Geometric and migrating characteristics
of superimposed bedforms under
oscillatory flows
By
Yovanni Cataño
And
Marcelo H. García
Ven Te Chow Hydrosystems Laboratory
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
2005
1
Outline







Acknowledgements
Motivation
Experimental setup
Formation of superposed bedforms under
oscillatory flows
Main results: (a) Sandwaves
(b) Ripples
Conclusions
Future work
2
Acknowledgements



Coastal Geosciences Program of the U.S.
Office of Naval Research Grant: N0001405-1-0083
Prof. James Best University of Leeds (UK)
Prof. David Admiral University of Nebraska
3
Motivation




Understanding formation and evolution of coexisting
bedforms under combined flows
Important for the interaction of bedforms with coastal
structures: pipelines, cables, cylinders, bridge piers,
breakwaters…
Other applications include the exploitation of sands for
construction purposes
Implications on effective roughness height induced by
bedforms.
4
Experimental setup
11
10
5
7
9
6
4
0.9 m 1.8 m
4
8
0.31 m
1.2 m 6.2 m
2
13
1.20 m
12
1
3
24 m
1.8 m 1.8 m
z
x y
49 m
1. wave flume; 2. wavemaker paddle; 3. injection of current; 4. wooden ramp; 5. waves; 6. Seatek sensors;
7. superimposed current; 8. sandy bed; 9. beach; 10. sediment trap; 11. movable carriage; 12. water
surface acoustic sensor; 13. ADV probe.
5
Bedform formation and evolution
6
Amalgamated bedforms
Survey with the Seatek sensors
Bed configuration with the presence of 2D and 3D ripples. Hydraulic conditions: Tw = 3.4 s, Hw =
10.7 cm, Lw = 7.7 m. Horizontal and transverse resolutions are 1 cm, and 4 cms, respectively.
7
Typical view of ripples superimposed on a sandwave under WA.
8
Results: sandwaves
10
Present study, WA
hsw / a
Present study, CF
1
Power (Present
study, WA)
Measured dimensionless sandwave
height as a function of the
Reynolds wave number.
0.1
h sw /a = 175.76R ew
ρ 2 = 0.34
-0.54
0.01
100000
1000000
R ew
1000
Present study, WA
Present study, CF
100
Power (Present study,
WA)
lsw / a
10000
Measured dimensionless sandwave
length as a function of the Reynolds
wave number.
10
l sw /a = 10024R ew -0.56
ρ 2 = 0.65
1
10000
100000
R ew
91000000
10
harmonics
Present study, WA
Dimensionless sandwave length as a
function of the Reynolds wave
number
1
0.1
10000
L sw / L w = 0.44
100000
1000000
R ew
10
1
Measured sandwave vertical growth
rate as a function of the Reynolds wave
number.
Vgr (cm/hr)
Lsw / Lw
Present study, CF
0.1
0.01
WA, present study
CF, present study
0.001
10000
100000
R ew
10
1000000
Evolution over time of a measured bed profile
11
0.8
0.7
Vgr (cm/hour)
0.6
0.5
0.4
0.3
0.2
0.1
0
0 to 0.5
0.5 to 1
1 to 1.5
1.5 to 2
2 to 3
3 to 4
Interval (hours)
4 to 6
6 to 26
26 to 50
Vertical growth rate of sandwave as a function of time.
Case of waves alone.
12
Csw / Uwc
0.0001
0.00001
Present study, WA
Present study, CF
0.000001
10000
100000
R ew
1000000
Measured dimensionless sandwave migration speed
as a function of the Reynolds wave number.
13
Main findings: Sandwave formation and evolution
Experiments for: 10 < ψwc < 88; 16000 < Rew < 500000, and 0.09 < θ < 0.54
For flat bed conditions
•Sandwave geometry parameters such as height, length, and steepness show less
scatter, although considerable, when plotted against Rew than for the case of ψwc or θ.
•Both sandwave length and height decrease as the Reynolds wave number increases
•Dimensionless sandwave migration speed increases as the Reynolds wave number
increases.
•Preliminary analysis suggest the existence of a simple relationship between the
sandwave length (Lsw) and wavelength of the surface wave (Lw)
14
Results: Ripples superimposed to sandwaves
Geometry
Ripples over crest
10
lr / a
Measured, WA
Predicted by Eq. 6.7, WA
Measured, CF
Predicted by Eq.6. 7, CF
Dimensionless mean ripple
wave length as a function of
the Reynolds wave number
defined as Rew = Uwc a / ν.
With ψwc
1
1
100000
R ew
1000000
0.1
Dimensionless mean ripple
wave height as a function of the
Reynolds wave number defined
as Rew = Uwc a / ν.
With ψwc
hr / a
0.1
10000
0.01
0.001
0.0001
10000
Measured, WA
Predicted by Eq. 6.10, WA
Measured, CF
Predicted by Eq. 6.10, CF
100000
R ew
1000000
15
Ripple speed
7
6
Cr (m/day)
5
4
3
2
1
0
Flat bed
Over Crest
Between crest and
trough
Trough
Variation of ripple speed depending on its relative position over
the sandwave under waves alone.
16
Larger asymmetry
Smaller asymmetry
Measured velocity profiles after 34 hrs. ΔX = 25.4 cm.
17
0.0010
0.0008
Cr/Uwc = 0.0002Ln(ψ wc) - 0.0003
2
R = 0.41
0.0006
Cr / Uwc
0.0004
0.0002
0.0000
Present study, WA
-0.0002
Present study, CF
Cr/Uwc = 0.0002Ln(ψwc) - 0.0007
R2 = 0.78
Faraci & Foti (2002), Regular
waves
Faraci & Foti (2002), Random
waves
-0.0004
-0.0006
1
10
ψ wc
100
Mean value of measured dimensionless ripple speed as a function
of the mobility number.
18
Main findings
10 < ψwc < 88 and 16000 < Rew < 500000, and 0.09 < θ < 0.54
For flat bed conditions

