the boundary condition and the kinematic boundary condition of the water surface, separating the wave-induced velocity field based on the laboratory wind-wave data. Through the cross-spectral technique, the contribution of wave-induced Reynolds stress to wind stress at different wind speed is obtained. The results are as follows. NSFM has higher accuracy and better applicability in treating wind waves under different working conditions. With the increase of wind speed, wave-induced stress decays faster along water depth, and the ratio of wave-induced stress at the free surface to the momentum transport mechanism should be gradually weakened.
Key words: wind wave; wave-current separation; stream function
JIANG Changbo , YANG Yang , TANG Hansong . An application of nonlinear stream function in analysis of experimental wind-wave field[J]. Journal of Tropical Oceanography, 2019 , 38(1) : 19 -26 . DOI: 10.11978/2018039
Tab. 1 Description of experimental data表1 实验数据统计描述 |
序号 | P/Hz | U∞/(m·s-1) | U*/(m·s-1) | H1/3/cm | Hrms/cm | Have/cm | T/s | Tf/s | N | Ac-rms/cm | At-rms/cm |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 10 | 3.4 | 0.134 | 0.83 | 0.65 | 0.62 | 0.26 | 1.5 | 17 | 0.41 | 0.26 |
2 | 15 | 6.1 | 0.363 | 1.80 | 1.42 | 1.32 | 0.30 | 1.5 | 17 | 0.78 | 0.55 |
3 | 20 | 7.8 | 0.506 | 2.33 | 1.73 | 1.61 | 0.36 | 1.5 | 17 | 0.94 | 0.81 |
4 | 25 | 10.1 | 0.762 | 3.66 | 2.69 | 2.47 | 0.43 | 2 | 23 | 1.55 | 1.16 |
5 | 30 | 12.2 | 0.940 | 4.04 | 3.04 | 2.83 | 0.47 | 2 | 23 | 1.89 | 1.78 |
6 | 35 | 14.6 | 1.239 | 6.47 | 4.95 | 4.68 | 0.54 | 3 | 35 | 2.74 | 2.56 |
注: P—风机功率; U∞—远场风速; U*—摩阻风速; H1/3—有效波高; Hrms—均方波高; Have—平均波高; Ac-rms—均方波峰; At-rms—均方波谷; Tf—样本数据时间长度。 |
Fig. 1 Sample of free surface elevation: a) 10 Hz, b) 20 Hz and c) 30 Hz图1 自由面高程样本片段a. 10Hz; b. 20Hz; c. 30Hz |
Fig. 2 Comparison of predicted waveforms by NSFM method with experimental data: a) 10 Hz, b) 20 Hz and c) 30 Hz图2 NSFM方法预测的波形与实验数据的比对a. 10Hz; b. 20Hz; c. 30Hz |
Tab. 2 Boundary condition error表2 边界条件误差 |
动力边界条件 | 运动边界条件 | |
---|---|---|
全局误差 | \({{E}_{1}}=\frac{1}{k}\sum\limits_{n=1}{k}{{{({{Q}_{\text{k}}}-\overset{\_}{\mathop{Q}}\,)}{2}}}\) | \({{E}_{2}}=\frac{1}{k}\sum\limits_{n=1}{k}{{{({{\eta }_{\text{pk}}}-{{\eta }_{\text{mk}}})}{\text{2}}}}\) |
局部误差 | \({{\delta }_{\text{1}}}\text{=}{{Q}_{\text{k}}}-\bar{Q}\) | \({{\delta }_{\text{2}}}={{\eta }_{\text{pk}}}-{{\eta }_{\text{mk}}}\) |
Fig. 3 Local errors of dynamic (a) and kinematic (b) boundary conditions图3 动力边界条件(a)和运动边界条件(b)的局部误差 |
Fig. 4 Wave-induced velocity field: a) 10 Hz, b) 20 Hz and c) 30 Hz图4 波生速度场a) 10Hz; b) 20Hz; c) 30Hz |
Fig. 5 Moment statistics of wave-induced velocity: a) skewness moment and b) kurtosis moment图5 波生速度的矩统计a. 偏度矩; b. 峰度矩 |
Fig. 6 Cross spectral analysis. a) 10 Hz, b) 20 Hz and c) 30 Hz图6 交叉谱分析a. 10Hz; b. 20Hz; c. 30Hz |
Fig. 7 Variation of \({{U}_{\text{w}}}{{V}_{\text{w}}}\text{/}u_{\text{w}*}{2}\) with water depth: a) 10 Hz, b) 20 Hz and c) 30 Hz图7 \({{U}_{\text{w}}}{{V}_{\text{w}}}\text{/}u_{\text{w}*}{2}\)随水深的变化a. 10Hz; b. 20Hz; c. 30Hz |
Fig. 8 Variation of \({{U}_{\text{w}}}{{V}_{\text{w}}}\text{/}u_{\text{w}*}{2}\) with wind speed at air-water interface图8 \({{U}_{\text{w}}}{{V}_{\text{w}}}\text{/}u_{\text{w}*}{2}\)在自由面附近与风速的关系 |
The authors have declared that no competing interests exist.
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