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

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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.