摘要或動機

打開水龍頭，水鉛直落到正下方的水平板時形成圓形水躍。我們實驗研究20＜Nr＜150 的低雷諾數圓形水躍的變因，探討圓形水躍半徑和流量、出水口高度、以及液體黏滯係數間的關係。改用高黏滯係數的液體（4：1 的乙二醇水溶液），鉛直落入板上方深h 的相同液體時，先形成圓形，h 漸大時形成環形圓紋曲面，再加大h，形成多邊形水躍，內外圍同方向旋轉，轉速ω；液中加水，黏滯係數高於及低於某定值，多邊形都消失，側面觀察，外圍液體作鉛直面旋轉。將水平板改置於旋轉盤上方，使高黏滯係數（4：1）的乙二醇水溶液鉛直落入板上方形成多邊水躍，逐漸加快旋轉盤的轉速至 ω 時，多邊形都消失；逐漸減少乙二醇的濃度，至完全用水實驗，亦有多邊形出現，我們認為；平板上方的液體的轉動是非圓形水躍的成因。When a jet of water falls vertically on to a horizontal plate, it spreads out rapidly in a thin layer until it reaches a critical radius at which the layer depth increases abruptly. This phenomenon commonly called the circular hydraulic jump. We study the variations of the circular hydraulic jump radius, as a function of volume flow rate of the jet, the drop height, and the viscosity of the
fluid at low Reynold numbers (20＜Nr＜150). When a jet of ethylene-glycol mixed with water (the kinetic viscosity is 10
times of water) falls on to a horizontal plate which is immersed in the same liquid with height h. We find the circular state frequently undergoes spontaneous breaking at its axial symmetry into a stationary polygonal shape. Rather than displaying the weak angular deformation generally seen in fluids, the jump forms clear corners and edges that are often straight. Several of these polygon formations show consistency in height h. And we find the polygon structure rotates in a horizontal motion. When a jet of water falls on to a horizontal plate, and the plate is rotated by a motor ,we find the axial symmetry of the free surface of circular hydraulic jump is spontaneously broken a various number of cornered polygonal shapes. We study the number of corners as a result of the volume flow rate of the jet, the drop height and the viscosity of the fluid in the experiment. And the frequency of rotation of the plate is taking into consideration.