ARW的方程集是完全可压缩的，欧拉和非静水…

还有另一组模型默认使用流体静力求解器(例如ECMWF)，并大概对地球大气做出以下假设。流体静力平衡描述了一种大气状态，在这种状态下，向上导向的压力梯度力(压力随高度而减小)与向下导向的地球引力平衡。平均而言，地球的大气总是接近流体静力平衡。< / p >

My question is what are the applications of each type of solver, i.e. when would you chose to use a non-hydrostatic model over a hydrostatic one? (which is presumably less computationally expensive?)

$$\dfrac{\partial p}{\partial z} = -\rho g$$

这是垂直压力梯度力和重力之间的平衡，没有净加速度。这往往适用于宽于高的大气现象。在天气尺度上，垂直运动的量级为1厘米^{-1}美元，这是成立的，但在雷暴中，上升气流的速度可以达到100米^{-1}美元，这种近似不成立。水静力模型使用水静力近似来代替$w$的方程，而非水静力模型使用动量方程来代替$w$。正如你所链接到的ECMWF页面所建议的那样，低网格分辨率的模型可以使用流体静力近似。一个dx=dy=10 km的模型意味着网格体积为100 km$^{2}$乘以垂直网格间距。网格框的$w$值需要代表整个体积，并且您不会在这个分辨率下显式地解析对流(对流将被参数化，通常模型只能解析比网格间距大4倍的特征)。

当您减小网格间距(提高分辨率)并开始解决非静力流体特征(雷暴上升气流、下降气流等)时，您需要确保使用的是非静力流体求解器。对于使用WRF-NMM, WRF-ARW, CM1, ARPS的中尺度高分辨率操作区域建模和研究建模，你会发现非流体静力求解器。非流体静力解算器比流体静力解算器的计算成本更高，并且通常在高分辨率模型中发现，这些模型本身比粗网格的计算成本更高。< / p >

In this simulation there are two fluids with different densities initially separated by a vertical imaginary gate (lock) at the center of the domain which is "removed" when the simulation begins. The heavier (colder) fluid is on the right and moves to the left under the lighter (warmer) fluid.

Because the hydrostatic simulation does not use the momentum equation in the vertical direction, it is not able to capture features for which the horizontal and vertical length scales are on the same order of magnitude. In this example, despite the resolution being the same between (a) and (b), only the non-hydrostatic code is able to capture the Kelvin-Helmholtz billows. However, the hydrostatic code can also be valuable. In this case, it is 8 times faster and it captures the large scale features of the flow such as the bore speed and interface thickness.