5% - eTheses Repository - University of Birmingham

the vortex axis. Vortex circulation was counter clockwise with
magnitude such that peak tangential velocity was 6VT (arbitrary
selection), ie the non-dimensional parameter AR/VT=6. We begin
our description with the trajectory marked (*--*), initially
deflected leftwards with the flow. The relative non-dimensional
transit times T^ (equal to actual fall time less the time taken
to fall an equal distance in quiescent water; the quiescent fall
time, TQ ) for these trajectories appear in figure 6b (recall:
non-dimensionalised on R and VT ) . Figure 6c shows magnified
details of key trajectories whereas figure 6d shows other
behaviour to which we shall return later. The forces acting on
the particle as it fell along the *'d trajectory are shown in
vector form in figure 6e. We see buoyancy force (B) acted
downwards throughout its transit whereas the instantaneous drag
(D) initially acted in the direction of the flow when the
particle was at rest, and at later times acted almost vertically
upwards as the particle approached vertical motion with slip
speed VT . Of course, contribution from the local pressure
gradient or fluid acceleration (PI) always acted towards the
vortex axis.
Returning to figure 6a, and shifting the starting position
rightwards, we see the trajectories are increasingly curved due
to the higher pressure gradient and drag forces. The trajectory
in figure 6f clearly exhibits this behaviour. For a starting
point immediately below the vortex axis (figure 6g) , this PI
force was dominant and the particle was accelerated inwards and
around the core until its angular momentum eventually overwhelmed
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