Rigidity of Three-Dimensional Internal Waves with Constant Vorticity
Rigidity of Three-Dimensional Internal Waves with Constant Vorticity
复制标题
恒涡度三维内波的刚度
DOI：
10.1007/s00021-023-00816-5
复制
发表时间：
2023
影响因子：
1.3
通讯作者：
Wheeler, Miles H.
中科院分区：
文献类型：
--
作者：
Chen, Robin Ming;Fan, Lili;Walsh, Samuel;Wheeler, Miles H.
本文研究了恒定涡度对航道中稳定三维内水波的结构影响。众所周知，在许多物理状态下，真空下具有恒定涡度的水波必然是二维的。对于沿着两种不混溶流体之间的界面传播的内波，情况更加微妙。当各层具有相同的密度时，存在一大类具有恒定涡度的显式稳态波，它们是三维的，因为速度场指向一个水平方向，而界面是另一个水平变量的任意函数。我们证明了以下刚性结果：每一个具有有界速度的三维行进内波，其上下层涡度非零、恒定且平行，都必须属于该族。如果每层的密度不同，那么实际上流动是完全二维的。该证明是使用一种完全新颖但基本上是基本的论证来完成的，该论证与从压力唯一地重建二维速度场的问题建立了联系。
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves in a channel. 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 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 is pointing in one horizontal direction while the interface is an arbitrary function of the other horizontal variable. 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. The proof is accomplished using an entirely novel but largely elementary argument that draws connection to the problem of uniquely reconstructing a two-dimensional velocity field from the pressure.
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