Vortex ring eigen-oscillations as a source of sound
Vortex ring eigen-oscillations as a source of sound
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涡环本征振荡作为声源
DOI：
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发表时间：
1997
影响因子：
3.7
通讯作者：
S. Chernyshev
中科院分区：
文献类型：
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作者：
V. Kopiev;S. Chernyshev
研究了两个耦合问题：理想不可压缩流体中长波涡环振荡的完整描述，以及弱可压缩流体中长波涡环振荡对声辐射的影响。本文第一部分讨论了理想不可压缩流体中薄涡环(μ[LT]1)的本征振动问题。问题的解以小参数μ的渐近展开式的形式得到。得到了完整的三维本征振动和轴对称模式(二维振动)。结果表明，与具有简单角谐形式的涡柱振荡不同，大多数薄涡环的本征振荡具有更复杂的形式，即在前导近似中由两个简谐组合而成。这导致与涡柱的相应模式相比，涡环模式产生的声辐射效率发生了显著变化。在本文的第二部分中，将所得到的解用于研究弱可压缩流体中涡旋扰动的声辐射过程。根据声辐射效率对涡环本征振荡进行了分类。结果表明，无因次频率为ω≈1/2的模式辐射声效率最高。它们是两个孤立模、两个无限族Bessel模和一组轴对称模。这些模式的频率在区间Δω=O(μ)内。将所得结果与已有的湍流涡环声辐射实验数据进行了比较。在推导出的理论范围内，对声辐射的主要特性进行了解释。
Two coupled problems are investigated: a complete description of long-wave vortex ring oscillations in an ideal incompressible fluid, and an examination of sound radiation by these oscillations in a weakly compressible fluid. The first part of the paper relates to the problem of eigen-oscillations of a thin vortex ring (μ[Lt ]1) in an ideal incompressible fluid. The solution of the problem is obtained in the form of an asymptotic expansion in the small parameter μ. The complete set of three-dimensional eigen-oscillations and axisymmetric modes (two-dimensional oscillations) is obtained. It is shown that, unlike the vortex column oscillations which have the form of simple angular harmonics, the majority of eigen-oscillations of a thin vortex ring have a more complex form which is a combination of two harmonics in the leading approximation. This leads to dramatic changes in the efficiency of sound radiation produced by modes of the vortex ring in comparison with the corresponding modes of the vortex column. In the second part of the paper the solution obtained is used to investigate the process of sound radiation by vortex perturbations in a weakly compressible fluid. The vortex ring eigen-oscillations are classified according to their sound radiation efficiency. It is shown that the modes with the dimensionless frequency ω≈1/2 radiate sound most efficiently. They are two isolated modes, two infinite families of Bessel modes and a set of axisymmetric modes. The frequencies of these modes are in the interval Δω=O(μ). The results obtained are compared with known experimental data on acoustic radiation of a turbulent vortex ring. Within the limits of the theory derived an explanation of the main characteristics of sound radiation is presented.