The Interaction Between Kinematics and Roughness on a Swimming Plate*

In this study, we examine the effects of the surface topography in the Self-Propelled Swimming (SPS) regime as found in swimming fishes or biomimetic robots. We look at a thin flat plate with length $L$ and undulatory swimming kinematics defined by $Re_L=12,000$ \& $St=0.3$. We add an egg-crate roughness texture to the plate, which changes shape depending on the wavelength. To find SPS for varying roughness wavelengths, we change the wave speed of undulatory locomotion until we have zero mean thrust. We then run an additional kinematically equivalent smooth simulation to decouple the kinematic and roughness effects.

Smaller wavelength roughness requires increased propulsive wave speed to achieve SPS. The increase in wave speed leads to an increase in required power. When the roughness wavelength is $\frac{1}{16} L$, resonant mixing occurs and causes a spike in enstrophy; the increased enstrophy results from forming multiple counter-rotating structures, which we visualise using the Q-criterion. Lastly, we decouple the kinematic and viscous effects on the powering and mixing characteristics to identify the cause of that resonant mixing. This study reveals the nonlinear interaction between roughness and motion, illustrating that roughness studies on static shapes do not transfer directly to swimming.