Multi-layered Turbulence Structure of Flow under Free Surface of Open Channel Flow Using Velocity-Vorticity Correlation Structure Method

Turbulence near a free surface is of multi-layered nature and of fundamental significance in understanding vast marine and ocean processes. Direct numerical simulation of an open channel with the free surface modeled by a free-slip boundary is performed. Complex multi-layered turbulence (i.e., the blockage layer, the slip layer, and the Kolmogorov layer) under the free surface are first identified based on predefined anisotropy indices. Later on, statistical features of the anisotropic turbulence inside the three turbulence layers are presented. Most importantly, considering the drastic variation of both velocity and vorticity in near-surface layers, we revisit the complex multi-layered turbulence by the velocity-vorticity correlation structure (VVCS) method [Chen et al., J. Fluid Mech. 742, 291-307 (2014)]. It is found that the VVCS can physically depict evolution of the hairpin vortex inside the channel, including generation in the bottom wall region, expansion in the bulk flow, process of getting flattened in the blockage layer, and then distortion and breakdown in the slip layer and the Kolmogorov layer. Specifically, the correlation structures VVCS11 for streamwise velocity and streamwise vorticity reflect how the hairpin legs are spatially distributed, while the correlation structures VVCS13 for streamwise velocity and spanwise vorticity describe the evolution of the hairpin vortex head. In the end, a cradle-like structure model is proposed based on the VVCS results and the vortex ring collision model is introduced to improve the understanding of the multi-layered turbulence under free surface. Hopefully, this research can be of value in future turbulence modeling work on free surface flows.