Contents
Mixing in the nearshore zone
Jonathan Pearson
School of Engineering, University of Warwick
Dye Tracing Workshop
20th September 2010
Coastal Research Facility
HR Wallingford
‘Scheldgoot’ wave - current
facility, Delft Hydraulics
Shallow Water Basin
DHI
L
Mean water
level
(a)
(b)
(c)
C
H
Still water
level
H/2
h
L/2
Bed
h=
H=
T=
L=
distance from bed to mean water level
wave height, distance between crest & trough
wave Period, the time interval for motion to reoccur at a fixed point
Wave length, distance between any two corresponding positions
Particle orbits under waves in a) deep water,
b) intermediate water & c) shallow water
Definition Sketch of a small amlitude wave
Mean wave
induced velocity
H
Crest-trough
layer
Still water
level
h
b
H
= 0.78
h
average
H
= 1.10
h
steep beaches
Undertow
layer
b
b
Classification of wave breaking under regular waves
Cross-shore flow in nearshore region
1
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
Background
What are the mixing processes?
Sources of pollution:
- Turbulent diffusion (ey)
Offshore boundary
- Outfalls (but becoming cleaner, but to increased regulation)
- Shear dispersion (ky)
Shoreline boundary
- Storm water overflows
e.g. Pattaya Beach
e.g. Nadaoka & Kondoh (1982)
H/L
= 0.026-0.029
oo
H/L
= 0.070-0.080
oo
200
- Polluted rivers flowing into
nearshore region
e.g. San Diego
Major source of
pollution :
storm water overflows
Cross-shore variation
in turbulence
b
v
1/2
Turbulent Intensity
(gd )
300
100
0
0
1
2
d/d
Water Depth / Depth
@ Breaking, h/hb
b
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
Coastal Research Facility
Coastal Research Facility
Recirculating Flow in the CRF
UKCRF
(HR Wallingford)
Flow straighteners
LONGSHORE CURRENT
SUMPS
Aim: On-offshore (transverse)
mixing under waves & current
Beach section
Gates for controlling
longshore currents
D
C
Location: seawards of the breaker point
10m
SHORELINE
A
Fluorometers
Office
Mutli-paddle
wavemakers
Coastal Research Facility
250
0
500
0
2
4
6
8
10
Distance from shore, y (m)
Long-shore velocity under
current only conditions
12
Normalised Transverse
Variance, σ2y (m2) {x10 -2 }
19.0
29.0
40
x=2.35m
1.28
Mean Offshore Wave Ht.=0.057m (y=15m from Shore)
y(m) H (mm)
1.5
57
2.0
60
3.0
62
4.0
63
30
0
-30
60
Mean Offshore Wave Ht.=0.086m (y=15m from Shore)
y(m) H (mm)
1.5
48
2.0
76
2.5
85
3.0
88
4.0
91
30
0
-30
90
1.82
x=3.85m
0.61
0
x=5.35m
30
0
1.05
x=8.35m
0.70
0.35
x=9.85m
0.50
0.25
0
3.5
4.0
4.5
5.0
5.5
-30
0
2
4
Dista nce from shore, y (m)
6
5
10
15
20
25
Distance from bed injection point, x (m)
0
0.75
0
0
0.53
0
y (m) H(mm)
3. 0 1 04
3. 5 1 21
4. 0 1 25
4. 5 1 29
5. 0 1 32
H = 57mm
H = 86mm
H = 120mm
1.06
Mean Offsh ore Wave H t .=0.120m (y=15 m from S hore)
60
No Waves
10
1.21
1.59
Transverse variance v’s
distance from injection
20
0.64
0
Measured waves across
nearshore region
30
Distance from shore, y (m)
Tracer conc. profiles under waves (H = 0.086mm)
dispersion
T raTransverse
n sve rs e d isp er
sion c o efficie nt, D y
) 2/s)
(m m
coefficient,
D2 /s
(mm
0
1.92
Concentration (ml/l) {x10-5}
Distance from inlet
gates , x (m)
-3
Water depth, -z ( m) {x10 }
-3
Water Elevation, z (m) {x10 }
Mixing in the Near-Shore Zone
Coastal Research Facility
(m s-1) {x10-3}
Longshore velocity, u
Current generating sumps
Mixing in the Near-Shore Zone
80
B
A
36m
Access bridge &
instrument carriage
120
D
C
B
Tests: 4 regular wave conditions
(constant period) superimposed on
longshore current
160
SUMPS
7.5m
Measured
Rough bed conditions
6000
