Asymptotic models have provided valuable insight into the atmosphere and its dynamics. Nevertheless, one shortcoming of the classic asymptotic models, such as the quasi-geostrophic (QG) equations, is that they describe a “dry” atmosphere and do not account for water vapor, clouds, and rainfall. Recently, precipitating QG (PQG) equations were derived in an asymptotic limit, starting from atmospheric equations that include changes of water between different phases (vapor, liquid, etc.). The PQG equations include Heaviside nonlinearities due to phase changes, which can potentially have a significant influence on QG turbulence. Here, simple numerical methods are presented for the PQG equations, accounting for the Heaviside nonlinearities, and an initial set of numerical experiments is conducted to probe the behavior of PQG turbulence. A two-vertical-level setup is used for an idealized vertical structure, as in the classic Phillips model. Due to phase changes and rainfall, the mid-latitude jet variability displays a variety of behaviors, including poleward propagation of the latitude of the jet. The simulations suggest a new set of phenomena that arise in QG turbulence due to phase changes, in a simplified model that is potentially amenable to mathematical analysis.

渐近模型为大气及其动力学提供了宝贵的见识。但是，经典渐近模型（如准地转方程）的一个缺点是它们描述的是“干燥”大气，没有考虑水汽，云层和降雨。最近，从大气方程开始，在渐近极限中得出了沉淀QG（PQG）方程，该方程包括水在不同相（蒸气，液体等）之间的变化。PQG方程包含由于相变而引起的Heaviside非线性，这可能会对QG湍流产生重大影响。在这里，给出了用于PQG方程的简单数值方法，考虑了Heaviside非线性，并进行了一组初始数值实验以探究PQG湍流的行为。与经典的Phillips模型一样，两层垂直设置用于理想化的垂直结构。由于相位变化和降雨，中纬度射流的变异性表现出多种行为，包括射流纬度的极向传播。这些模拟在简化的模型中提出了一组新的现象，这些现象在QG湍流中由于相变而产生，该模型很容易进行数学分析。