Llewellyn Smith Stefan G, Chu T, Hu Z
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA.
Scripps Institution of Oceanography, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0209, USA.
Philos Trans A Math Phys Eng Sci. 2022 Jun 27;380(2226):20210052. doi: 10.1098/rsta.2021.0052. Epub 2022 May 9.
Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, , using a Rayleigh-Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales [Formula: see text] and [Formula: see text]. Examples are given for co-rotating and co-propagating vortex pairs. The former show a correction to the rotation rate and, in general, to the centre and radius of rotation, while the latter recover the known result that the steady propagation velocity is unchanged. For unsteady configurations, the vortex solution matches to a far field in which acoustic waves are radiated. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
利用瑞利 - 扬森展开式和匹配渐近展开法，在小马赫数极限情况下，得到了平面中可压缩点涡的运动方程。涡旋之间区域的解与每个涡旋核心周围的解相匹配。涡旋的运动在长时间尺度[公式：见正文]和[公式：见正文]上会发生改变。给出了同向旋转和同向传播涡旋对的例子。前者显示了对旋转速率的修正，一般来说，对旋转中心和半径也有修正，而后者恢复了已知结果，即稳定传播速度不变。对于非定常构型，涡旋解与辐射声波的远场相匹配。本文是主题为“物理流体动力学中的数学问题（第2部分）”的一部分。