Estimated
Mixing processes due to:
Longshore current
Wave induced turbulence
Stokes Drift
4000
Mixing processes
seawards
of the
breaker point
Assumed Conditions
T = 1.2s
y = 5.0m
M = 0.01
m = 1:20
γ = 0.69
2000
0
0
40
80
120
Wave Height,
height, H (mm)
Wave
H (mm)
Summary: Increase in Transverse Mixing due to Waves
2
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
Summary
‘Scheldgoot’ wave – current facility
Crest-trough
layer
Aim: Vertical mixing under waves & combined
currents using Laser induced fluorescence
Mean wave
induced velocity
Still water
level
Undertow
layer
Diffusion / Dispersion
300
Ho/Lo = 0.026-0.029
Ho/Lo = 0.070-0.080
200
b
1/2
Turbulent(gdvIntensity
)
Vertical variation in crossshore velocity
100
0
0
1
2
Water Depth / Depth @ Breaking, h/hb
Shear Dispersion
(which varies with distance from shore)
Turbulent diffusion
(which exchanges material between the ‘2’ layers )
Mixing in the Near-Shore Zone
‘Scheldgoot’ wave – current facility
Facility set-up
overall length: 56 m
width: 1 m
height: 1.2 m
d/db
Water Depth / Depth @ Breaking, h/hb
Experimental water
Depth: 0.5m
Mixing in the Near-Shore Zone
Mean longitudinal velocity
profiles under waves
1000
Fluoresced 6G dye passing thro’
lightsheet (~1m up stream)
‘Scheldgoot’ wave – current facility
Laser / Light sheet generator
Distance from bed, z (mm)
100
LDA system
Direct Measurement of Tracer
Concentration - 3 dye injection
points (bed, +100mm, +200mm)
Detailed Measurement of
hydrodynamics - Detailed LDA
velocity profiles ( +20 points over
vertical)
10
Direction of
flow
Fluoresced dye particle
Emitted laser light
Current + Waves (H=0m)
Current + Waves (H=60m)
Current + Waves (H=120m)
Current + Waves (H=150m)
Current + Waves (H=180m)
0.1
Facility bed
0
0.04
0.08
0.12
0.16
0.2
Fibre optic Laser
light sheet
Velocity (m s-1)
Mixing in the Near-Shore Zone
Vertical variance v’s
distance from injection
Wave
35 Condition No Waves ( ) H=0.06m, T=1.2s ( )
Vertical Variance, σz2
{x10-3} (m2)
Distance from bed (mm)
5.0m
4.0m
3.0m
150
2.0m
1.0m
100
50
0
0.0
∂σ2 z {x10-4 }
∂x
30
1.0
1.5
2.0
-4
Concentration (g/l) {x10 }
2.5
20
H=0.09m, T=1.2s ( )
50
70
25
20
Aim of study: Investigate the near
shore (mainly transverse / crossshore) mixing processes by
fluorescent tracer experiments and
by detailed velocity measurements
Tracer near injection (offshore region)
15
10
5
0
0.5
Schematic of LIF
Wave Current facility at DHI
Vertical concentration
distribution from bed
injection
Distance from injection
CCD Camera
Absorbence
filter
Mixing in the Near-Shore Zone
‘Scheldgoot’ wave – current facility
200
Dye particle
Excited dye particle
1
Test conditions - 5 Regular
waves (H=0, 60, 120,150
&180mm), T=1.2s tested
superimposed on current.
250
Key
0
1
2
3
4
5
Distance from source (m)
Summary: Increase in Vertical Mixing due to Waves
1:20 plain smooth beach, all wave conditions superimposed on
longshore current (north -south) which approached shorenormal (i.e. no wave driven current)
3
Mixing in the Near-Shore Zone
Undertow
layer
… we can get a basic estimate of the
overall transverse mixing coefficient in
the surfzone:
Dy =
+ vv+
Bed, z=-d
Dy = ky + e y =
(v + − v − ) 2 d 2
+ ey
48e z
gH 4
+ ey
768dez
1:20 beach
The turbulent diffusion (ez, ey) can be
estimated from Svendsen’s work [e.g.
Svendsen (1987), Svendsen & Putrevu
(1994)]
ν t = Md gd
Inside surfzone
−4
ν t = (0.8(d /db )
… standard solution
Paddle
Mean wave
induced velocity
+ 0.2)ν tb
Outside surfzone
how does the simple model compare to
measured data?
