Effect of aspect ratio in free-swimming plunging flexible plates

• Three dimensional computer simulations are used to study sinusoidally plunging elastic plates in free swimming.
• Effects of changing aspect ratio and driving frequency are investigated.
• Swimming velocity is fastest near the first natural frequency regardless of aspect ratio.
• Low aspect ratio plates swim faster and more economically due to reduced drag associated with side edge vortices.

We use three dimensional computer simulations to investigate the free swimming of plunging elastic plates with aspect ratios ranging from 0.5 to 5 in a viscous fluid with Reynolds number 250. We show that maximum velocity occurs near the first natural frequency regardless of aspect ratio, whereas the maximum swimming economy occurs away from the first natural frequency and is associated with a specific swimmer bending pattern. Moreover, we show that the low aspect ratio swimmers, those with wider spans, are not only the fastest but also the most economical. The faster speeds are associated with a decrease in effective drag for low aspect ratio plunging swimmers. We find that the recently proposed vortex-induced drag model adequately explains the drag reduction by suggesting that the smaller relative size of side vortices in low aspect ratio swimmers creates less drag per unit width.