The decay of Hill's vortex in a rotating flow
The decay of Hill's vortex in a rotating flow
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DOI：
10.1017/jfm.2021.386
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发表时间：
2021-05
影响因子：
3.7
通讯作者：
M. Crowe;Cameron Kemp;E. Johnson
中科院分区：
文献类型：
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作者：
M. Crowe;Cameron Kemp;E. Johnson
希尔旋涡是不可压缩欧拉方程的经典解，它由轴对称的恒涡度球面区域与无旋外流相匹配组成。这个解已经被证明是定常涡环的单参数家族的一员，因此通常被用作涡环的简单解析模型。在这里，我们模拟了在弱旋转流动中由于惯性波的辐射而导致的Hill旋涡的衰减。在旋转率或反Rossby数较小的情况下，我们利用渐近方法得到了旋转效应对涡旋结构和产生的波场的修正的解析结果。利用该模型，将涡流能量流向波场和峰值涡度守恒相结合，对涡速和涡径的衰减进行了预测。我们用全轴对称Navier-Stokes方程的数值模拟来检验我们的结果。
Abstract Hill's vortex is a classical solution of the incompressible Euler equations which consists of an axisymmetric spherical region of constant vorticity matched to an irrotational external flow. This solution has been shown to be a member of a one-parameter family of steady vortex rings and as such is commonly used as a simple analytic model for a vortex ring. Here, we model the decay of a Hill's vortex in a weakly rotating flow due to the radiation of inertial waves. We derive analytic results for the modification of the vortex structure by rotational effects and the generated wave field using an asymptotic approach where the rotation rate, or inverse Rossby number, is taken to be small. Using this model, we predict the decay of the vortex speed and radius by combining the flux of vortex energy to the wave field with the conservation of peak vorticity. We test our results against numerical simulations of the full axisymmetric Navier–Stokes equations.