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Chapter 3
Results and Discussion
3.1 Temporal Development of Horizontal Vortices
The development of horizontal vortices can be described by using numerical computation
as follow:
a. Velocity and vorciticy field as shown in figure 3.2 and 3.3, respectively, at several
times, , , , , and , indicating that
small scale horizontal vortices appear first and they grow by merging with each
other. In the beginning flow, appears weak flow with the corresponding
accumulation of vortices in five regions. After t = 90 s, the spatial pattern of
velocity and vorticity has been found to reach an equilibrium state which the two
large vortices formed.
b. The longitudinal wavelength of vortices varies between 60 cm and 110 cm in
statistical equilibrium.
c. The value of the wavelength both experiment and simulation are shown in table
3.1. The mean value of the wavelength of the vortices predicted (simulation) at the
observation point is 61.4 cm. The corresponding length was 58.6, which agrees
with the prediction. The calculation for finding the time period (T) of the
wavelength is done with Fast Fourier Transform (FFT). The result of spectrum
graph is depicted in figure 3.3.
d. Figure 3.5 and 3.6 give comparison which it is found that the regions with water
surface depression nearly coincide with the central parts of horizontal vortices.
Table 3. 1 Comparison value of wavelength ( ).
u (cm/s) Re Froude T (s) λ measured (cm)Simulation 23.9675 14381 0.312 2.56 61.4Measured 20.55 12330 0.268 2.85 58.6
32
CHAPTER 3 RESULTS AND DISCUSSION
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (sec)
h (m
m)
Figure 3. 1 Variation of water surface elevation at measurement point (numerical calculation)
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (sec)
l (c
m)
Figure 3. 2 Variation of wave length at measurement point (numerical calculation)
33
CHAPTER 3 RESULTS AND DISCUSSION
Figure 3. 3 Result of FFT
34
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(a) t = 10 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(b) t = 30 sFigure 3. 4 Temporal development of horizontal vortices; Spatial distribution velocity at (a) t=10 sec, (b) t = 30 s.
35
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(c) t = 60 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(d) t = 90 sFigure 3.4 Temporal development of horizontal vortices; Spatial distribution velocity at (c) t=60 sec, (d) t = 90 s (continued).
36
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(e) t = 120 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.3m/secFlow
Frame 001 25 Aug 2006 Vector
(f) t = 150 sFigure 3.4 Temporal development of horizontal vortices; Spatial distribution velocity at (e) t=120 sec, (f) t = 150 s (continued).
37
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(a) t = 10 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(b) t = 30 sFigure 3. 5 Temporal development of horizontal vortices; Spatial distribution vorticity at (a) t=10 sec, (b) t = 30 s.
38
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(c) t = 60 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(d) t = 90 sFigure 3.5 Temporal development of horizontal vortices; Spatial distribution vorticity at (c) t=60 sec, (d) t = 90 s (continued).
39
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(e) t = 120 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Flow
Frame 001 25 Aug 2006 Vector
(f) t = 150 sFigure 3.5 Temporal development of horizontal vortices; Spatial distribution vorticity at (c) t=120 sec, (d) t = 150 s (continued).
40
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(a) t = 10 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(b) t = 30 sFigure 3. 6 Temporal development of horizontal vortices; spatial distribution water surface at (a) t=10 sec, (b) t = 30 s.
41
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(c) t = 60 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(d) t = 90 sFigure 3.6 Temporal development of horizontal vortices; spatial distribution water surface at (c) t=60 sec, (d) t = 90 s (continued).
42
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(e) t = 120 s
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012mFlow
Frame 001 14 Sep 2006 Vector
(f) t = 150 sFigure 3.6 Temporal development of horizontal vortices; spatial distribution water surface at (e) t=120 sec, (f) t = 150 s (continued).
43
CHAPTER 3 RESULTS AND DISCUSSION
3.2 Instantaneous Flow Field
The instantaneous 2D velocity with water surface contour and vorticity field are depicted
in figure 3.5 and 3.6, respectively, in which the velocity field is seen in the frame moving
with the temporally averaged velocity at the boundary of the main channel and the flood
channel (y = 16 cm). The maximum vorticity locates upstream of the geometrical center of
the vortex. The vortices are inclined toward the longitudinal direction, which is important
in producing the Reynolds stress.
The instantaneous free surface elevation calculated is shown in Figure 3.4, in which it is
clear that the elevation is low near the center of the vortices. The variations of free surface
elevation at y = 16 cm are depicted in figure 3.7 and 3.8 for the measurement and
prediction, respectively. In the measurement graph, the form is quite different with the
prediction, but the range of the variation of height water surface and time period are
similar. The calculation of period time gives the same result.
44
CHAPTER 3 RESULTS AND DISCUSSION
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
eta: -0.00016m -0.00012m -8E-05m -4E-05m -8.13152E-20m 4E-05m 8E-05m 0.00012m0.3 m/secFlow
Frame 001 14 Sep 2006 Velocity
Figure 3. 7 2D velocity with water surface contour.
x (m)
y(m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
vor: -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.50.3 m/secFlow
Frame 001 25 Aug 2006 Velocity
Figure 3. 8 2D velocity with vorticity contour.
45
CHAPTER 3 RESULTS AND DISCUSSION
Figure 3. 9 Temporal variation of free surface (measured).
Figure 3. 10 Calculated variation of free surface.
3.3 Temporally-averaged Flow Field
The lateral velocity distribution is shown in figure 3.9 The agreement is reasonable.
However, the measured values near y = 17 cm are a little smaller than the prediction, the
reason for which is the existence of secondary flow which is fairly large near the boundary
of the main channel and the flood plain. It transports near-bottom small fluid momentum
toward the free surface, inducing small longitudinal flow velocity at around y = 20 cm. The
present model cannot include the effect of secondary flow.
46
CHAPTER 3 RESULT AND DISCUSSION
0
5
10
15
20
25
30
35
40
45
50
00.050.10.150.20.250.30.350.4
y (cm)
(cm
/sec
)
ExperimentNumerical Simulation
u
Figure 3. 11 Transverse profiles of mean velocity.
47
(cm/s)
CHAPTER 3 RESULT AND DISCUSSION
Chapter 3..............................................................................................................................32
Result and Discussion..........................................................................................................32
3.1 Temporal Development of Horizontal Vortices...................................................32
3.2 Instantaneous Flow Field.....................................................................................44
3.3 Temporally-averaged Flow Field.........................................................................46
Figure 3. 1 Variation of water surface elevation at measurement point (numerical calculation)................................................................................................33
Figure 3. 2 Variation of wave length at measurement point (numerical calculation).......................................................................................................................33
Figure 3. 3 Result of FFT.............................................................................................34
Figure 3. 4 Temporal development of horizontal vortices; Spatial distribution velocity at (a) t=10 sec, (b) t = 30 s.............................................35
Figure 3. 5 Temporal development of horizontal vortices; Spatial distribution vorticity at (a) t=10 sec, (b) t = 30 s............................................38
Figure 3. 6 Temporal development of horizontal vortices; spatial distribution water surface at (a) t=10 sec, (b) t = 30 s.............................41
Figure 3. 7 2D velocity with water surface contour........................................45
Figure 3. 8 2D velocity with vorticity contour...................................................45
Figure 3. 9 Temporal variation of free surface (measured).........................46
Figure 3. 10 Calculated variation of free surface.........................................46
Figure 3. 11 Transverse profiles of mean velocity.......................................47
Table 3. 1 Comparison value of wavelength ( )................................................................32
48
