中文摘要：

球形的晶体成长在上的对流流动的效果在下面冷却与中等的远地流动融化被学习。球形的晶体成长的接口的进化的 asymptotic 答案被匹配的 asymptotic 扩大方法获得。分析结果表演对流流动在在下面冷却融化在球形的晶体成长的进化上有强壮的效果。远地流动导致的对流流动使成长的接口成为球形的水晶在远地流动的在上游的方向提高它的生长速度并且在下游的方向禁止生长，并且腐烂的接口球形的水晶进一步在在上游的方向腐烂并且在下游的方向禁止腐烂。远领域流动影响的球形的水晶的接口的最大的生长速度被获得。

英文摘要：

The effect of convective flow on a spherical crystal growth in the undercooled melt with a moderate far field flow is studied. The asymptotic solution of the evolution of the interface of the spherical crystal growth is obtained by the matched asymptotic expansion method. The analytic result shows that the convective flow in the undercooled melt has a strong effect on the evolution of spherical crystal growth. The convective flow induced by the far field flow makes the interface of the growing spherical crystal enhance its growth velocity in the upstream direction of the far field flow and inhibit growth in the downstream direction, and the interface of the decaying spherical crystal further decay in the upstream direction and inhibit decay in the downstream direction. The maximum growth velocity of the interface of the spherical crystal influenced by the far field flow is obtained.