The Effects of Spatially Complex Shoreface Roughness on
Boundary Layer Turbulence and Bed Friction
L. Donelson Wright1, Arthur C. Trembanis1, Malcolm O. Green2, Terry M.Hume2,
Carl T. Friedrichs1
1Virginia Institute of Marine Science, College of William and Mary, Supported by theNational Science FoundationINT-9987936
2National Institute of Water and Atmospheric Research, New Zealand Supported by theNZ Foundation for Research Science and TechnologyFRST-CO1X0015
Questions Addressed
• How does spatially varying roughness type affect boundary-layer turbulence and bed friction?
• How do temporal changes in bedforms affect drag and turbulence?
• What is the appropriate drag coefficient at the local and shoreface scale?
Instrumented tripods were deployed on a complex shoreface over contrasting substrates in order to examine the effects of
spatially varying bed roughness on boundary layer turbulence and bed friction.
Main Points
• Estimates of bed stress and drag coefficients were made via the inertial dissipation method.
• A sharp contrast in Cd exists between the rough and smooth sites such that the former is ~4-6 times as hydrodynamically rough as the latter.
• The spatial gradient in the drag coefficient and bed roughness was at a maximum during the storm events
• The morphodynamic behavior of bed roughness is spatially and temporally complex.
Location/ ObservationsNEWZEALAND
TASMANSEA
SOUTHPACIFIC
175ºE
37ºS
NEWZEALAND
TASMANSEA
SOUTHPACIFIC
175ºE
37ºS
Coromandel Peninsula- East coast of North Island
Energetic wave dominated- Hs~1.0 m ; Ts~8-10 s
Microtidal- tidal range ~1.5 m
Sharply contrasting seabed substrates
36 day tripod deployment two storm events
0
10
20
30
40
50
60
70
80
2/16/01 2/23/01 3/2/01 3/9/01 3/16/01 3/23/01
Date
0
2
4
6
8
10
12
14
16
Uwsig UcTavg 6 per. Mov. Avg. (Tavg)6 per. Mov. Avg. (Uwsig) 6 per. Mov. Avg. (Uc)
Sp
ee
d (
cm/s
)
Pe
riod
(s)
TropicalCyclonePaula
Uorb
Uc
Ts
h = 22 m
z = 0.70 mab
Field Methods
900KHz 20m range
Rough
Smooth
1.701.60.2016Fine
3.88.70.7522Coarse
cr
(dyn/cm)^2s
(cm/s)D50
(mm)H
(m)Facies
Methods
• Inertial Dissipation Method (IDM) to estimate shear stress
• Compare turbulent characteristics temporally and spatially
• Estimate Cd from shear stress
• Estimate kb from ripple model
*
0
= ln c
c
u zU
z
von Karman-Prandtl equation
0 5 10 15 20 25 3010
1
102
Burst mean speed (cm/s)
heig
ht a
bove
bed
(cm
)
Rough Site Burst Averaged Velocity Profile
Hei
ght a
bove
bed
(cm
)
0 5 10 15 20 25 3010
0
101
102
Burst mean speed (cm/s)
heig
ht a
bove
bed
(cm
)
Smooth Site Burst Averaged Velocity Profile
Hei
ght a
bove
bed
(cm
)
Uc (cm/s)
Smooth SiteRough Site
Uc (cm/s)
1/ 25/31/3 ww
*
( )U ( z)
0.68
k k
2*
Dc
UC
Uu
Friction velocity via inertial dissipation method using the spectral density
of vertical fluctuations isww
and the drag coefficient averaging instantaneous currents is
Computations followed the methodologies of Stapleton and Huntley, 1995 and Feddersen and Guza, 2000
Turbulence ( ) in the Boundary LayerwS
pect
ral d
ensi
ty (
m/s
)^2
-5/3 slope
Frequency Hz
smooth
rough
Uc=7.7 cm/sUorb=42 cm/s
Uc=0.4 cm/sUorb=47 cm/s
Bed Friction• Estimate Drag coefficient from IDM estimate of
shear stress
• Estimate bottom roughness from Nielsen Model results
• Estimate wave friction factor from Swart Model
2*
Dc
UC
Uu
28bk
0.194
5.213 5.977bk
A
wf e
Cd and kb Variation During Storm EventRough Site
0
0.05
0.1
0.15
0.2
0.25
0.3
3/4/01 3/5/01 3/6/01 3/7/01 3/8/01
Date
Cd
0.05
0.07
0.09
0.11
0.13
0.15
0.17
kb
Cd(IDM) kb (Nielsen)12 per. Mov. Avg. (Cd(IDM)) 12 per. Mov. Avg. (kb (Nielsen))
kb
Kb
(m)
Cd
Cd
Smooth Site
0
0.05
0.1
0.15
0.2
0.25
0.3
3/4/01 3/5/01 3/6/01 3/7/01 3/8/01
Date
Cd
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
kb
Cd(IDM) kb (Nielsen)12 per. Mov. Avg. (Cd(IDM)) 12 per. Mov. Avg. (kb (Nielsen))
Cd
Kb
(m)
Cd kb
Cd and fw Variation During Storm Event
Smooth Site
0
0.05
0.1
0.15
0.2
0.25
0.3
3/4/01 3/5/01 3/6/01 3/7/01 3/8/01
Date
Cd
0.01
0.03
0.05
0.07
0.09
0.11
fw
Cd(IDM) fw (Swart)
12 per. Mov. Avg. (Cd(IDM)) 12 per. Mov. Avg. (fw (Swart))
Cd fwfw
Cd
Rough Site
0
0.05
0.1
0.15
0.2
0.25
0.3
3/4/01 3/5/01 3/6/01 3/7/01 3/8/01
Date
Cd
0.1
0.11
0.12
0.13
0.14
0.15
0.16
fw
Cd(IDM) fw (Swart)
12 per. Mov. Avg. (Cd(IDM)) 12 per. Mov. Avg. (fw (Swart))
Cd
fw
fw
Cd
Cd and kbestimates for rough site and smooth site
2.2 cm0.0068Smooth Uc>0.10m/s
11 cm0.030Rough Uc>0.10m/s
Kb
(Nielsen)
Cd
(IDM)
Site
N=10
Conclusions
• Near-bed shear stress estimated via Inertial Dissipation Method
• Velocity profile structure significantly altered by presence of large ripples
• Drag coefficient (Cd) highly variable in space and time
• Wave friction factor model (fw) does not capture the relationship between drag coefficient and bed roughness