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inclined downwards whereas the time-dependent trajectory follows a near
cycloid path.
Figure 18. Table of maximum fluctuating velocities u,v=f. Johns (1991)
prescribes u=E and v=0.35E where E is the turbulence energy density in (m/s) 2
which has a peak value 0.018. We then assume a sinusoidal distribution for
the fluctuating parameters which classically gives (f 2 )max = 1.414 (f 2 )mean.
Data from Nakagawa & Nezu (1987) gives u,v directly.
Chapter 6
Figure 1. Schematic of the shear layer that develops after the crest of a
sandwave with oncoming mean flow U. The first generation vortices form at a
distance d 0 downstream of the crest with a radius R0 . Two such vortices pair,
after travelling a distance x, forming a second generation vortex with double
the length scale and hence half the vorticity (circulation/area).
Figure 2. The parameter space diagram for a particle of quiescent fall speed
V=0.076m/s at a vortex growth rate G=0.01m/s. The pictures A-F show the
particle trajectories, in a frame of reference moving with the vortex, at the
point in parameter space where the centre dotted circle (core radius) lies.
The vortices rotate in an anti-clockwise direction. Below the low (L) and
high (H) values of A, at one specific radius, the particle trajectory contains
a number of loops (the capture trajectories) .
Figure 3. Seven trajectory plots corresponding to the points in parameter
space marked by the circles in figure 2. G&H correspond to trajectories in
the particle dominated region whereas K,L & M correspond to three in the fluid
dominated region. I & J are capture trajectories seen in the central region
of the parameter space where neither fluid forces nor gravity is dominant.
Figure 4. An example of the internal structure within the region of parameter
space enclosed by the heavy lines in figure 2. The number on each line
corresponds to the number of times that the particle loops up to the
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