Diapositive 1

1
Wave-current interactions from theory to
practical applications
Dr. Fabrice Ardhuin Service Hydrographique et
Océanographique de la Marine
Collaborating colleagues R. Baraille, A.
Pichon, Y. Morel, B. Chapron (Ifremer), F.
Collard (Boost-Technologies), T. Elfouhaily
(RSMAS), A. Jenkins, R. Magne, N. Rascle,
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Processes, forecasting and observations for the
upper ocean are we coherent?
Waves and Operational Oceanography workshop
Brest, France, June 2003 (proceedings available
ardhuin_at_shom.fr)
SST
U(z0)
F. Ardhuin 2 / 35
NOAA/NCEP Seminar 02/28/2005
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Outline 1 . Ocean circulation and wave
modeling at SHOM 2. Wave-current interactions
theory 3. Ocean surface velocities new
observations that could help fill the altimeter
gap 4. Conclusions and perspectives
F. Ardhuin 3 / 35
NURC Workshop High-Res. Coupled Coastal
Prediction
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1. Wave forecasting today
Offshore taking Wavewatch III, from version 2.22
to 3.xx
Calculations with 6-hourly winds, no assimilation
S.I. root mean square error (RMSE)
normalized by the obs. N.B. S.I.0.23 lt-gt corr.
0.990, S.I. 0.12 lt-gt corr. 0.995
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NOAA/NCEP Seminar 02/28/2005
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1.a Offshore sea states a giant leap forward
ECMWF winds at 62163, 6h-averages
-
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wind sea off North Carolina
Ardhuin al., In revision for JPO
(fetch in km)
S W N E
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NOAA/NCEP Seminar 02/28/2005
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1.b From offshore to the coast Brittany Storms,
rugged coastline, broad and deep shelf
Computation with Ref-Dif parabolic
model (version Kirby 1983)
F. Ardhuin 7/ 35
NOAA/NCEP Seminar 02/28/2005
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Coastal models validation

• several field measurement programs by SHOM,
  CETMEF, IUEM,
• GESMA, Météo-France

Sheltered sites Red propagation of buoy
data Green propagation of WW3 output
F. Ardhuin 8 / 35
NOAA/NCEP Seminar 02/28/2005
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Coastal sea states sources of error

• Offshore boundary condition (Hs OK other
  parameters ?)
• Coastal transformation
• processes
• refraction and shoaling (Ardhuin al. JPO 2001,
  2003a, 2003b, Peak 2004)
• bottom friction and scattering on a sandy
  bottom
• (Ardhuin al. JPO 2001, 2003a, 2003b, Ardhuin
  Herbers JFM2002,
• Magne al. JWPCOE 2005, Magne al. PoF 2005,
  Magne Ardhuin JFM 2006?)
• diffraction (Magne al. JGR 2006? analysis of
  NCEX 2003 off Scripps)
• effects of currents (ongoing analysis of EPEL
  2003 experiment )
• dissipation over mud
• deep water processes generation, Snl4,
  dissipation
• shallow water non-linear effects (breaking,
  Snl3)
• ? N.B. relocatable model-gt everything (that can
  be well modeled) has to be included ?
• numerics (Ardhuin Herbers JTECH2005)
• Coastal wind fields (paper with Cavaleri al.
  Ocean Engineering, in press).
• a lot of work to be done !

F. Ardhuin 9 / 35
NOAA/NCEP Seminar 02/28/2005
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HYCOM modelling (R. Baraille, A. Pichon and Y.
Morel)

• Coastal applications for the French Navy how do
  we go from basin-scale (Mercator consortium) onto
  the shelf ?
• gt2001-2007 RD program with demonstration of
• 1/60 HYCOM nested into both NRL-RSMAS s HYCOM
  and
• Mercator, from Ireland to Belgium and from the
  U.K. to
• Morocco. Including, tides, rivers, atmospheric
  forcing, SST
• altimetry assimilation and validation with field
  cruises
• (R/Vs Beautemps-Beaupré Pourquoi Pas?), HF
  radars,
• drifters
• First results at 1/60 32 levels forced with
  Mercator 3D density fields tides, 7-day
  relaxation on the open boundaries, air-sea fluxes
  from Météo-France
• -gt next RD program being defined for 2007-2012
  (waves are in there)

F. Ardhuin 10 / 35
NOAA/NCEP Seminar 02/28/2005
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Hindcast of 2004
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• Model SST for 08 June 2004.

