Immersed Boundary Method for Simulation of Oscillatory Flow Past a Submerged Cylinder Near Above a Horizontal Bed

In the present work, the oscillatory flow past a submerged cylinder near above a horizontal bed is simulated by a Navier-Stokes equations solver. The boundary conditions, i.e., the no-slip condition on solid boundaries are imposed with the immersed boundary method. A Cartesian grid with variable size is used for the spatial discretization, and a time-splitting scheme is used for the temporal discretization. The numerical method was validated simulating the unidirectional flow past a cylinder at Reynolds number Re_D = 300. For the oscillatory flow past a cylinder of diameter D at a distance G above a horizontal bed, all variables were rendered dimensionless using the maximum velocity, U_o, and the amplitude of the orbital motion, α_o, of the oscillatory flow. Several tests with differing values of α_o/D and G/D were considered, for Reynolds number Re_α = 5,000 and Keulegan–Carpenter numbers in the range from 6.28 to 62.8. Results show that the critical range for the suppression of vortex shedding at the lower side of the cylinder is G/α_o<0.01, while the critical range for the generation of vorticity uplift from the bed boundary layer is G/α_o<1.0. Also, as G/D decreases, both the amplitude of the drag force and the bias towards positive values of the lift force increase.