LARGE EDDY SIMULATION OF TURBULENT FLOW OVER A WALL UNDERGOING STREAMWISE TRAVELLING WAVE MOTION

Turbulent channel flow with a wall undergoing travelling wave motion in streamwise direction was investigated using large eddy simulations at friction Reynolds number Re*=1000. Phase average and decomposition were used in the analysis of the flow field. Compared to flat wall turbulence, the large-scale motions in the outer layer are significantly enhanced by the traveling wave boundary. Obvious large-scale peaks in outer layer for all the three velocity components could be observed in the spanwise pre-multiplied energy spectra. A strengthened superposition effect of streamwise velocity fluctuation could also be seen in both energy spectra and conditionally averaged flow fields. The analysis of the two-point correlation function transport equation shows that the wave motion of the wall taking effect on the largescale motion in the outer layer is mainly through the wave-induced production. INTRODUCTION The coupling dynamic processes between surface waves and turbulent flow are related to many complicated flow phenomena, such as the effect of the wind-induced wave to momentum flux at the ocean surface, and to the mixing and transport in the upper ocean. A fundamental understanding of the interaction of wave and turbulence is of significance in geophysics and ocean engineering. Existing researches show that turbulent flow over moving boundary has a significant difference with canonical flat plate boundary layer. For instance, Sullivan et al (2000) and Yang & Shen (2010) used the progressive wave wall as the idealized water wave and investigated the influence of wave to the momentum flux and coherence structures of turbulence. In recent years, the large-scale motions scaled by the outer scale in the outer region of wall turbulence were found and confirmed at high Reynolds numbers (Kim & Adrain, 1999; Hutchins & Marusic, 2007a). Moreover, the influence of large-scale motions on near-wall fluctuations could be summarized to the superposition and modulation effects (Hutchins & Marusic, 2007b). In the present work, we studied the turbulent flow over a traveling wavy wall by using large-eddy simulation and focused on the influence of the wavy boundary on the large-scale motions in the outer layer. In order to identify the wave-turbulence interactions, phase average and decomposition (Hussain & Reynolds, 1970) were used in the analysis of the flow field. The significantly enhanced effect on large-scale motions by wavy boundary could be observed in spanwise energy spectra of fluctuating velocity components and conditionally averaged flow fields. We also performed a spectral analysis of the twopoint correlation function transport equation to investigate the mechanism of the wave motion of the wall effecting the large-scale motions in the outer layer. PROBLEM FORMULATION AND NUMERICAL METHOD The problem considered is a fully developed threedimensional turbulent flow in a half channel over a wall undergoing traveling wave motion in the streamwise direction. A sketch of computational domain and coordinate system are shown in Figure 1. We adopt a Cartesian frame fixed in the physical space, with x, y and z 10 International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 2 4B-3 being the streamwise, vertical and spanwise coordinates (also denoted as x1 , x2 , and x3 ). The corresponding velocity components in three directions are u, v, and w, respectively. A free-slip condition is applied on the upper boundary and a periodic condition in the streamwise and spanwise directions. The bottom wall undergoes a vertical oscillation in the form of the prescribed streamwise traveling wave. The flow is driven by an averaged streamwise gradient of pressure which is dynamically adjusted and makes the flow rate to be strictly constant in time. The Reynolds number based on the total drag (τ) and half channel width (δ) is about 1000. The wave steepness ak=0.1, where a is the wave amplitude, k is the wave number. Four wave phase speeds c are considered to investigate the effects of wave age. See Table 1 for the computational parameters. In the present simulations, the filtered incompressible Navier-Stokes equation is solved by large-eddy simulation, and the subgrid-scale stress is modelled using the dynamic Smagorinsky model (Germano et al, 1991; Lilly 1992). The governing equations are integrated in time with a third-order time-splitting scheme. The accurate no-slip condition is satisfied at the wall by adopting the curvilinear coordinate system. A pseudospectral method in horizontal directions in conjunction with a second-order finite-difference method on a staggered grid in the vertical direction is used for spatial discretization. The computational domain size is Lx×Ly×Lz=4πδ×δ×2πδ, and the corresponding grids are 288×144×288. The grid sizes in the two horizontal directions are uniform with the resolution that Δx≈45, and Δz≈23. The vertical grid sizes Δy are changed from 0.05 near the bottom boundary to 10 near the top boundary. Table 1. Computational parameters ak a c/Uτ Re* 0 0