Geoscience Reference
In-Depth Information
7.1 Turbulent Bursting
Experimental evidences on the viscous sublayer by Kline et al. (
1967
), Corino and
Brodkey (
1969
), and Grass (
1971
) revealed a viscous dominating flow characteris-
tic that consists of large three-dimensional high- and low-speed fluid steaks. The
near-bed flow has an extremely complex structure producing large turbulence
(Nezu and Nakagawa
1993
). The emission of low-speed fluid streaks entraining
to high-speed fluid streaks initiates the process of turbulent burst. The sequence
turbulence bursting is described by two significant features as ejections and sweeps,
which play an important role on entrainment of sediments. During the ejections, the
upward flow enlarges the shear layer and the associated small-scale flow structures
to a wide region. The ejection process is prevalent as low-speed fluid streaks that
oscillate in three-dimension lifts up from the bed and then collapse to entrain into
the main body of flow. The ejected fluid streaks which remain as a result of
retardation are brushed away by high-speed fluid approaching to the bed in a
process called the sweeps. During sweeps, the downward flow generates a narrow,
highly turbulent shear layer containing multiple small-scale eddies. The turbulent
bursting process and the contributions from the conditional Reynolds shear stress
towards the total shear stress can be described by a quadrant analysis.
7.2 Quadrant Analysis
To understand the characteristics of the bursting events, it is necessary to study the
conditional statistics of the velocity fluctuations (
u
0
and
w
0
) plotting them to quad-
rants on a
u
0
w
0
-plane (Lu and Willmarth
197
3
).
A
hole-size
parameter
H
is used
discriminating the larger contributions to
u
0
w
0
from each quadrant leaving the
smaller
u
0
and
w
0
correspon
ding
to
more
quiescent periods (Nezu and Nakagawa
1993
). The curve
u
0
w
0
0
:
5
determines the hyperbolic hole region.
In this way, a clear distinction is achieved between the strong and the weak events for
a small hole-size and only strong events for a large hole-size. The types of bursting
events are characterized by four quadrants
i
(
0
:
5
j
j ¼
H
ð
u
0
u
0
Þ
ð
w
0
w
0
Þ
¼
1, 2, 3 and 4). They are (1)
outward
1;
u
0
>
0,
w
0
>
interactions or Q
1
events
(
i
¼
0), (2)
ejections or Q
2
events
(
i
¼
2;
u
0
<
0,
w
0
>
3;
u
0
<
0,
w
0
<
0), (3)
inward interactions or Q
3
events
(
i
¼
0), and
4;
u
0
>
0,
w
0
<
(4)
sweeps or Q
4
events
(
i
0 implies that
all data of
u
0
and
w
0
are taken into account. The quadrant
anal
ysis pr
ovid
es an
estimation of the fractional contributions
S
i ;H
ð¼
¼
0). The hole-size
H
¼
u
0
w
0
from
the bursting ev
ents
for quadrant
i
outside the hole region of size
H
. The contribution
u
0
w
0
u
0
w
0
i
i;H
=
u
0
w
0
)to
h
u
0
w
0
from the quadrant
i
outside the hole of size
H
is estimated by:
h
i
i
;H
to
ð
T
1
T
u
0
w
0
u
0
ð
w
0
ð
h
i
i;H
¼
lim
T!1
t
Þ
t
Þl
i;H
ð
z
;
t
Þ
dt
(19)
0
