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On Reynolds Stresses over Wind Waves
On Reynolds Stresses over Wind Waves
Tel-Aviv University
School of MechanicalEngineering
Supported by Israel Science Foundation
Lev Shemer and Andrey ZavadskyLev Shemer and Andrey Zavadsky
TAU Wind-Wave Flume
Test Section Dimensions:
5 m Long, 0.4 m Wide, 0. 58 m High
Water Depth 0.2 m Max Wind Speed: > 15 m/s
View of the sensors
Pitot tube
X-hot film
Static pressure sensor
Capacitance wave gauges
Max. crest height detector
View within the test section in operating conditions
Experimental conditions7 Fetches (x) Each 40 cm; 100 cm ≤ x ≤ 340 cm
4 Wind VelocitiesU10= 16.5 m/s; 18.6 m/s; 21.0 m/s; 25.4 m/s
At each fetch, 40 vertical locations
5 mm ≤ z<≈ 150 mm above the highest crest
Simultaneously Recorded Parameters
Temperature is maintained constant for thermo-anemometry
Surface Elevation η, Static pressure p, instantaneous horizontal u and vertical w air velocities
Continuous SamplingDuration: 5 – 10 min @ sampling rate of 120 Hz or 1200 Hz
Automatic sensor calibration and data recording at each fetch
Measurement session for 4 wind speeds and all elevations lasts overnight (about 16 hours)
Vertical Air Velocity Profiles
101 1026.5
7
7.5
8
8.5
9
9.5
Height above Mean Water Level , mm
Ua,
m/s
U10
= 18.6 m/s
x=100 cmx=140 cmx=180 cmx=220 cmx=260 cmx=300 cmx=340 cm
101 1028.5
9
9.5
10
10.5
11
11.5
12
Height above Mean Water Level, mm
Ua,
m/s
U10
=25.4 m/s
x=100 cmx=140 cmx=180 cmx=220 cmx=260 cmx=300 cmx=340 cm
Vertical Distribution of –u’w’
0 20 40 60 80 100 120 140 160-0.05
0
0.05
0.1
0.15
0.2
Height above Mean Water Level, mm
-u'w
' m2/s
2
U10
= 16.5 m/s
x=100 cmx=140 cmx=180 cmx=220 cmx=260 cmx=300 cmx=340 cm
0 20 40 60 80 100 120 140 160-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-u'w
', m
2/s
2
Height above Mean Water Level, mm
U10
= 25.4 m/s x=100 cmx=140 cmx=180 cmx=220 cmx=260 cmx=300 cmx=340 cm
Friction Velocity u* (m/s)
100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
Fetch, cm
u*,
m/s
Log Profile U10
=16.5 m/s
U10
=18.6 m/s
U10
=21.0 m/s
U10
=25.4 m/s
Reynolds Stress U10
=16.5 m/s
U10
=18.6 m/s
U10
=21.0 m/s
U10
=25.4 m/s
The values of the friction velocity u*
determined from fitting the log velocity profile (κ=0.4) and from the Reynolds stress measurements agree within 10-20%
Full symbols – from log velocity profile; Empty symbols – from Reynolds stresses
Air velocity fluctuations
0 50 100 1500
0.1
0.2
0.3
0.4
0.5
Z, mm
(w'2
)1/2
m/s
x=100cmx=140cmx=180cmx=220cmx=260cmx=300cmx=340cm
0 50 100 1500
0.2
0.4
0.6
0.8
1
Z, mm
(u'2
)1/2
m/s
x=100cmx=140cmx=180cmx=220cmx=260cmx=300cmx=340cm
u’ w’U10=16.5 m/s
0 50 100 1500
0.2
0.4
0.6
0.8
1
Z, mm
(w'2
)1/2
m/s
x=100cmx=140cmx=180cmx=220cmx=260cmx=300cmx=340cm
0 50 100 1500
0.5
1
1.5
Z, mm
(u
'2)1
/2 m
/s
x=100cmx=140cmx=180cmx=220cmx=260cmx=300cmx=340cm
U10=25.4 m/s
Records of velocity components u and w and pressure fluctuations p in air compared to the
surface elevation η; U10=25.4 m/s
100 100.5 101 101.5 102 102.5 103 103.5 104 104.5 105-20
-10
0
10
20
30
40
t, sec
u, m/sw, m/s, mm Pressure, Pa
Simultaneous measurements at x=300cm, 5 mm above the highest crest
Cross-Spectral AnalysisCross-Spectral Analysis
Measured records of 2 signals:
f(t) = f(ti) and g(t) = g(ti); ti = (i-1)Δt; i=1,…N
2
2
1( ) ( ) ( )
T
fgT
R t f g t dT
Cross-correlation function
and cross-spectrum
Magnitude Squared Coherence (MSC)
2
2
1( ) ( )
Ti t
fg fgT
S R t e dtT
22 ( )
( )( ) ( )
fgfg
f g
S
S S
Coherence between turbulent velocity components u’, w’ and surface elevation
ηU10=16.5 m/s U10=25.4 m/s
0 2 4 6 8 100
0.02
0.04
0.06
0.08
0.1
0.12
0.14
frequency, [Hz]
MS
C (
-u)
z=5mmz=6mmz=7mm
η - u
η - w
0 2 4 6 8 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
frequency, [Hz]
MS
C (
-w)
z=5mmz=6mmz=7mm
0 2 4 6 8 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
frequency, [Hz]
MS
C (
-u)
z=5mmz=6mmz=7mm
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Frequency, [Hz]
MS
C (
-w)
z=5mmz=6mmz=7mm
Phase relations between surface elevation and air velocity fluctuations
240 260 280 300 320 340 360-60
-40
-20
0
20
40
60
80
fetch, [cm]
, [
de
g]
w
; U10
=16.5 m/s
w
; U10
=18.6 m/s
w
; U10
=21.0 m/s
w
; U10
=25.4 m/s
u
; U10
=16.5 m/s
u
; U10
=18.6 m/s
u
; U10
=21.0m/s
u
; U10
=25.4 m/s
“Coherent” wave-induced velocity fluctuations do not contribute to Reynolds shear stress
Conclusions Detailed experimental results on the structure of
turbulent air flow over waves are presented, including spatial distributions of normal and shear Reynolds stresses and phase relations between waves and air flow
To enable those measurements, a fully automated procedure was developed to control the experimental conditions and to record data simultaneously from numerous sensors
These results can serve a basis for validation of theoretical models dealing with wind-wave interactions
Extensive further experiments, also involving mechanically generated waves are now in progress
ThankThank you !you !