• AVHRR SST for June 16 2004

The validation stage has just begun .
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NOAA/NCEP Seminar 02/28/2005
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Nice things that HYCOM can handle internal tides
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2. Waves and the upper ocean general principles
Sds
Sin
Energy
Wind
waves
turbulence
heat
Sbfric
turbulence
currents
Work of Srad Adiabatic part
Sin / C
Sds / C
Momentum
Wind
waves
currents
-gt verification of wave dissipation using
turbulence data -gt parameterization of mixing in
ocean circulation models
F. Ardhuin 13 / 35
NOAA/NCEP Seminar 02/28/2005
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2. Example of momentum balance Wave shoaling
without friction nor reflection energy flux Cg E
conserved
3
1b
2b
1a
2a
No mean force on the bottom (except for
hydrstatic pressure) Error in Kenyon (J. Oceangr.
2004)
Momentum balance 3 2b 2a (1b 1a )
Set-down well verified by Bowen et al.
(1968) if wave breaking -gt set-up (16 of
offshore Hs)
In addition wave mass flux E/C -gt balanced by
mean flow divergence With friction -gt
Longuet-Higgins (JFM 2005)
F. Ardhuin 14 / 35
NOAA/NCEP Seminar 02/28/2005
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2. Mathematical and numerical modelling in 3D
Problem 2 the moving free surface
air
air and water
water

• vertically-integrated equations Phillips 1977,
  Garrett 1976 ...
• 3D -gt moving coordinates following the free
  surface, and air/water
• separation in averaged quantities
• Andrews McIntyre 1978 (generalized
  Lagrangian coordinates)
• Teixeira Belcher 2002 (curvilinear
  coordinates) , Mellor 2003 ( wave-sigma )

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The most simple solution (conceptually)
Changing only the vertical coordinate (Mellor
2003) Easily generalized to random waves (e.g.
Ardhuin coll., CRAS 2004)
Streamlines for two superimposed waves in
Cartesian ( z ) coordinates
Same waves in ? coordinates iso- ? are
streamlines for the wave motion
F. Ardhuin 16 / 35
NOAA/NCEP Seminar 02/28/2005
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total momentum waves mean flow ?w Us
Problem 2
Why a problem - Stokes drift Us strongly
sheared near the surface (in deep water) -gt
high vertical resolution needed (e.g. for drift
calculation) But Us is not mixed over the
vertical and propagates ! (wave motion is
stable !!)
How ? plan A equation for û and another for Us
(en 3D) -gt Generalized Lagrangian Mean (GLM
AndrewsMcIntyre 1978a,b, Groeneweg
1999) -gt quasi-Eulerian mean (truly Eulerian
under the troughs McWilliams et al. 2004)
plan B solving for U with a forcing by Us
(approach used in Delft 3D)
F. Ardhuin 17 / 35
NOAA/NCEP Seminar 02/28/2005
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Summary
problem 2 wave - mean flow separation
mean flow momentum only
Total momentum
Garrett 1976 Ardhuin, Chapron Elfouhaily JPO
2004, Smith 2006
Hasselmann 1971,
Phillips 1977
2D
3D supposedly Eulerian
Craik-Leibovich 1976 McWilliams al. 2004
problem 1 air-water separation
Generalized Lagrangian Mean (AndrewsMcIntyre
1978) Ideal C-L (Holm 1996) Groeneweg 1999
alternative GLM (Andrews McIntyre1978) Rivero
Sanchez-Arcilla 1995 Mellor 2003
3D chgt. Coord.
F. Ardhuin 18 / 35
NOAA/NCEP Seminar 02/28/2005
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Basic principle of Generalized Lagrangian Mean
-gt simple way to compute volume-averaged mean
shears -gt production of TKE due to wave-induced
shear lt-gt wave attenuation (Ardhuin
Jenkins, JPO, in press)
F. Ardhuin 19 / 35
NOAA/NCEP Seminar 02/28/2005
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Re-writing GLM equations (starting from Groeneweg
1999) -gt equations for the mean flow UL-p
Advection with û
Coriolis
hydrostatic pressure
Mass conservation in Sigma coordinates
F. Ardhuin 20 / 35
NOAA/NCEP Seminar 02/28/2005
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Vortex force ? Stokes drift ? vorticity
In 2D broadening of a jet (Ismail Wiegel, J.
Waterways 1983)
without waves
Source of momentum for the mean flow, the vortex
force compensates the divergence of the wave
momentum flux due to refraction over the
current (total momentum is conserved locally)
F. Ardhuin 21 / 35
NOAA/NCEP Seminar 02/28/2005
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Turbulent closure application to the ocean mixed
layer prescribed mixing
length l maxz0 , (z0-z)
Modification of Craig Banner (1994)
with
Equation for TKE
F. Ardhuin 22 / 35
NOAA/NCEP Seminar 02/28/2005
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3.a Modeling surface velocities û, U, Us
û lt 1 of wind speed
Quasi-Eulerian velocities are uniform within a
few Hs of the surface (Agrawal et al. 1992
Santala Terray 1992) -gt coherent with the model
by Blumberg Mellor (JPO 2004)
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NOAA/NCEP Seminar 02/28/2005
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Realistic application with Stokes drift Prestige
oil spill hindcast HYCOM 1/3 degré ATLMED,
assimilating altimetry, forcing ARPEGE winds
WAM (ECMWF) waves
Standard HYCOM
HYCOM with wave forcing
F. Ardhuin 24 / 35
NOAA/NCEP Seminar 02/28/2005
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1D shoaling waves, Hs3 m, T12 s
Velocity profiles. Dashed no Coriolis Solid
full Coriolis (including Stokes-Coriolis)
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Satellite remote sensing From traditional
use of SAR to new applications
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small bit of an image
(Collard, Ardhuin Chapon,, IEEE-JOE 2005)
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3.b Surface velocities the ocean seen by
ENVISAT
ASAR instrument (Advanced Synthetic Aperture
Radar)
(picture courtesy of ESA)
1 month of wave-mode data over the globe winds
?? (Chapron et al., 2004)
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NOAA/NCEP Seminar 02/28/2005
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Tilt bias wind, wind sea, and Doppler
(Chapon, Collard Ardhuin, JGR 2005)
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Observation and simple theory for the
wind-Doppler correlation
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uniform wind -gt Doppler current
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3. c Doppler velocities and coastal sea states
Doppler image SLC
Tidal current (SHOM)
-gt Correcting for the tilt bias ? -gt we need a
good coastal wave model !
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Doppler centroid in wide swath image of Ivan
use for improving wind / wave estimates ?
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Summary

