论文标题
持续涡度的三维内波的刚度
Rigidity of three-dimensional internal waves with constant vorticity
论文作者
论文摘要
本文研究了恒定涡度对稳定的三维内部水波的结构意义。众所周知，在许多物理方面，具有恒定涡度的真空下的水波必定是二维的。对于沿着两种不混溶的流体之间的界面传播的内部波的情况，情况更为微妙。当层具有相同的密度时，具有恒定涡度的大量显式稳定波是三维的，因为速度场和压力取决于一个水平变量，而界面是另一个的任意函数。我们证明了以下刚度结果：每个具有有界速度的三维行进内波，上层和下层中的涡度不零，恒定和平行必须属于该家族。如果每一层的密度都不同，则实际上流量是完全二维的。
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two dimensional. The situation is more subtle for internal waves that traveling along the interface between two immiscible fluids. When the layers have the same density, there is a large class of explicit steady waves with constant vorticity that are three-dimensional in that the velocity field and pressure depend on one horizontal variable while the interface is an arbitrary function of the other. We prove the following rigidity result: every three-dimensional traveling internal wave with bounded velocity for which the vorticities in the upper and lower layers are nonzero, constant, and parallel must belong to this family. If the densities in each layer are distinct, then in fact the flow is fully two dimensional.
