Numerical investigation on the turbulent structures in the bottom boundary layers under the effects of waves
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摘要: 本文基于
$ k $ -$ \varepsilon $ 模型研究了波流边界层内湍流结构特征。研究结果表明，时均流速分布数值解与实验结果高度吻合。一个波周期内湍流结构特征（如：涡量、湍动能、湍动能耗散率等）呈周期性变化规律，波浪作用引起涡量、湍动能及湍动能耗散率均在减速阶段减小，在波谷处达到最低值，而后在加速阶段增大，并在波峰处达到最大值。近壁面处湍流结构变化幅值较大（湍动能耗散率变化可达53%），远离壁面处变化幅值较平均值较小（仅3%）。波流边界层厚度在减速阶段增加，在加速阶段减小。本文所建立的数值模型克服了现有模型因采用“高雷诺数方法”引起的近壁区精度不高问题，可较好地描述波浪作用下湍流结构演变过程的物理机制，为河口海岸地区泥沙运动、岸滩演变及海洋可再生能源的开发利用提供一些指导意义。Abstract: This paper investigates the characteristics of turbulent structures in combined wave-current boundary layers based on the standard$ k $ -$ \varepsilon $ model. Good agreements were found between the numerical results and experimental data of the time-averaged mean velocity profiles. Periodic variations of turbulence parameters within a wave cycle (i.e. vorticity magnitudes, TKE and TKE dissipation rates etc.) were observed. The vorticity magnitudes, TKE and TKE dissipation rates all decrease during the deceleration phase, reach their minimum values during the wave trough, increase during the acceleration phase and reach their maximum values during the wave crest. The variations of turbulent structures are very high in the near-wall regions (53% for TKE dissipation rates), and are quite low in the outer regions (3% for TKE dissipation rates). The wave-current boundary layer thickness increases (decreases) during the deceleration phase (acceleration phase). The model developed in this study has solved the existing issue of low accuracy in the near-bed region by previous models based on the “high Reynolds number methods”. The present model performs well in describing the physical process of turbulence variations under the effects of wave-current interaction. This can provide some guidance for the sediment transport in coastal areas, beach erosion prediction and developments of marine renewable energy.-
Key words:
- wave-current interaction /
- bottom boundary layer /
- turbulence /
- CFD /
- k-ε model
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图 2 波浪底摩擦系数与粗糙系数变化关系
Fig. 2 Friction factors versus the roughness in wave bottom boundary layers
图 3 波流同向作用下时均流速剖面图，WCA1，时均流速0.185 m/s
a. 线性坐标；b. 半对数坐标
Fig. 3 Time-averaged mean velocity profiles in combined wave-current flows, WCA1，mean velocity of 0.185 m/s
a. Linear axis；b. semi-log scale
图 4 WCA1工况下底部边界层内波致流速
数值结果用实线表示；实验结果通过点表示
Fig. 4 Wave-induced velocity profiles in the bottom boundary layers of WCA1
Lines for the numerical results; dots for the experimental results
图 5 WCA1工况下全水深范围内相位平均流速分布（18°时间间隔）
Fig. 5 Phase-averaged mean velocity profiles in the whole water column (18° time intervals) of WCA1
图 6 自由液面（a）及底部剪应力时间序列（b），
$ {d} $ = 200 mm,$ {T} $ = 1 s,$ {H} $ = 0.02 m,$ {U} $ = 0.185 m/sFig. 6 Free surface elevations (a) and the time series of the bed shear stress (b),
$ {d} $ = 200 mm,$ {T} $ = 1 s,$ {H} $ = 0.02 m,$ {U} $ = 0.185 m/s
图 7 时间、空间分辨率对时均流速剖面计算结果影响，WCA1测试
a. 网格敏感性测试，时间步长为0.001 s，网格分别为50 000和200 000；b. 时间步长敏感性测试，网格为50 000，时间步长分别为0.005 s和0.001 s
Fig. 7 Sensitivity tests of the temporal and spatial resolution for the mean velocity profiles, WCA1
a. Meshing tests, time step of 0.001 s, meshing of 50 000和200 000；b. time step tests，meshing of 50 000，time steps of 0.005 s and 0.001 s
图 8 WCA1工况下不同相位时期涡度大小分布
a. 减速阶段全水深范围内涡度分布；b. 减速阶段近壁处涡度分布；c. 加速阶段全水深范围内涡度分布；d. 加速阶段近壁处涡度分布
Fig. 8 Vorticity distributions at different phases of WCA1
a. Vorticity distributions during deceleration phases in the whole water column; b. vorticity distributions during deceleration phases near the wall; c. vorticity distributions during acceleration phases in the whole water column; d. vorticity distributions during acceleration phases near the wall
纯流工况CA 波流工况WCA1 摩阻流速 $ {u}_{*} $ /（mm·s−1） 8.66 8.89 底摩擦力 $ {\tau }_{{\mathrm{b}}} $ /（$ {{10}^{-3}} $ Pa） 75.0 79.1 边界层动量厚度 $ \theta $/mm 11.6 8.1 外层流速 $ \overline{u}_{{\infty }} $ /（mm·s−1） 205 196 黏度系数${\nu } $ /（mm·s−2） 1.16 1.02 雷诺数$ {Re}_{\theta }=\;\overline{u}_{{\infty }}\theta /{\nu } $ 2 060 1 550 
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