A heavy body translating in a boundary layer: ‘crash’, ‘fly away’ and ‘bouncing’ responses

Abstract

The study concerns a slender, heavy body moving with streamwise velocity in a boundary layer. Modelling assumptions on body size reduce the governing equations for the body motion to a pair of nonlinear integro-differential equations (IDEs) which displays a wide range of distinguished behaviours, including eventual collision with the wall (‘crash’), escape to infinity (‘fly away’) and repeatedly travelling far from the wall and back again without ever colliding or escaping (‘bouncing’). The paper gives a survey of the variety of behaviour, as well as asymptotic analysis and insight into each category of fluid/body interaction and the conditions under which crash, fly away and bouncing occur.

On modelling fluid/body interactions, impacts and lift-offs

“…The study of impacts in external flows as in Fig. 1b constitutes more recent work [21,22]. It is similar to the work which has been described above but it accommodates three extra or novel factors.…”

“…Here there is body-air-wall interaction in which the body travels through an air boundary layer on top of a wall 2) [21].…”

“…Features of fly-away in other contexts are described in more recent works. These address the influence of nonzero incident vorticity in both inviscid and viscous scenarios 2) [20,21]. An alternative outcome is so-called bouncing [21] as illustrated in Fig.…”

“…These address the influence of nonzero incident vorticity in both inviscid and viscous scenarios 2) [20,21]. An alternative outcome is so-called bouncing [21] as illustrated in Fig. 8, where, repeatedly, the body nearly impacts on the wall but then flies to large heights before once more returning to nearly hit the wall and so on.…”