Acoustic destablilization of vortices
Acoustic destablilization of vortices
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DOI：
10.1098/rsta.1979.0003
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发表时间：
1979
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中科院分区：
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一个核心涡度为2Ω0的线涡受到一个小的二维扰动，该扰动与极角的关系为eimθ。根据等熵介质中可压缩无粘流动方程，对其稳定性进行了检验。无限远处的边界条件是出射声波的边界条件，与相应的稳定不可压缩涡旋相比，发现这种辐射能力导致了缓慢的不稳定。数值特征值是根据涡的周向速度计算模数m和马赫数m的函数。这些结果与低马赫数下m = 2模态的渐近分析进行了比较，发现增长率为（π/ 32） M4Ω0，与数值结果吻合得很好。
A line vortex which has uniform vorticity 2Ω0 in its core is subjected to a small two-dimensional disturbance whose dependence on polar angle is eimθ. The stability is examined according to the equations of compressible, inviscid flow in a homentropic medium. The boundary condition at infinity is that of outgoing acoustic waves, and it is found that this capacity to radiate leads to a slow instability by comparison with the corresponding incompressible vortex which is stable. Numerical eigenvalues are computed as functions of the mode number m and the Mach number M based on the circumferential speed of the vortex. These are compared with an asymptotic analysis for the m = 2 mode at low Mach number in which it is found that the growth rate is (π/ 32) M4Ω0 in good agreement with the numerical results.