Interaction between open-channel flow and the wind over the surface

为了研究二次流及其对一次流的影响，在长径比为1阶的两个风浪槽垂直截面上系统地测量了平均流的垂直和水平剖面。众所周知，在风浪储罐中，逆压梯度由表面的风应力来平衡。然而，在本研究中，我们发现逆压梯度也产生了由一对Langmuir涡组成的二次流。此外，我们发现沿展向形成了二维泊泽维尔流，即中心方向的迎风电流最小，侧壁方向的电流最大。通过引入与朗缪尔涡流相关的涡流粘度，而不是水的粘度，从动量方程推导出二维泊泽维尔流，其中涡流粘度由水在表面的摩擦速度和水箱跨度长度的乘积给出。因此，我们建议将风浪槽内的动量平衡方程进行推广，使压力梯度由风应力项和与朗缪尔涡相关的涡流粘度项的总和来平衡。另一个有趣的发现是，在两个水槽中，一个大水槽的纵横比为1.25，一个小水槽的纵横比为0.75，它们之间的横向平均垂直水流剖面是系统地不同的。我们解释了为什么在两个风浪槽中可能有明显不同的垂直剖面，从实验事实来看，与朗缪尔涡旋相关的垂直尺度和电流强度强烈地依赖于水槽的长径比和跨度长度。

Vertical and horizontal profiles of mean currents were measured systematically in vertical cross-sections of two wind-wave tanks with aspect ratio of order one to study the secondary flow and its effect on the primary flow. As is well known, in a wind-wave tank the adverse pressure gradient is balanced by the wind stress on the surface. In the present study, however, we found that the adverse pressure gradient also generated the secondary flow which consisted of a pair of Langmuir vortices. Furthermore, we found that a two-dimensional Poiseuille flow formed in the spanwise direction, that is, the minimum windward current at the center and the maximum current along the side-walls. Instead of the viscosity of water, this two-dimensional Poiseuille flow is derived from the momentum equation by introducing the eddy viscosity associated with the Langmuir vortices, where the eddy viscosity is given by the product of the friction velocity of water at the surface and the span length of the tank. Thus, we propose that the momentum balance equation in a wind-wave tank is extended in such a way that the pressure gradient is balanced by the sum of the wind stress term and the eddy viscosity term associated with the Langmuir vortices.Another interesting finding in the two tanks, which consist of a large tank with an aspect ratio of 1.25 and a small tank with 0.75, is that the lateral mean vertical current profiles were systematically different between them each other. We account for the reason why markedly different vertical profiles are possible in two wind-wave tanks, from the experimental fact that the vertical scale and current strength associated with the Langmuir vortices depend strongly on both the aspect ratio and span length of the tanks.