On Interaction Between Falling Bodies and the Surrounding Fluid

Abstract

Abstract. Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body-fluid interaction holding for the case of many bodies. §1. Introduction. The study of interactions between moving solid bodies and the surrounding fluid has many natural, industrial and biomedical applications. These and background motivations are considered in §1.1. Previous studies are discussed in §1.2, and §1.3 focuses on the present work.1.1. Applications and motivation. A great many applications arise across nature such as with falling leaves and moving seeds and coffee grains (e.g. [4, 7, 27, 52]), not to forget the motion of frozen ice particles and hailstones as well as sedimentation and fluidization phenomena. Applications also arise in sporting contexts such as running and cycling groups and to some extent in longdistance swimming competitions. The behaviours of various swarms similarly have an interactive fluid-dynamical element to them, while a communication to the authors has pointed out the collisions of ships due to rushing water and suction between them, as occurred for example during the UK-Iceland cod war and the similar danger of suction for barges in the Suez Canal.Three industrial applications are concerned with the falling of lumps of ice into an engine intake in an aerodynamic safety context, the travel of windblown particles of ice along a wing surface again in the aerodynamic safety context, and the falling of rice grains down a chute in a food-sorting context. In addition various disintegration, deposition, oil-well and sequestration modelling applications exist for interactions between solid bodies and fluids.There are also many biomedical applications in principle, for example to travel of solids within vessels of major networks in the human body. Specific applications are to transport of blood clots, embolization procedures in stroke

Collisions, rebounds and skimming

“…These produce in particular spin-off suggestions on tackling anew multi-body problems as in [13][14][15] and are even linked through the dynamics of fluid-body interactions to predictions and observations on the movement of dust on the planet Mars [15]. They can also include viscous effects as in the theory of air cushioning in [3], which in turn leads on to air-pocket properties in [5] and most recently to Hicks et al [28], who show close and encouraging connections between theory and experimental measurements.…”

“…Special mention should be made of phenomena in aircraft icing, storms, engine intakes, ship-slamming and meteor impacts. There is a wide background of recent literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], major aspects of which we summarize later in the introduction.…”

“…The third area of direct relevance is fluid-body interactions [13][14][15]. Interactions between a finite number of bodies and the surrounding fluid are investigated in [13].…”

“…Interactions between a finite number of bodies and the surrounding fluid are investigated in [13]. The bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid.…”

Fluid–body interactions: clashing, skimming, bouncing

“…There is also a huge number of biomedical applications [21][22][23][24][25][26][27][28][29][30][31], while sports applications are such as in skeleton bobsleigh. The work is on fluid-body interaction [32]. The article is aimed mostly at analytical understanding and results.…”