Direct Measurement of Tracer
Concentration - 3 dye injection
points (offshore, around breaker
point & in surfzone)
Detailed Measurement of
hydrodynamics - Detailed
velocity profiles at
y=1,2,3,4,5,6m from shoreline
Test conditions - 3 Regular waves
(sop 2, 3.5, 5%) & 1 Random
Ho ~120mm
200
Cross-shore variation in wave height
180
Wave Wave
Height,
H (mm)
Height, Hs (mm)
Crest-trough
layer
Still water
level
Mixing in the Near-Shore Zone
assuming the idealized case, that mean
velocities can be estimated from the
mass flux of the breaking wave
Shore
Wave Current facility at DHI
160
140
120
100
80
60
Sop ~ 3.5%
Sop ~ 5.0%
Sop ~ 2.0%
Sop ~ 3.5%- RANDOM
40
20
0
0
1
2
3
4
5
6
7
SWL (m) y (m)
DistanceDistance
fromfromshore,
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
LDA velocity measurements
LDA velocity observations
Z Y velocity
a) near surface,
b) near bed
0.4
0.3
0.2
Velocity (m/s)
(a)
0.1
0
0
1
2
3
4
5
4
5
(b)
Velocity (mm/s)
-0.1
-0.2
Blue - vertical direction
(s) direction
GreenTime
- on/off
0.2
250
Measured
cross-shore
velocity
0.1
0
0
1
2
3
-0.1
-0.2
-0.3
Time (s)
Time series
a) near surface,
b) near bed
Distance
from Bed (mm)
Distance from bed (mm)
Velocity (m/s)
0.3
-0.3
Distance from shore (m)
1m
2m
3m
4m
5m
6m
200
150
100
50
0
-100
-50
0
50
100
150
Cross-shore velocity (mm/s)
200
250
300
Cross-shore velocity (mm/s)
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
Tracer measurements
Tracer measurements
Constant head of
fluorescent dye injected
into facility
Dye collected by pumping
samples from flow (for 180
seconds)
… into suitable containers and
analysed by fluorometer to
determine dye concentration
Plan view
Direction of flow
resultant dye
concentration measured
at a number of locations
down stream to
determine the mixing
coefficient / processes
4
Mixing in the Near-Shore Zone
Mixing in the Near-Shore Zone
Plan view
Tracer results
…comparisons in the surf zone for all measured conditions
Inshore, y=2m
Current + waves H=0.12 T=1.2
60
Concentration (ppb)
50
In shore
Off shore
Concentration (ppb)
40
x = 0.55 m
x = 0.95 m
x = 0.35 m
x = 0.75 m
30
20
Surfzone
10
Direction of flow
0
2500
2000
1500
1000
500
0
-500
-1000
-1500
-2000
-2500
Offshore, y=5m
Current + waves H=0.12 T=1.2
-10
Location from y=2m
Approximate
breaker point
location from y=2m
Concentration (ppb)
60
Off Shore
In shore
y=
2m
3m
Dy~
80x
60x
x = 2.35m
x = 3.15m
x = 1.35m
x = 3.75m
x = 1.85m
30
20
5m
Concentration (ppb)
50
40
10
2x
0
2000
1500
1000
500
0
1
This EPSRC study
Pearson et al. (2002)
Harris et al. (1963)
Harris et al. (1963)
{Lab.}
Inman et al. (1971)
{Field}
Tanaka et al. (1980)
{Field}
Theoretical Mixing -this
{Field}
study
0.1
0.01
70
Offshore
Measured on-offshore dispersion
coefficient, Dy (m2/s)
10
Approximate
breaker point
-500
-1000
-1500
-2000
0.001
0.001
0.01
0.1
Wave height at breaking, Hb
1
1.5
10
(m)
Summary: Transverse mixing increases in surfzone &
coefficient varies by orders of magnitude
-10
location from y=5m
Location from y=5m
OutSide –
SurfZone
Transverse dispersion
Summary
Transverse dispersion coefficient, Dy
2
(mm
coefficient,
D /s)
(mm 2/s)
Mixing in the Near-Shore Zone
Measu red
Ro ug h bed conditions
6000
Es tim ated
Mixing processes due to:
Longsho re current
Wave ind uced tu rbulenc e
Sto kes Drift
4000
Increase in Transverse Mixing due to Waves
As sum ed Condit ions
T = 1 .2s
y = 5.0 m
M = 0 .0 1
m = 1 :2 0
2000
γ = 0.6 9
0
0
40
80
120
WWave
a ve height,
H e ig hHt,(mm)
H (mm)
Vertical Variance, σz2
{x10-3 } (m2)
Wave
35 Condition No Waves ( )
Vertical
Mixing
(NonBreaking)
∂σ2z {x10 -4}
∂x
30
H=0.06m, T=1.2s ( )
H=0.09m, T=1.2s ( )
50
70
20
25
Increase in Vertical Mixing due to Waves
20
15
10
5
0
0
1
2
3
4
5
Distance from source (m)
Measured on-offshore dispersion
coefficient, Dy (m2/s)
10
Inside
Surfzone
1
This EPSRC study
Pearson et al. (2002)
Harris et al. (1963)
Harris et al. (1963)
{Lab.}
Inman et al. (1971)
{Field}
Tanaka et al. (1980)
{Field}
Theoretical Mixing -this
{Field}
study
Transverse mixing increases in surfzone &
coefficient varies by orders of magnitude
0.1
0.01
0.001
0.001
0.01
0.1
Wave height at breaking, Hb
1
1.5
10
(m)
5