中文摘要：

本文通过室内水槽试验,形成一个自由表面立轴漩涡,并采用对流场无干扰的二维粒子图像测速技术（PIV）对自由表面漩涡的流速场进行了测量,获得了立轴漩涡的切向速度分布、环量分布及水面线数据。另外在试验数据的基础上,通过理论分析建立了描述漩涡水力特性的数学模型,包括切向速度以及漩涡水面线的分布方程。经过与前人的数学模型对比显示,本文提出的模型与试验结果拟合更好,切向速度最大值为in m0.716Γ2πr与试验数据相符,另外公式的变化趋势与实测数据相同且光滑连续。本文的研究结果可以为解决实际工程中的漩涡问题,以及更深入的研究提供数据和理论依据。

英文摘要：

In this study, a flume experiment was conducted on free surface air-core vortices and the data was measured using Particle Image Velocimetry（PIV）. Tangential velocity distributions, circulation distributions and water surface profiles of the vortices have been obtained. Based on these experimental data and theoretical analysis, we developed a mathematical model that describes the vortex characteristics including the equations for tangential velocity distributions and water surface profiles. Comparison with previous mathematical models shows that our model agrees with the experimental data better, and it gives a maximum tangential velocity of in m0.716 Γ 2πr that is close to the measurements. The formulae presented in this paper can predict the same tendency of smooth and continuous variations as shown by our measurements. The results would help solve the vortex problems in the research and engineering application of hydraulic intakes.