Analytic Study on Potential Instability and Spiral Structure of Rain Clusters

This paper presents a study on potential instability and spiral structure of unstable rain clusters. First, we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution. Second, we discuss the potential instability of non-axisymmetrical rain clusters. Finally, we conclude that spiral structures can exist in rain clusters. Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero. Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient. The simpler the vertical structure of perturbation, the thicker the inversion layer; additionally, the smaller the radius of the rain clusters, the larger the unstable growth rate. Simulation results agree well with those from observation and forecast. The spiral structure simulated by our model is similar to a radar echo, suggesting that rain clusters with spiral structures can occur in the atmosphere. In addition, they are generally close to the model solution in this work.