Effect of roughness on the velocity profile of a laminar boundary layer

Streak formation in flow over biomimetic fish scale arrays

The surface topology of the scale pattern from the European sea bass (Dicentrarchus labrax) was measured using a digital microscope and geometrically reconstructed using computer assisted design modelling. Numerical flow simulations and experiments with a physical model of the surface pattern in a flow channel mimic the flow over the fish surface with a laminar boundary layer. The scale array produces regular rows of alternating, streamwise low-speed and high-speed streaks inside the boundary layer close to the surface, with maximum velocity difference of approximately 9%. Low velocity streaks are formed in the central region of the scales whereas the high velocity streaks originated in the overlapping region between the scales. Thus, those flow patterns are linked to the arrangement and the size of the overlapping scales within the array. Because of the velocity streaks, total drag reduction is observed when the scale height is small relative to the boundary layer thickness, i.e. less than 10%. Flow simulations were compared with surface oil-flow visualisations on the physical model of the biomimetic surface placed in a flow channel. The results show an excellent agreement in the size and arrangement of the streaky structures. The existence of streaks is also shown on sea bass and common carp (Cyprinus carpio) by surface flow visualisation. From comparisons with recent literature on micro-roughness effects on laminar boundary layer flows, it is hypothesised that the fish scales could delay transition, which would further reduce the drag.