Ripples size, shape and speed vary depending
on their relative position over the sandwave.

Measured ripple length and height show strong
dependency on the Reynolds wave number Rew
for WA and CF.
19
Thank you!
Any questions?
20
Proposed experimental work (continuation)
• Since the ripple washout mechanism continues to be unclear, it is proposed to
reproduce higher values of the mobility number similar to those observed in the field.
• Since bedforms are subjected to irregular flows in the field, it is easy to understand the
urgent need to conduct laboratory experiments with the combination of irregular waves
and currents.
• Perform measurements of sediment concentration profiles along sandwave.
Signal Analysis of Time Series and Bottom Records
• To explore convenience of using Hilbert and wavelet techniques along of FFT, and
Spectral Analysis
Predictive tools
• It is proposed to explore the use of analytical approaches, such as stability analysis and
weakly non-linear theory, Mei theory.
21
Shortcomings &
Recommendations

Use of linear small wave theory (Rigorously: Cnoidal, 2nd order Stoke’s theory)

Include in the calculations of θ the effect of form drag due to ripples and
sandwaves.

Non-linearity due to beach reflection, and wavemaker?

So far, work with Uc < 20 cm/s

Due to a changing bed (Ripples and sandwaves), only mean velocity are suitable for
description of global processes.

No turbulence characterization over ripples and sandwaves.

Better to use of PIV (Particle Image Velocimetry) or ADVP techniques (Acoustic
Doppler Velocimeter Profiler)-> resolve turbulence, others….
22
Additional work would include:

To perform refined velocity measurements over an artificial fixed sandwave (If ADV is the
only instrument available).

-Examine Reynolds stresses distribution and momentum fluxes over three and two
dimensional ripples superimposed on sandwaves.
- Estimation of the distribution of the friction factor fw, and roughness length zo, over the
bedforms.
- The implications for sediment transport characteristics would also be understood.
- Will help future development of numerical and analytical models dealing with the
morphodynamics of the studied bedforms.

With movable bed: The effects due to ripples and sandwaves must be separated to obtain a
better description of the hydrodynamic processes over the whole flow field. ADV not
suitable. It is better to use PIV (Particle Image Velocimetry) or ADVP (Acoustic Doppler
Velocity Profiler) techniques where spatial and temporal resolution can be significantly
improved.

Since bedforms are subjected to irregular flows in the field, it is easy to understand the
urgent need to conduct laboratory experiments with the combination of irregular waves and
currents.
23
References
Cataño-Lopera, Y. and García, M.H., (2005e). “Geometry and Migration Characteristics of Bedforms under
Waves and Currents: Part 1, Sandwave morphodynamics.” Submitted to Coastal Engineering.
Cataño-Lopera, Y. and García, M.H., (2005f). “Geometry and Migration Characteristics of Bedforms under
Waves and Currents: Part 2, Ripples Superimposed on Sandwaves.” Submitted to Coastal Engineering.
Cataño-Lopera, Y. and García, M.H., (2005g). "Geometric and migrating Characteristics of Amalgamated
Bedforms under Oscillatory Flows." Proceedings of the 4th IAHR Symposium on River, Coastal and
Estuarine Morphodynamics, University of Illinois, October 4-7.
Faraci, C. and Foti, E., (2002). “Geometry, migration and evolution of small-scale bedforms generated by
regular and irregular waves.” Coastal Engineering, 47, 35-52.
Williams, J.J., Bell , P.S. and Thorne, P.D., (2005). “Unifying large and small wave-generated ripples.” J.
Geophys. Res., 110 (CO2008).
24
a
d = fluid orbital diameter
RE 
U
fm
 
