Abstract: A non-linear and non-hydrostatic two-dimensional numerical model is used to study the development,evolution and structure of meso-mode transversal instability.The numerical test states that development and evolution of transverse instability are affected by Ri number.The smaller Ri is,the larger it s incresing rate and the shorter its wave length with the largest incresing rate is.The initial growing of the transverse instability perturbations canbe fairly well approximated by lineartheory.With increase of the perturbations,non-linear interaction of advection termenhances,and its sturctrues has great change,at last clock-wise circulations dominate in the disturbance structures.