On the vortex wake of an animal flying in a confined volume

Abstract

When an animal flies near a boundary, the airflows it generates interact with that boundary. These interactions may have a significant effect on flight performance, as measured by quantities such as the energy rate to sustain flight, or the circulation of the vortices bound on the wing or shed in the wake (or, equivalently, by the lift and induced drag coefficients). The problem of hovering and slow flight within a confined volume is considered by a theoretical model based on helicopter practice, and by flow visualization experiments. The wake takes the form of a strong recirculating flow within the volume, and because of this recirculation the boundaries appear to cause a large reduction in the induced power required for sustained flight, even when their distance from the animal is several times greater than the wingspan. The correction factor relative to ideal momentum jet theory is greater than for the hovering ground effect, forward flight ground effect, or wind tunnel wall interference problems at comparable distances. The flow pattern that develops in the presence of floor and wall interactions in hovering or slow flight includes a large-diameter vortex ring trapped underneath the animal; this vortex ring is conjectured to be analogous to that below a helicopter in slow descending flight in the 'vortex ring state’. Performance measurements for animals in hovering flight within a confined volume may underestimate power for free hovering by a significant margin. Comparable boundary effects may also be important in confined forward flight. Because of speed-related changes in the wake, and the rise in induced power at lower speeds, the appropriate correction to total mechanical power is dependent on air speed, becoming progressively greater as speed reduces. Some wind tunnel measurements of total metabolic power have produced the apparently anomalous result that power is independent of flight speed within measurement error. These observations may be explained - at least in part - by boundary effects caused by interaction between the wake and the walls of the wind tunnel.