WALKING ON WATER: Biolocomotion at the Interface

Abstract

We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics.

Capillary-Gravity Waves Generated by a Slow Moving Object

“…We consider the special case of a uniform circular trajectory, a situation of particular importance for the study of whirligig beetles (Gyrinidae, [16]) whose characteristic circular motion might facilitate the emission of surface waves that they are thought to be used for echolocation [17,18]. This work is therefore restricted to the effect of a wake stationary in the rotating frame, and do not consider time dependent contributions, like vortex shedding [27,29].We consider the case of an incompressible infinitely deep liquid whose free surface is unlimited. In the absence of external perturbation, the free surface is flat and each of its points can be described by a radius vector r = (x, y) in the horizontal plane.…”

“…It would be very interesting to know if whirligig beetles can take advantage of such spirals for echolocation purposes. Although restricted to stationary wakes and thus excluded effects such as vortex shedding, the results presented in this letter should be important for a better understanding of the propulsion of water-walking insects [26,27,28,29] where accelerated motions frequently occurs (e.g when hunting a prey or escaping a predator [30]). Even in the case where the insect motion is rectilinear and uniform, one has to keep in mind that the rapid leg strokes are accelerated and might produce a wave drag even below c min .…”

Can flexibility help you float?

“…Many biological organisms that float, such as hydrophytes (e.g., water lilies) and water walking insects, 3 are not entirely rigid. There are several reasons for organisms to be flexible, including decreased weight and increased robustness when subjected to external forces.…”

“…The insect Anurida attracts others of its kind by bending its back and deforming the interface, so that a colony can behave like a self-assembling raft. 3 Other such living rafts may form from assemblages of mosquito eggs 6 or whirligig beetles. 7 Though individual ants flounder at the interface, ant rafts, comprised of thousands of individuals, are able to stay afloat for months in the flood-prone rain forests of Brazil.…”

“…Plates with k s < k * s are bent and support slightly smaller loads, while stiffer plates remain flat. For plates much larger than the capillary length, β 1, the force and torque balances become, respectively: 2βD ≈ β 2 cos α sin α, and 4k s α + Dβ 2 cos α ≈ β 3 3 sin α, when k s ∼ O(β 3 ). The force and torque balances are now prescribed by the spring, the weight of the plate, and hydrostatic pressure.…”