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