Numerical investigation of fish exploiting vortices based on the Kármán gaiting model

To understand the mechanism of fish exploiting vortices, this paper, for the first time, employs the Kármán gaiting model to numerically investigate the hydrodynamics of fish swimming in the vortex street. Considering the time-consuming computations during our large-scale simulations, we implement a parallel mesh deformation method based on the radial basis function(RBF) interpolation. Based on simulations over a wide range of controlling parameters, we discuss in detail the efficiency of fish exploiting vortices, the force coefficient and the hydrodynamic interactions between fish and vortices. It is observed that as the phase difference between fish's lateral translation and the shedding vortex changes, the efficiency presents a variation trend opposite to the mean thrust on the fish body; the optimum swimming distance downstream from the cylinder is positively affected by the inlet velocity and the diameter of the cylinder, which is consistent with the experimental results. From the hydrodynamic characteristics in the flow fields, we qualitatively draw a conclusion that the maximum efficiency is obtained when the fish is undulating with the tail flapping towards the center of the vortex, and the optimum distance is gained where vortices are drifting with the slipping mode.