Analytical solution for two-dimensional thermal plume updraft velocity is obtained under the assumption of a uniform temperature excess inside the plume. In this way, the thermal plume motion is modeled in both mixed layer and entrainment zone. Also, a semi-analytical solution is obtained using an empirical model for the plume temperature excess in the mixed layer. In addition, an analytical model for entrainment zone thickness is obtained by computing the overshoot distance of the modeled plumes, and a semi-analytical model by using the empirical model for plume temperature. By using a nonlinear profile for the lapse rate in the surface layer based on the Monin–Obukhov similarity theory, our model predicts that the characteristics of the surface layer plays an important role in the structure of the entrainment zone. Finally, our solutions for plume velocity allow us to consider the effect of the lateral entrainment on the plume excess temperature and velocity in the convective boundary layer. It is shown that the lateral entrainment has an important role on the plume dynamics and the solutions in the zero entrainment limit offer large overestimated values for the plume velocity, which also result in overestimated values of the entrainment zone thickness.

二维热羽上升速度的解析解是在羽内部均匀温度过量的假设下获得的。这样，就可以在混合层和夹带区域对热羽运动进行建模。同样，使用经验模型获得混合层中羽流温度过高的半解析解。另外，通过计算模型羽的过冲距离获得了夹带区厚度的解析模型，并通过使用羽温度的经验模型获得了半解析模型。通过基于莫宁-奥布霍夫相似性理论，通过对表层的消失速率使用非线性分布，我们的模型预测表层的特征在夹带区域的结构中起着重要作用。最后，我们对羽流速度的解决方案使我们能够考虑横向夹带对对流边界层中羽流过高温度和速度的影响。结果表明，横向夹带对羽流动力学具有重要作用，零夹带极限中的解提供了较大的羽流速度高估值，这也导致了夹带区厚度的高估值。