Thispaperpresentsastudyonpotentialinstabilityandspiralstructureofunstablerainclusters.First,wedevelopalinearizednon-axisymmetricalmathematicmodelforrainclustersincircularcylindricalcoordinatesandacquireitsanalyticsolution.Second,wediscussthepotentialinstabilityofnon-axisymmetricalrainclusters.Finally,weconcludethatspiralstructurescanexistinrainclusters.Ouranalysisindicatesthatpotentialinstabilityoccurswhenhumidstratificationcoefficientislessthanzero.Unstablegrowthrateincreaseswiththeincreaseoftheabsolutevalueforhumidstratificationcoefficient.Thesimplertheverticalstructureofperturbation,thethickertheinversionlayer;additionally,thesmallertheradiusoftherainclusters,thelargertheunstablegrowthrate.Simulationresultsagreewellwiththosefromobservationandforecast.Thespiralstructuresimulatedbyourmodelissimilartoaradarecho,suggestingthatrainclusterswithspiralstructurescanoccurintheatmosphere.Inaddition,theyaregenerallyclosetothemodelsolutioninthiswork.
