Abstract Three examples of wave–vortex interaction are studied, in analytically tractable weak refraction regimes with attention to the mean recoil forces, local and remote, that are associated with refractive changes in wave pseudomomentum fluxes. Wave-induced mean forces of this kind can be persistent, with cumulative effects, even in the absence of wave dissipation. In each example, a single wavetrain propagates past a single vortex. In the first two examples, in a two-dimensional, non-rotating acoustic or shallow-water setting, the focus is on whether or not the wavetrain overlaps the vortex core. In the overlapping case, the recoil has a local contribution given by the Craik–Leibovich force on the vortex core, the vector product of Stokes drift and mean vorticity. (For a quantum vortex this contribution is called the Iordanskii force arising from the Aharonov–Bohm effect on a phonon current.) However, in all except one special limiting case there are additional “remote” contributions, mediated by Stokes-drift-induced return flows that can intersect the vortex core well away from locations where the waves are refracted. The third example is a non-overlapping, remote-recoil-only example in a rapidly rotating frame, in which the waves are deep-water gravity waves and the mean flow obeys shallow-water quasigeostrophic dynamics. Contrary to what might at first be thought, the Ursell “anti-Stokes flow” induced by the rotation – an Eulerian-mean flow tending to cancel the Stokes drift – fails to suppress remote recoil. There are nontrivial open questions about extending these results to regimes of stronger refraction, especially regarding the scope of the “pseudomomentum rule” for the wave-induced recoil forces.

中文翻译：

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波-涡相互作用和有效平均力：三个基本问题

摘要 研究了波涡相互作用的三个例子，在分析易处理的弱折射区域中，注意与波假动量通量的折射变化相关的局部和远程平均反冲力。即使在没有波浪耗散的情况下，这种波浪引起的平均力也可以是持久的，具有累积效应。在每个示例中，单个波列传播经过单个涡流。在前两个示例中，在二维、非旋转声学或浅水环境中，重点是波列是否与涡核重叠。在重叠的情况下，反冲具有由涡核上的 Craik-Leibovich 力、斯托克斯漂移和平均涡度的矢量积给出的局部贡献。（对于量子涡旋，这种贡献称为由 Aharonov-Bohm 效应对声子电流产生的 Iordanskii 力。）然而，除了一个特殊的极限情况外，还有其他“远程”贡献，由斯托克斯漂移引起的返回介导可以与涡核相交的流动，远离波折射的位置。第三个例子是快速旋转坐标系中的非重叠、仅远程反冲的例子，其中波浪是深水重力波，平均流服从浅水准地转动力学。与最初可能想到的相反，由旋转引起的 Ursell“反斯托克斯流”——一种倾向于抵消斯托克斯漂移的欧拉平均流——未能抑制远程后坐力。