水筒中直线涡运动的理论探讨

本文讨论了正方形截面水筒中直线涡的运动。当涡线不位于水筒的轴中心线上时,数值计算指出,它在水筒横截面上的运动轨迹为近似螺旋线。若直线涡位于水简轴中心线附近,则轨迹为一个近似圆。本文详细讨论了水筒轴中心线的直线涡的运动稳定性,其结论是在除零波数外的任意波数扰动下,该涡线总能保持在轴中心线上,运动是稳定的。零波数扰动情况与不在水筒轴中心线上的直线涡运动情况一样,将逐渐偏离水筒轴中心线。

THEORETICAL INVESTIGATION ON MOTION OF STRAIGHT VORTEX LINE IN WATER TUNNEL

In this paper the motion of a straight vortex line in a water tunnel, which has a square cross section, is discussed. When the vortex line is not positioned at centric line of water tunnel, it is found through numerical calculation that this vortex line will move along a trace of approximate spiral in the cross section plane. If the vortex line is close to centric line of water tunnel the trace is nearly a circle. As for vortex line located in centric line of water tunnel its motion stability is analysed in detail and the conclusion is that it can always be kept at centric line of water tunnel for any wavenumber perturbation other than zero wavenumber. In the case of perturbation of zero wavenumber the situation is the same as in the case of a vortex line which is not located at centric line of water tunnel and it will gradually depart from the centric line of water tunnel.