Buoyant turbulent plumes are often categorized by their geometry and described as either round plumes, issuing from a point source, or line/planar plumes, issuing from an elongated source. As line plumes rise above their source they get thicker (normal to the source axis) and, far from the source, they will no longer be planar but more resemble a round plume. However, the vast majority of experimental measurements of line plumes focus on the near source region, where they are still planar and the flow is two-dimensional. Further, these experiments constrain the ends of the plume with barriers to prevent entrainment through the ends of the plume and maintain a two-dimensional flow. Herein, results are presented from a series of experiments that were conducted to measure the transition of an unconstrained line plume into a round plume. A model is presented that allows the calculation of the entrainment into a plume of arbitrary cross sectional shape in terms of the hydraulic radius of the plume defined as the cross-sectional area divided by the perimeter over which entrainment is occurring. This formulation, along with a smooth transition function that changes both the geometry and entrainment coefficient, is used to make predictions of the front position over time for a line plume in a filling box. The model was run for different values of the nozzle width to box height ratio. Results of the model were compared to the experimental front position measurements and show that an unconstrained line plume will transition to a round plume at a height equal to approximately three times the source width. This is consistent with the idea that the line plume will transition when its thickness is similar in magnitude to its nozzle width.

浮力湍流羽流通常按其几何形状分类，并被描述为从点源发出的圆形羽流，或从细长源发出的线/平面羽流。随着线羽上升到其源上方，它们变得更厚（垂直于源轴），并且远离源，它们将不再是平面的，而是更像圆形羽流。然而，绝大多数线羽的实验测量集中在近源区域，在那里它们仍然是平面的并且流动是二维的。此外，这些实验用屏障限制羽流的末端，以防止夹带通过羽流的末端并保持二维流动。在此，展示了一系列实验的结果，这些实验旨在测量不受约束的线羽流向圆形羽流的转变。提出了一个模型，该模型允许根据羽流的水力半径计算任意横截面形状的羽流中的夹带，该半径定义为横截面积除以发生夹带的周长。该公式与改变几何形状和夹带系数的平滑过渡函数一起用于预测填充箱中线羽的前沿位置随时间的变化。该模型针对喷嘴宽度与箱高比的不同值运行。该模型的结果与实验前沿位置测量结果进行了比较，结果表明不受约束的线羽将在高度等于源宽度的三倍时转变为圆形羽。