Numerical study of water depth effect on vortex shedding

Abstract

The effect of bathymetry on the characteristics of vortex streets is numerically studied in this paper. The numerical model is based on the non-conservative, two-dimensional depth-averaged shallow-water equations with the least-squares finite-element formulation in space and θ-method in time integration. Flow past a circular cylinder with the same boundary and initial conditions, in three different bathymetries, including the horizontal bed, constant slope bed, and irregular bed, is investigated. Water surface around the cylinder and the dynamics of the vortex streets are examined. Computed results compared well with available experiment data and other numerical solutions. It shows that pairs of symmetric, alternatively cyclonic-anticyclonic vortices are found in the symmetric bathymetry setting, and highly asymmetric, alternating vortices with opposite rotations in the non-symmetric bathymetry setting. The bathymetry has a direct effect on the formation, strength, and characteristics of the vortex shedding, and consequently on the water surface around the cylinder and flow field upstream. 本文中，我們利用數值模式，探討地形水深對渦流射出之影響。數值模式係使用空間最小平方有限元素法與θ-時間積分方法，求解非守恆形式之二維水深平均淺水方程式。我們考慮相同邊界條件與起始條件情況下，三種不同地形（包括：水平地形、傾斜地形、與不規則地形），水流流經一圓柱之流況，探討圓柱周圍之水面變化與渦街之動態特性。計算結果與實驗數據及其他數值解相當吻合。結果顯示在對稱於水流方向之地形情況下，卡門渦街是對稱、且一對一對以順時鐘與反時鐘之渦流交替出現；而在不對稱於水流方向之地形情況下，卡門渦街是不對稱、且一對一對以順時鐘與反時鐘之渦流交替出現。由此可見，地形水深對渦流之形成、強度、與變化有關，而且會影響到圓柱周圍及上游之流場。