A systematic investigation into the effect of roughness on self-propelled swimming plates

Abstract

This study examines the effects of surface topography on the flow and performance of a Self-Propelled Swimming (SPS) body. We consider a thin flat plate with an egg-carton roughness texture undergoing prescribed undulatory swimming kinematics at a Strouhal number of $0.3$ and tail amplitude to length ratio of $0.1$; we use plate Reynolds numbers of $\mathit{Re}=6,12,$ and $24\times 10^3$, and focus on $12,000$. As the roughness wavelength is decreased, we find that the undulation wave speed must be increased to overcome the additional drag from the roughness and maintain SPS. Correspondingly, the extra wave speed raises the power required to maintain SPS, making the swimmer less efficient. To decouple the roughness and the kinematics, we compare the rough plates to equivalent smooth cases by matching the kinematic conditions. We find that all but the longest roughness wavelengths reduce the required swimming power and the unsteady amplitude of the forces when compared to a smooth plate undergoing identical kinematics. Additionally, roughness can enhance flow enstrophy by up to 116\% compared to the smooth cases without a corresponding spike in forces; this suggests that the increased mixing is not due to increased vorticity production at the wall. Instead, the enstrophy is found to peak strongly when the roughness wavelength is approximately twice the boundary layer thickness over the $\mathit{Re}$ range, indicating the roughness induces large-scale secondary flow structures that extend to the edge of the boundary layer. This study reveals the nonlinear interaction between roughness and kinematics beyond a simple increase or decrease in drag, illustrating that roughness studies on static shapes do not transfer directly to unsteady swimmers.