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本文由两部分组成。第一部分研究和分析了物体表面上的分离形态,指出若分离线从奇点始,该奇点为鞍点;若在奇点终,该奇点为结点。若分离线上有很多奇点,其鞍点和结点是交替分布的。分离线的起始,可能有三种形态:一种称之为闭式分离的鞍点起始;一种为正常点起始;一种为鞍、结点组合形态起始。可以把正常点起始和距离很近的鞍、结点组合形态起始称之为开式分离。在一定条件下,闭式分离的形态,先转变为鞍、结点组合的形态,然后过渡到正常点的开式分离。第二部分研究了旋涡沿其轴线发展过程中,其横截面流线形态的发展,指出旋涡轴线上物理量λ=(1/ρ)(ρw/z)是决定流线形态的重要参量。如果λ>0,截面流线在涡心附近是稳定的螺旋点形态。如果λ<0,为不稳定的螺旋点形态,如果λ=0,流线形态是中心型的,当沿涡轴λ由正变负或由负变正时,相应在涡心附近截面流线由稳定螺旋点形态变为不稳定螺旋点形态,或由不稳定螺旋点形态变为稳定螺旋点形态;并且从λ由正到负的变号点起,截面流线产生稳定的极限环,或从λ由负到正的变号点起,产生不稳定的极限环。旋涡破裂只能发生在截面流线为不稳定螺旋点形态的区域中,在通过涡轴的纵向平面内,破裂点处的流线形态是鞍型的。破裂涡的合拢点处在不稳定的极限环区域内。
This article consists of two parts. In the first part, we study and analyze the form of separation on the surface of the object, and point out that if the separation line starts from the singular point, the singular point is the saddle point; if it is the singular point, the singular point is the node. If there are many singular points on the separation line, the saddle points and nodes are alternately distributed. The beginning of the line of separation may have three forms: one is called the beginning of the saddle point of the closed separation; the other is the beginning of the normal point; the other is the saddle, the beginning of the combination of nodes. Can start normal and close to the saddle, the beginning of the combination of forms called open split. Under certain conditions, the form of closed separation, the first change to saddle, the combination of node morphology, and then transition to the normal point of the open separation. In the second part, the development of the cross-sectional streamlines of the vortex along its axis is studied. It is pointed out that the physical quantity λ = (1 / ρ) (ρw / z) on the vortex axis is an important parameter that determines the shape of the streamlines. If λ> 0, the cross-sectional streamlines are stable spiral point near the vortex center. If λ <0, the instability of the spiral point morphology, if λ = 0, the streamline shape is central, along the vortex axis from positive to negative or positive from negative, corresponding to the cross-section near the vortex streamline From stable helical point morphologies to unstable helical point morphologies or from unstable helical point morphologies to stable helical point morphologies; and from λ to positive negative signpoint points, a streamlined limit stream of cross-section produces or Starting from the point of change from negative to positive, an unstable limit cycle results. The vortex rupture can only occur in the area where the streamline is unstable, and the streamline shape at the rupture point in the longitudinal plane through the vortex axis is saddle-shaped. The collapse point of the rupture vortex is in the area of the unstable limit ring.