Download - Wind-wave growth in the laboratory studies
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Wind-wave growth in the laboratory studies
S. I. Badulin (1) and G. Caulliez (2)
(1) P.P. Shirshov Institute of Oceanology, Moscow, Russia
(2) Institut de Recherche sur les Phénomènes Hors Equilibre, Marseille, France
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Experimental conditions
• various fetches ranging from 2 to 26.5 m: X = 2, 4, 6, 9, 13, 18, 26 m• various wind speeds Uref ranging from 2.5 m/s to 13 m/s: U10 2.5 to 17 m/s
Fetch
W IN D
video camera
light box
wavemaker
carriage
XHR or fast-speed
video cameras
laser sheet
laser slope gauge
The large IRPHE-Luminy wind-wave tank
water tank: L= 40 m, l = 2.6 m, d = 0.9 m air tunnel: L= 40 m, l = 3.2 m, h = 1.5 m
U10 2.5 to 17 m/s
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A crazy question
•Can we reproduce wind-sea growth in the
wind-wave tank?
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A regular answer
•NO
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The tiny IRPHE-Luminy wind-wave tank
Length = O(102) wavelengths
Width = O(10) wavelengths
Height = O(10) wavelengths
Depth = O(10) wavelengths
Problems
•Scales
•Capillarity
•Drift currents
•Air flow
•etc
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A. We certainly cannot model growth of wind-
driven seas in wind-wave channels
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Why Wave growth in wave tanks is consistent both
qualitatively and quantitatively with wave growth in open sea?
Ex.: The Toba 3/2 law (Toba, 1972, 1973)
Hs=B(gu*)1/2Ts3/2
B=0.061
May be it is just happy chance when formally invalid tool works well
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Try to answer within the statistical approach(formally invalid)
The kinetic equation for wind-driven seas(the Hasselmann equation)
knl in diss
dN S S Sdt
1. Nonlinear transfer is described from `the first principles’
2. External forcing is parameterized by empirical formulas
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Try to answer within the weakly turbulent self-similar wave growth law (Badulin et al., 2007)
The split balance of wind-driven seasHyp. Nonlinear transfer dominates over wind input and dissipation
knl
kin diss
dN Sdtd N
S Sdt
1. Conservative Hasselmann equation assures universality (self-similarity) of nonlinear transfer
2. External forcing (spectral fluxes) controls evolution as total quantities. Details of the forcing are of no importance
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31
2
3
2
4
gdt
d
g
p
ssp
Total energy
p - peak frequency
ss - self-similarity parameter
Self-similar solutions dictates Kolmogorov-like wave-growth lawBadulin, Babanin, Resio & Zakharov, JFM, 2007
0.55 0.25ss
1. Integral net wave input is rigidly linked to instantaneous wave parameters: characteristic wave energy and wave frequency;
2. Dependencies of sea wave growth of field experiments are consistent with the law
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Measurements were carried out in the Large IRPHE-Luminy wind-wave channel in 2006 with no reference to the problem of
growth of wind-driven seas
Experimental conditions
• various fetches ranging from 2 to 26.5 m:
X = 2, 4, 6, 9, 13, 18, 26 m• various wind speeds Uref ranging from
2.5 m/s to 13 m/s: U10 2.5 to 17 m/s
Tools: wave capacity probes,
laser slope gauge
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Our data cover wider range of conditions (cf. Toba, 1972`Traditional’ wave speed scaling gives high dispersion
(good in logaritmic axes only)
Blue stars – data by Toba (1972)New approach – new knowledge ?
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Weakly turbulent scaling (energy-to-flux)Not so bad if locally measured frequency is used
(perfect! Axes are linear!)
ss
31
2
3
2
4
gdt
d
g
p
ssp
E
p4 /g2 =
Ste
epne
ss2
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dominant wavelength
X = 6 m: d 30 cm
X = 13 m: d 45 cm
X = 26 m: d 80 cm
total mean square slope
E* 4/g2 = mssd
E/X 2/2g = X
Capillary and drift effects are included , i.e taken into account in mssd
Below d 30 cm, gravity-capillary and capillary- gravity waves: action of T/ and shear drift effects
Problems of the new presentation: derivatives and instantaneous quantities (wave heights and frequencies)
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Better than perfect !
ss
31
2
3
2
4
gdt
d
g
p
ssp
<ak
>2 =
Ste
epne
ss2
Rate of energy=(d(a2k2)/dt/(2p))1/3
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Concl.: We showed consistency of the wind-channel data and the weakly turbulent law (Badulin et al., 2007)
The talk is over (?)
No, it is just the very begining
31
2
3
2
4
gdt
d
g
p
ssp
We are the best !
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Try to estimate net wave input and scale it
in physically consistent way
The weakly turbulent Kolmogorov-like law gives us a
chance
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Very preliminary results: Wave input vs u* or vs Cp
(Air flow vs wave dynamics)<d/dt> ~
Different symbols are used for different wind speeds
Scaling in wave phase speed looks more attractive
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The well-known Toba’s law as a particular case of weakly turbulent wind-wave growth
31
2
3
2
4
gdt
d
g
p
ssp
Let 3
2const ~d H Tdt
One can estimate energy production from instantaneous Hs, Ts
const~ 3* udt
d
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3*Toba_input=1.3 a
w ss
u
g
Very preliminary resultsWave input normalized by the Toba input vs Cp
The scaling is relevant to constant in time production of wave energy
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The less-known Hasselmann, Ross, Muller & Sell, 1976
(“Special solutions” for a parametric wave model)
31
2
)(3
gdt
dM
g
M pMss
p
Let 5
3
2*
const ~
~ ~ php
dM H Tdt
dMdtd C udt
M - total wave momentum
Get
See alsoResio, Long, Vincent, JGR 2004
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Very preliminary resultsWave input for scaling Resio et al. 2004
Relevant to constant in time production of wave momentum
2*Resio_input ~ phC u
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Summary• Wind-wave tank data (Toba 1973, Caulliez 2006)
are consistent with weakly turbulent scaling – Kolmogorov’s energy-to-flux rigid link
• The weakly turbulent approach and the new data allow one – to identify qualitatively different physical regimes
of wave growth;
– to describe quantitatively wind-wave interaction
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Summary
Wind-wave tanks can give usreal physics
at unreal conditions
Marseille, 07/01/2009
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Welcome to Marseille !
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Motivation
• “With a wider perspective and in the long term, we need the wild horse that comes out with unconventional ideas…”
L. Cavaleri et al. / Progress in oceanography, 75 (2007) 603–674