U ma


Reynolds wave number
fw
Um
2
U 2fm
Shear velocity
Shields parameter
Go back
g ( s  1)d
U m2
w 
s  1gd 50
Mobility number
25
45
40
35
30
25
20
15
10
5
0
0
500
1000
1500
2000
2500
26
Influence of development and migration of bedforms on
the burial process
Type of bedforms
Typical length
L
0.04 – 0.6 m
Ripples
0.6 – 30 m
Mega ripples
30 – 1000 m
Sandwaves
Typical height
H
Length/height ratio
0.003 – 0.06 m
8 – 15
0.06 – 1.5 m
> 15
1.5 – 15 m
> 30
Table 1. Ref. Reineck, H.-E, Singh, I.B., and Wunderlich, F., 1971.
Bedform
type
(sandy bed)
Related flow
Wavelength
L (m)
Amplitude
A (m)
Time scale
T
Migration
rate C
Ripples
Instant flow
~1
~ 0.01
hrs
~ 1 m/day
Storm, surges
~ 10
~ 0.1
Days
~ 100
m/ye
ar
Years
~ 10
m/ye
ar
Megaripples
Sandwaves
Long bed
waves
Tidal
sandb
anks
Tide
~ 500
~5
Unknown
~ 1500
~5
Unknown
Tide
~ 5000
~ 10
Century
Laser image of a sharp boundary between
sand waves (top left corner) and
Unknown
smooth seafloor.
~ 1 m/year
Table 2. Ref. Characteristics of offshore sand bedforms, Morelissen, R., et al.
Coastal Engineering (2003), 197-209
27
Also…..
Other contributors:
ONR program: Theoretical and field: Gallagher et al. (1998)
Theoretical and Laboratory: C. C. Mei, MIT (2002)
Theoretical (Stability analysis), numerical modeling, and field of sandwaves: Amos,
Németh, Komarova, Holsters, Gekerma, others....
28
10
lr / a
Regular waves, (Faraci & Foti, 2001)
Irregular waves, (Faraci & Foti, 2001)
Lab. data (Nielsen, 1981)
Field data (Nielsen, 1981)
Waves alone (Khelifa & Ouellet, 2000)
Combined flow (Khelifa & Ouellet, 2000)
Lab. data, CF (Khelifa & Ouellet, 2000)
Present study, WA
Present study, CF
1
0.1
1
10
ψwc
100
1000
Dimensionless ripple length as a function of the mobility
number under waves alone and combined flow.
Back
29
hr / a
1
Regular waves, (Faraci & Foti, 2001)
Irregular waves, (Faraci & Foti, 2001)
Lab. data (Nielsen, 1981)
Field data (Nielsen, 1981)
Waves alone (Khelifa & Ouellet, 2000)
Combined flow (Khelifa & Ouellet, 2000)
Lab. data, CF (Khelifa & Ouellet, 2000)
Present study, WA
Present study, CF
0.1
0.01
1
10
ψwc
100
1000
Dimensionless ripple height as a function of the mobility
number under waves alone and combined flow.
Back
30
Experimental Instrumentation
ADV (SonTek) for 3D velocity
profiles and sinking of the mine
Back
Back
A 32 composite element array of sub-aquatic acoustic
sensors (SeaTek - Multiple Transducer Arrays) for
3D mapping of the bottom
Acoustic sensor (STI) for measurement of
time series of water surface profile
31
Velocity profiles recorded after 34 hours. The duration of each velocity point
was 180 s covering more than 60 wave periods. Vertical velocity profiles are
spaced every 25.4 cm in the x-direction over the centerline of the flume.
Hydraulic conditions: Tw = 4.1 s, Lw = 9.4 m, Hw = 10.4 cm, h = 56 cm under
waves alone.
32
Velocity measurements
Contour map of the sandy bottom and velocity vectors over the centerline of the center sandwave.
Flow conditions for waves alone: Tw = 2.3 s, Lw = 4.9 m, Hw = 17.4 cm, h = 60 cm. Average values
of morphodynamic characteristics, for ripples: length, lr = 12.7 cm, height, hr = 1.5 cm and speed,
cr = 8.4 cm/day; for sandwave: length, lsw = 8.4 m, height, hsw = 40 cm and speed, csw = 95
m/year. Up to date only two experiments include this type of velocity measurements.
back
33
Go back
34
Go back to
theoretical
background
Go back to
recommendations
35
Support
Go back
36
6
4
2
η (cm)
η (cm)
6
5
4
3
2
1
0
-1
-2
-3
-4
0
-2
-4
-6
0
2
4 Time (s)
6
8
10
0
5
10
15
20
Time (s)
Examples of surface profiles (case of waves alone) for: (Left) Quasi-sinusoidal
wave type with Tw = 1.5 s, Lw = 3.0 m, Hw = 7.1 cm, Cw = 2.1 m/s, Stroke=6.1
cm. (Right) Stokes’ wave type with Tw = 2.9 s, Lw = 6.6 m, Hw = 8.7 cm, Cw =
2.1 m/s, Stroke=15.2 cm. Notice that η = 0 cm corresponds to the undisturbed
water level of h = 56 cm
37
1000
Lsw measured / Lsw predicted
(a)
Theoretical, Németh et al. (2002)
(agree with field data) …but not present study!
100
Present study, WA
l sw 
20
k
Csw 
10 i
2 Tm
Present study, CF
2

2

10
10000
100000
R ew
1000000
Tm = (Time scale) ??
1000
Ratio between measured data and
predicted values as a function of the
Reynolds wave number, Re: (a)
Sandwave length, (b) Sandwave
migration speed.
Csw measured / Csw predicted
(b)
100
10
Present study, WA
Present study, CF
1
10000
100000
R ew
1000000
38