Gravity waves of the Stokes-type in a system of two horizontal layers of inviscid, stratified and miscible fluids are studied by applying a Lagrangian description of fluid motion. It is shown that for the total vertically-integrated Stokes drift (the Stokes flux) to become zero, the density must be continuous at the interface. This is not the case in a system of two immiscible homogeneous layers of different densities. For miscible fluids, however, one can extend the density of the lower layer continuously to that of the upper layer through an infinitely thin interface. This introduces a negative Stokes drift with a delta-function behavior. The corresponding finite negative Stokes flux obtained by integrating the Stokes drift across this infinitely thin layer adds to the original positive Stokes fluxes in the upper and lower layer, yielding the required vanishing total Stokes flux between the bounding planes of the model. The delta-function behavior of the Stokes drift at the interface also induces additional Lagrangian mean displacements in the vertical so that the position of the Lagrangian mean interfacial level is the same as in the absence of waves.

通过应用流体运动的拉格朗日描述，研究了由不粘，分层和可混溶流体组成的两个水平层系统中的斯托克斯型重力波。结果表明，为了使垂直积分的总Stokes漂移（Stokes通量）变为零，密度必须在界面处连续。在具有不同密度的两个不混溶的均匀层的系统中不是这种情况。但是，对于可混溶的流体，可以通过无限薄的界面将下层的密度连续扩展到上层的密度。这引入了具有增量功能行为的负斯托克斯漂移。通过积分穿过该无限薄层的Stokes漂移而获得的相应的有限负Stokes通量，将上下层的原始正Stokes通量相加，在模型的边界平面之间产生所需的消失的总Stokes通量。界面处斯托克斯漂移的δ函数行为还引起垂直方向上的其他拉格朗日平均位移，因此拉格朗日平均界面能级的位置与不存在波时相同。