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(a)
(c)
(b)
(d)
Sweep front
Sweep front
(e)
hv
hv
hv
hv
Fig. 4.18 Visualizations of turbulence structure: (a) Sketch by Leonardo to show turbulence generated at a hydraulic jump. Note impression of
“coils” of turbulent eddies. (b)-(d) Views from above to show deformation of H 2 -bubbles generated along a speck-insulated platinum wire on
the left of each frame (see Fig. 29.2). Each instantaneous view is taken successively higher in the same flow: (b) shows sublayer streaky struc-
ture developing downflow, (c) shows streaks entangling and mixing as the vortices rise up through the boundary layer, and (d) shows a view
high in the boundary layer where turbulence is restricted to a few advected “blobs.” (e) Side view of smoke visualization to show the 2D
structure of large-scale turbulence and the pattern of subsidiary hairpin burst vortices (hv) lifted by the upstream-inclined shear layers (dashed
white lines) that define sweep inflows at the interface of major fast outer (dark) and slower (white) inner flow fluid. Smoke was released at the
bed just upstream from the frame.
Making the assumption that viscous stresses dominate, the
simplest option open to us is to assume that Newton's vis-
cous stress equation,
z
0, yields the appropriate flow law, u
0 z /
, where
0 is the viscous shear stress at the boundary.
Further out in the flow, observations (Section 4.3) show
a decrease in rate of change of velocity, d u /d z , with height
d u /d z operates. Integration
(Cookie 10) for the no-slip boundary condition, u
0 at
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