Boundary layer formulations in orthogonal curvilinear coordinates for flow over wind-generated surface waves
Boundary layer formulations in orthogonal curvilinear coordinates for flow over wind-generated surface waves
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DOI：
10.1017/jfm.2020.32
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发表时间：
2020-02
影响因子：
3.7
通讯作者：
K. Yousefi;F. Veron
中科院分区：
文献类型：
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作者：
K. Yousefi;F. Veron
在表面跟随坐标系中流体流动的控制方程的发展对于研究由传播波变形的界面附近的流体流动是必不可少的。本文在与表面水波相关的正交曲线坐标系中推导了流体流动的控制方程，包括质量守恒、动量守恒和能量平衡。将所有方程进一步分解，提取平均分量、波浪分量和湍流分量。完整的变换方程包含了显式的额外几何项。例如，湍流应力和生产项包括坐标曲率对流体流动结构的影响。此外，通过考虑周期准线性表面波上的流动，进一步简化了运动控制方程，其中扰动的波长比波幅大。采用拟线性分析方法，用平均场、波动场和湍流场的分解方程来表示正交随波曲线坐标系下的边界层方程。最后，在正交曲线坐标系下推导了涡度方程，以表达相应的速度涡度表达式。本文所建立的方程可用于分析和解释风表面波上流体流动的实验数据。实验结果在另一篇论文中给出。
The development of the governing equations for fluid flow in a surface-following coordinate system is essential to investigate the fluid flow near an interface deformed by propagating waves. In this paper, the governing equations of fluid flow, including conservation of mass, momentum and energy balance, are derived in an orthogonal curvilinear coordinate system relevant to surface water waves. All equations are further decomposed to extract mean, wave-induced and turbulent components. The complete transformed equations include explicit extra geometric terms. For example, turbulent stress and production terms include the effects of coordinate curvature on the structure of fluid flow. Furthermore, the governing equations of motion were further simplified by considering the flow over periodic quasi-linear surface waves wherein the wavelength of the disturbance is large compared to the wave amplitude. The quasi-linear analysis is employed to express the boundary layer equations in the orthogonal wave-following curvilinear coordinates with the corresponding decomposed equations for the mean, wave and turbulent fields. Finally, the vorticity equations are also derived in the orthogonal curvilinear coordinates in order to express the corresponding velocity–vorticity formulations. The equations developed in this paper proved to be useful in the analysis and interpretation of experimental data of fluid flow over wind-generated surface waves. Experimental results are presented in a companion paper.