Anguilliform swimming has attracted the attention of researchers from diverse scientific fields ranging from neuroscience to hydrodynamics. A number of open question remain, however, regarding the correlation of the swimming motions with the biological functions of the swimming organisms. We propose to identify the body motions via evolutionary optimization by maximizing cost functions pertaining to efficient and fast swimming modes.


The computational model is based on the solution of the 3D Navier-Stokes equations for the incompressible viscous flow around an unsteadily deforming three dimensional anguilliform body. The motion of the body is coupled to the external flow field and the deformation of the body is defined by the 2D deformation of the mid-line. The fluid-body interaction includes forces in all three coordinate directions and the torque perpendicular to the plane of the deformation of the mid-line (yaw). The three dimensional geometry of the anguilliform swimmer is constructed from spatially varying ellipsoid cross sections (Fig. 1). The motion is parameterized by describing the instantaneous curvature of the mid-line of the body. The parameters of the motion are obtained by an evolution strategy with adaptation of the covariance matrix (CMA-ES).
We present results for two different swimming modes optimized for efficiency and swimming speed and analyze the swimming kinematics, hydrodynamic forces, and wake morphology. The two swimming modes are compared against each other and to experimental data. The mean swimming velocities obtained in the present simulations lie well in the range of 0.26-0.5 body length per undulation cycle reported in the experimental studies. The wake structure in both cases includes double vortex rings and the appearance of the characteristic lateral jets that have been previously reported in experimental studies.
Figure 1. Snapshot of the three dimensional geometry
Figure 2. Longitudinal (solid line) and lateral velocities