Three-dimensional Lattice Boltzmann Simulation Of Oscillatory Boundary Layer Flow Over A Rough Bed

In coastal and estuarine area, the oscillatory boundary layer over rough beds has a close relationship with sediment transport, flow risistance, wave energy dissipation and so on. The deep understanding of this subject is very important for theoretical research and engineering. A fully resolved three-dimensional lattice Boltzmann (LB) model is developed and direct numerical simulation of oscillatory boundary layer over rough beds is carried out. Turbulence characteristics, hydrodynamic forces on the particles and flow resistance are investigated. The main results are summarized as follows:(1) Several benchmark problems are solved with the LB model including oscillatory boundary layer over a smooth bed, oscillatory boundary layer flow past a spherical particle and oscillatory boundary layer over a rough bed at low Reynolds number. It indicates that the LB model is feasible to solve this kind of problem from the mesoscale view.(2) Simulation of rough turbulent oscillatory boundary layer is carried out. Results indicate that the turbulence intensity strengthens as the amplitude Reynolds number Re_a and d /δ(the ratio of the diameter to the Stokes boundary layer thickness) increase. Meanwhile, the spanwise flow enhances and the pressure distribution becomes asymmetric which make the effect of the spanwise force non-negligible. Re_a and d /δare the main influence factor of the force coefficients according to the dimensional analysis. The variation of the force coefficients with respect to Re_a and d /δis analyzed. After that, the expressions for the maximum of the ensemble-averaged drag and lift force coefficients, < C_D>_max and < C_L>_max are suggested with introducing the porosity to characterize the effect of the bed pattern.(3) The log-fit method based on the minimum value for the error squares is employed to analyze the position of the theoretical bed, equivalent roughness height and friction velocity. It can give reasonable results.(4) The rough bed in computational domain is composed of a layer of spherical particles placed regularly in two patterns. One is cubic packing and the other is hexagonal packing. For both of them, it shows that the theoretical bed is located at 0.19 0.25 times diameter below the crests of spherical particles. The non-dimensional equivalent roughness height k_s/d is nearly 2.8 in most cases, which shows a good agreement with the recommended value of 2.5.(5) The log-fit results indicate that non-dimensional friction velocity for fixed beds appears to be a sinusoidal-like behavior in the oscillatory period. The maximum friction velocity leads over the maximum free-stream velocity. The phase lead is found to be in the range 10° 30°for the computational values of relative roughness a / k_s= 0.47 6.58. The friction factor for small values of a / k_s does not seem to tend to a constant value suggested by some previous investigators, but constantly increases with decreasing a / k_s.