On the basis of the theory of resonant instability due to liquid inertial wave inside the system established by Stewartson-Wedemeyer-Murphy,the dynamic behaviour of nonlinear angular motion of the rotating liquid-filled system is analysed by means of the Melnikov's method in the global bifurcation theory. The condition under which the chaotic motion does not appear in the system is concluded.
In particular, under a suitable assumption, if F is a cyclic group, then the topological space which admits a chaotic action of Z × F must admit a chaotic homeomorphism.
The observations were made by hydrogen bubble method in a water channel 6.8 m long by 0.4m wide and 0.3m deep. A flat plate 6m long was set along one side of the channel. After the observations of TBL structures in zero pressure gradient flow, a curved wall was set opposite to this plate to form a two-dimensional convergent-divergent passage as shown in Pig. 1. There were small separated bubbles appearing intermittently at x = 200 to 300 mm but no separation in the downstream part. Plate 1 is a plane view o...
The wake of a circular disk in a water channel during starting was observed by hydrogen bubble method with two different disks while the accelerations of the free stream were approximately constant during the starting stage.In the starting stage the vortex sheet separated from the disk edge rolled up into a helical vortex ring named starting vortex as shown in Fig. (a ) to ( f ). Both its diameter dv and abscissa xv increased linearly (Figs 5 and 6 ). Induced by the starting vortex, the flow in the center o...
The aim of this paper is to bring to engineer's attention to a new research area, which is still unfamiliar to them. After describing the history of the development of the subject briefly, some examples are given, in which chaotic behaviours appear. Then some known mathematical conclusions are presented, and the importance and the potential applications of the investigation are pointed out.