由于自诱导作用,椭圆涡会产生自旋运动,利用周线动力学结合涡声理论可得到理想流体中椭圆涡自旋运动辐射的远场声。在椭圆涡稳定自旋的前提下,推出了声源强度的解析表达式,并得到了数值模拟验证。研究表明:①椭圆涡的声源由两个振幅和周期相同、相位差π/2的横向四极子组成;②对横截面积和涡量相同的椭圆涡而言,其声辐射效率主要由椭圆涡的长短轴比σ决定。当σ=1时,其声辐射效率为0,即圆柱涡不辐射声;当σ≈2.618时,其声源强度最大;③椭圆涡辐射的声频率为其自旋频率的两倍。本文的方法不仅适用于σ接近于1的椭圆涡,对σ较大的稳定自旋椭圆涡也同样适用。
The elliptical vortex will rotate because of self-induction.Using contour dynamics method and vortex sound theory,the far-field sound pressure radiated by spinning elliptical vortex in an inviscid fluid can also be acquired.On the assumption that the elliptical vortex rotates stably,an analytical expression of the sound source strength is derived which has been confirmed by numerical simulation.The sound source of the rotating elliptical vortex consists of two lateral quadrupoles which have the same amplitude and period but are π/2 out of phase.For the elliptical vortex with same cross-section area and vorticity,the sound source strength is mainly determined by the aspect ratio σ.The sound source strength is zero when σ=1,that is,the cylindrical vortex does not radiate noise.The sound source strength reaches a maximum when σ≈2.618.The frequency of sound generated by elliptical vortex is twice of the rotating frequency.This method can be used not only for the ellipti-cal vortex whose σ closes to 1,but also for the stable rotating elliptical vortex with larger σ.