Vertical water entry of disks at low Froude numbers

Abstract

As basilisk lizards (Basiliscus basiliscus) and shore birds run along the water surface they support their body weight by slapping and stroking into the water with their feet. The foot motions exploit the hydrodynamic forces of low-speed water entry. To determine the forces that are produced during water entry at low speeds, we measured directly the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1–80). Also, we measured the period during which the air cavity behind the disk remains open to atmospheric air. We found that the force impulse produced during the impact phase is due to the acceleration of the virtual mass of fluid associated with a disk at the water surface. A dimensionless virtual mass M, defined as M=mvirtual/(4/3)πρr3, has a value near 1/π for disks. After impact, as penetration depth of the disk increases, the drag force can rise by as much as 76% even though the downward velocity is steady. However, a dimensionless force which includes the contribution from hydrostatic pressure [CD*=Drag(t)/(ρSgh(t)+0.5ρSu2)] takes a constant value near 0.7 regardless of disk size, speed, or cavity depth. Over the entire range of disk sizes and velocities, the period between impact and cavity closure, Tseal, can be described by a single value of dimensionless time, τ=Tseal(g/r)0.5, near 2.3. We con- clude that the fundamental phenomena associated with the low-speed water entry of a disk can be characterized by three dimensionless numbers (M, CD*, and τ).