A study of Richardson number and instability in moist saturated flow
湿饱和流中的Richardson数和不稳定的研究

We have derived the Ri equations in dry and moist saturated flow in the atmosphere. A rainfall case which occurred in Northern China is numerically simulated, and the model output data is used to calculate and analyze comparatively the terms of Ri equations in dry air and moist saturated flow. The analysis shows that the vertical shear of horizontal velocity dominates the influence on Ri change and instability in dry process, whereas in the moist case, the influence of numerator of Ri (i.e., Brunt-Vaisala frequency, named BVF) on Ri change and instability can reach up to the same magnitude order as the denominator of Ri. Since BVF has very important influence on instability in the moist case, we have looked for the expression of BVF which is more appropriate for the real moist case. Thus Ri is modified, so that we can estimate instability in the moist process. It is found that, due to considering the virtual temperature effect and the change of total water mixing ratio (i.e., part liquid water is dropped out the parcel), the stability in the rainy region is effectively decreased. Therefore, the modified moist Ri formula may be more appropriate to diagnose the instability in rainy regions.