Title: Structural implication of constant vorticity to three-dimensional internal waves

Abstract: 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 is pointing in one horizontal direction while the interface is an arbitrary function of the other horizontal variable. We prove that 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. This is a joint work with Lili Fan, Samuel Walsh, and Miles Wheeler.

报告人：陈明（匹兹堡大学）

报告时间及地点：2024年07月29日10：00-11：00 维格堂319