There are infinite numbers of possible arrangements of two parallel cylinders positioned at right angles to the approaching flow direction. Of the infinite arrangements, two distinct groups may be identified: in one group, the cylinders are in a tandem arrangement, one behind the other at any longitudinal spacing; and in the second group, the cylinders face the flow side by side at any transverse spacing. All other combinations of longitudinal and transverse spacings represent staggered arrangements. The tandem arrangement will be treated first. A critical survey of previous research revealed some “odd” features which had been observed and overlooked by various authors. The discontinuity of vortex shedding implies that a similar discontinuity should be expected for the drag force on both cylinders. The measurements of the front (gap) pressures of the downstream cylinder and the base pressures of both cylinders at various spacings reveal a discontinuous “jump” at some critical spacing. The discontinuity is caused by the abrupt change from one stable flow pattern to another at the critical spacing. A new interpretation is given for the existing data on the drag force for both cylinders. The effects of Reynolds number and surface roughness are treated in some detail. Following this, two cylinders arranged side by side to the approaching flow are considered. All the available data on measured forces are compiled together with additional measurements in the range of intermittent changes of drag and lift forces. The bistable nature of the asymmetric flow pattern around each cylinder produces two alternative values of the drag force coupled with two alternative values of the lift force. The introduction of the interference force coefficient exposes the physical origin of two different forces experienced by the cylinders when arranged side by side. Finally, the least reported arrangement of two staggered cylinders is reviewed. The various arrangements are grouped into classes according to the sign of the lift force, or whether the drag force is greater or less than that for a single cylinder. The measurements of drag and lift forces for various arrangements reveal two different regimes for the lift force. In one regime, the lift force directed toward the wake of the upstream cylinder is due to the entrainment of the flow into the fully developed wake of the upstream cylinder. The lift force in this regime reaches a maximum value when the downstream cylinder is near to the upstream wake boundary. In the second regime, at very small spacings, the lift force becomes very large due to an intense gap flow which displaces the wake of the upstream cylinder. The maximum lift force occurs with the downstream cylinder near to the horizontal axis of the upstream cylinder. A discontinuity in the lift force for some staggered arrangements is found and attributed to the bistable nature of the gap flow.
A Continuum Model of Drag and Lift Forces for Inclined Planes Dragged Through Granular Beds