We consider a drop of constant density and uniform interfacial tension rising in a linearly density stratified fluid. In the limits of weak inertia and stratification effects, we calculate the drag acting on the drop, the flow fields inside and outside the drop, the drop deformation, and the drift volume associated with the drop using the method of matched asymptotic expansions. Stratification or inertia increase the drag and this enhanced drag acting on a drop is equal to ${\left(\frac{3\lambda +2}{3(\lambda +1)}\right)}^2$ times the enhanced drag acting on a rigid sphere, where $\lambda$ is the viscosity ratio. This relation between the enhanced drags of a drop and a rigid sphere holds even in the presence of both these effects (stratification and inertia). On the other hand, stratification does not result in any deformation of the drop up to the first order of approximation. At zero inertia and small advective transport rate of density, the drift volume associated with the drop rising in a stratified fluid is finite (but large compared to the drop’s volume) unlike the drift volume in a homogeneous fluid which is infinite.

中文翻译：

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与密度分层流体中的液滴上升相关的惯性阻力，变形和漂移量

我们考虑线性密度分层流体中恒定密度下降和均匀界面张力下降。在弱惯性和分层效应的极限下，我们使用匹配渐近展开法计算作用在液滴上的阻力，液滴内部和外部的流场，液滴变形以及与液滴相关的漂移量。分层或惯性增加了阻力，而这种作用在下落上的增强阻力等于${（\frac{3\lambda +2}{3（\lambda +\mathrm{1个}）}）}^2$ 乘以作用在刚性球体上的增强阻力， $\lambda$是粘度比。即使同时存在这两种效果（分层和惯性），液滴的阻力增加与刚性球体之间的这种关系仍然成立。另一方面，分层不会导致液滴下降到第一阶近似值。在零惯性和较小的对流输运速率下，与分层流体中液滴上升相关的漂移体积是有限的（但与液滴体积相比较大），与均匀流体中的漂移体积是无限的不同。