• a lot of work -gt reliable forecasting of waves
  20 for Hs, if winds OK.
• Other parameters ?
• Waves over mud ? Currents ?
• Wind-wave generation in coastal areas ?
• Sea state is importat for
• - air-sea fluxes and upper ocean mixing
• - sediment resuspension and transport
• - nearshore circulation
• -remote sensing of the ocean (altimeter SSB,
  SSS roughness bias, )
• What coherent description should one use ?
• - Correction to Mellor 2003 but applicable to
  total momentum
• - GLM and McWilliams al. (2004) are coherent
  to 2nd ordre in slope
• -gt û U - Us
• Separation waves mean flow -gt strong shear of
  drift
• strong mixing

F. Ardhuin 34 / 35
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How do we go forward ?

• - Integration of waves mean flow in the
  numerical models
• HYCOMWW3, ROMSSWAN, POLCOMS(WAM)
• ? collaborative effort with NCEP ?
• -gt biogeochemistry application, sediment
  transport (drift ?)
• Which tools (which models ?) -gt modularity
• -gt convergence of models
• (HOME, NEMO, ROMS )
• -Deepening our understanding and validating our
  models
• high-res modelling with LES, VOF
• in-situ observations sonar, micro-structure
• getting to model lab data (Ismail Wiegel 1983
  )
• applying GLM or other to in-situ data (e.g. ADCP
  lt-gt Argus video)
• - Managing complexity networking, building
  consensus

F. Ardhuin 35 / 35
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Turbulence closure in the presence of waves

• Inhibition of mixing by wave motion (Belcher
  Hunt JFM 1993, Miles JFM 1996)
• Modulation of Kz -gt modified current (Groenweg
  Klopman JFM 1998, Huang Mei JFM 2003)
• - production of TKE by waves (Ardhuin Jenkins,
  JPO in press)
• GLM average of the shear production term

Waves propagating in the wind direction are
dissipated - 20 of the swell dissipation ? -
Source of energy for Langmuir turbulence -gt
mixing in the mixed layer
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005
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Equations for horizontally uniform conditions, no
stratification
The body force Tds includes all wave dissipation
effects TdsTwcTturb (whitecapping and
turbulence)
wave-induced stress
wind stress
With surface boundary condition
Turbulence closure
with
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005
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1.b From offshore to the coast North Carolina
swells Straight coastline, shallow wide shelf
A shallow and wide shelf can lead to - A
strong bottom friction and damping of the waves
due the the formation of sand ripples (Ardhuin
coll. JPO 2001, 2003a, 2003b Ardhuin coll. JGR
2002)
CREST model (ray-tracing) without (S0) or
with bottom friction SfricSfric,JONSWAP or Sfric
Sfric,SHOWEX
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005
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Current effects on waves
Model comparison study with 2003 field data With
participation of P. Osuna and J. Wolf (POL, UK)
M. Benoit (EDF/LNHE) Main contractor F. Girard
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005
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Current effects on waves
SWAN results at the most offshore buoy Solid
total sea Dashed swell Dotted wind sea Black
obs. Cyan model, no tide Red model with
tide Both swell and wind sea Are modulated by
the Tidal current.
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005
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Current effects on waves
SWAN results at the most onshore buoy Solid
total sea Dashed swell Dotted wind sea
F. Ardhuin BONUS
NOAA/NCEP Seminar 02/28/2005