Modeling of wake patterns behind cylinder in the shallow water

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Shallow wake is defined explicitly compared with deep wake by Chen & Jirka as follow:when the transverse body dimension of obstacle D greatly exceeds the water depth H,D/H > > 1,the wake behind the obstacle is called shallow wake.In nature,the shallow wakes usually appear behind islands,mountains,and occur in wide rivers,estuaries,lakes and coastal regions.They have significant effect on the transportation and diffusion of pollutant,the living conditions of creatures,the settlement and accumulation of sediment,and so on.Compared with deep wakes where the flow characteristics are determined mainly by the Reynolds number Re,the flow characteristics of shallow wakes depend on a shallow wake parameter,S =CfD/H,where Cf is a quadratic law friction coefficient.In this paper,two-dimensional (2D) depth-averaged shallow equations and three-dimensional (3D) RANS equations with RNG k-ε turbulence model are used to simulate the flow structures of shallow wake behind cylinder,respectively.The calculation results are compared with Chen & Jirka s experimental data.Three types of the wake patterns are verified,namely,vortex street(VS) wake,unsteady bubble(UB) wake,and steady bubble(SB) wake.The vorticity contours,transverse velocity variation with time,Strouhal number and distribution of time-averaged longitudinal velocity along the centerline are compared with the experimental results.The results show the 2D shallow water model can get better results when the S value is smaller than 0.27,yet the 3D model performs more exactlywhen S value exceeds 0.34.
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