The merging of a single row of plumes in a quiescent environment has been studied using irrotational flow theory (Rooney 2015, {J. Fluid Mech.}, vol.~771, R1). The present study extends this theory by considering (i) two parallel rows of plumes in a quiescent environment, and, (ii) a single row of plumes in a crosswind, with and without a pressure drag term. For plumes in two rows with and without offset, the effect of varying the spacing ratio on the plume dynamics is investigated. Two definitions of the contact height are suggested according to the shape of the velocity potential contours. For a single row of plumes in a crosswind, the governing equations are closed using an entrainment flux evaluated by the irrotational flow theory. This novel theory predicts the correct near- and far-field similarity solutions in both modest and strong crosswinds. A comparison of the theory in question to previous towing tank experiments yields satisfactory agreement in terms of plume trajectory. The present theory of single and dual rows of plumes is applied to long rows of cooling tower plumes.

中文翻译：

---

长排羽流的合并：侧风，多排羽流和应用于冷却塔

已使用非旋流理论研究了静态环境中单排羽流的合并（Rooney 2015，{J。Fluid Mech。}，第〜771卷，R1）。本研究通过考虑（i）静态环境中的两行平行羽状流，以及（ii）带有或不带有压力阻力项的侧风中的单行羽状体来扩展该理论。对于具有和不具有偏移的两行羽流，研究了改变间距比对羽流动力学的影响。根据速度势轮廓的形状，提出了两种接触高度的定义。对于侧风中的单排羽流，使用由非旋流理论评估的夹带通量来封闭控制方程。这个新颖的理论预测了在适度和强侧风中正确的近场和远场相似性解决方案。将该理论与先前的拖曳罐实验进行比较，就羽流轨迹而言获得了令人满意的一致性。当前的单排和双排羽流理论适用于长排的冷却塔羽流。