涡环相互穿梭产生的声及频谱特性

Sound generated by leapfroging of vortex rings and its spectrum

涡环的诱导与自诱导会引起同轴涡环的相互穿梭运动。在忽略涡核形状改变的前提下,利用涡声理论和理想流体中涡冲量守恒,可将远场声压用系统涡质心的轴向加速度表示。涡质心轴向运动加速度的变化是产生声的根本原因。在利用Biot-Savart公式得到涡环运动轨迹的基础上,对涡环穿梭运动产生的声及频谱特性进行了分析。涡环之间的初始轴向距离越远,所产生声的频率成分越丰富;相反,所产生声的频率成分越单一。

Leapfrogging of coaxial vortex rings is happened due to the induction and self-induction of vortex rings. According to the vortex sound theory and conservation of impulse in an inviscid fluid, the far field sound pressure can be expressed as the axial acceleration of vortex centroid on condition that the shape changing of vortex core is neglected. It is the non-uniform axial acceleration of vortex centroid that resulted in the sound generation. Based on the trajectory of vortex rings obtained by Biot-Savart equation, the sound and its spectrum character are analyzed. The farther the initial separation is, the more abundant the frequency components are; on the contrary, the frequency components are more monotonic.