1. IMPACT OF WAVES ON THE OCEAN CIRCULATION
PHD THESIS DEFENSE, 2004 – 2007
NICOLAS RASCLE
IMPACT OF WAVES ON THE OCEAN CIRCULATION
Thesis supervisor : Fabrice ARDHUIN (SHOM, Brest)
Financial support : DGA / CNRS
Laboratories :
(1) Centre Militaire d’Océanographie, Service Hydrogaphique et Océanographique de la Marine, Brest
(2) Laboratoire de Physique des Océans, Université de Bretagne Occidentale, Brest

2. Impact of waves on the coastal and nearshore currents (3D) Conclusion
PHD THESIS DEFENSE, 2004 – 2007
NICOLAS RASCLE
Introduction
General concepts
Impact of waves on the currents of the surface layer in the open ocean (1D)
Impact of waves on the coastal and nearshore currents (3D)
Conclusion
2 / 38

3. interactions Atmosphere / Waves / Ocean
INTRODUCTION
Context of the thesis :
interactions Atmosphere / Waves / Ocean
Subject of the thesis :
impact of waves on the ocean circulation
Atmosphere
Energy and momentum exchanges
Waves
Ocean
3 / 38

4. Impact on ocean surface drift ?
INTRODUCTION
The waves :
Impact on ocean surface drift ?
Impact on the mixing of the near-surface ocean ?
Impact on the ocean circulation at global scale ?
Impact on the currents close to the coast ?
4 / 38

5. Try to bring a better knowledge of : surface currents
INTRODUCTION
Try to bring a better knowledge of :
surface currents
near-shore and inner-shelf currents
temperature and other tracers close to the surface
Practical applications ?
survey of surface drifts of particles or objects
(pollutions, search and rescue)
survey of drifting materials in nearshore and costal waters
(larvae recrutement, sedimentary transport)
vertical mixing in the near-surface ocean
(formation of diurnal thermoclines, blooms)
teledetection
(velocities and slopes of the surface)
Analyse of the existing ocean circulation models (without waves)
Importance of waves ?
5 / 38

6. z x Short gravity wave : Wavelength = 100 m Period = 10 s Height = 1 m
GENERAL
Waves ? z x
Short gravity wave :
Wavelength = 100 m
Period = 10 s
Height = 1 m
But the mean length scales for the variations of the wave field are longer : 100 km, a few days…
6 / 38

7. z z u x Eulerian description of the Stokes drift Waves (linear)
GENERAL
Eulerian description of the Stokes drift
Waves (linear)
 = acos(kx-t)
u = acos(kx-t) exp(kz) si z < 
w = asin(kx-t) exp (kz) z z u x
The Stokes transport occurs between crests and throughs.
7 / 38

8. z z u = Us x Lagrangienne description of the Stokes drift Waves
GENERAL
Lagrangienne description of the Stokes drift
Waves
 = acos(kx-t)
u = acos(kx-t) exp(kz) si z < 
w = asin(kx-t) exp (kz) z z
u = Us x
The orbits of particles are not closed :
-> Stokes drift
The transport occurs over a depth of the order
of a ten of meters.
8 / 38

9. 2 difficulties to model the current when waves are present :
GENERAL
2 difficulties to model the current when waves are present :
The motion of the free surface
-> imposes a special averaging close to the surface
2. Different physics between the Stokes drift and the mean current
(vertical mixing, propagation : Cg >> u, …)
-> imposes to separate waves and mean current
Use of the Generalized Lagrangian Mean theory (GLM)
(Andrews et McIntyre, 1978, Ardhuin et al., 2007)
9 / 38

10. Once made a GLM averaging, one obtains :
GENERAL
Once made a GLM averaging, one obtains :
The free surface is moved back
to its mean position.
The Stokes drift in agreement
with its Lagrangian description.
The mean current described by
a quasi-Eulerian mean, and not an
Eulerian mean.
Lagrangian drift
= quasi-Eulerian velocity
+ Stokes drift :
Wave field dynamics <-/->
Quasi-Eulerian current dynamics
10 / 38

11. Dynamics of the mean current dynamics of the total Lagrangian drift
GENERAL
Dynamics of the mean current dynamics of the total Lagrangian drift
Ex : Equilibrium in an horizontaly uniform case (and without stratification)
Coriolis
Turbulent diffusion
Stokes-Coriolis force :
(action of the Coriolis force
on the wave field, momentum
then given to the mean flow)
Wind stress
11 / 38

12. The Stokes-Coriolis force (Hasselmann, 1970)
GENERAL
The Stokes-Coriolis force (Hasselmann, 1970)
Case of a wind sea
Wind waves
At long time scales, the Stokes-Coriolis force creates a (vertically integrated) transport which compensates the Stokes transport
-> no modifications of the Ekman pumping by waves
(Hasselmann, 1970)
-> no modifications of the ocean circulation at global scale
Stokes transport
Wind stress
Stokes-Coriolis
transport
Ekman transport y
Stokes-Coriolis
force x
12 / 38

13. Stokes-Coriolis force (Hasselmann, 1970)
GENERAL
Stokes-Coriolis force (Hasselmann, 1970)
Vertically integrated, no net transport induced by waves.
But there still might be a net Lagrangian drift :
Transport of
Stokes-Coriolis
Stokes transport
Mean Current
Stokes drift
Lagrangian
drift
No net
Lagrangian drift
+ vertical
mixing
Case of a wind sea
Case of a long swell
13 / 38

14. PART 1 : VELOCITIES IN THE SURFACE LAYER
Partie 1 : Impact of waves on the surface currents (1D)
Surface drift offshore :
Surface drift due to the wind : 2 or 3% of U10 (Huang, 1979)
The Ekman currents at the surface strongly depend on the vertical mixing Kz : 0.5 to 4% of U10
Stokes drift of waves of same magnitude order : 3% de U10 (Kenyon, 1969)
Coherent description?
Which one dominates the surface drift ?
14 / 38

15. PART 1 : VELOCITIES IN THE SURFACE LAYER
The Stokes drift
Modelisation of the wave field by a freq-dir spectrum (Kudryavtsev et al., 1999) of the sea surface elevation (spectral approach in phase in the mean) :
Stokes drift (uncorrelated phases) :
15 / 38

16. PART 1 : VELOCITIES IN THE SURFACE LAYER
Energie spectra E(f) (=height^2)
Spectra f^3 E(f) (Stokes drift at
the surface)
Height, Periods
Hs=1.6m, Tp=5.5s
Hs=2.8m, Tp=8s
Hs=2.8m, Tp=12s
Stokes drifts
Us=10. cm/s
Us=12. cm/s
Us=5.2 cm/s
Us=1.6 cm/s
(Wind : U10=10 m/s)
Young wind sea
Developed wind sea
Short swell
Long swell ---
16 / 38

17. PART 1 : VELOCITIES IN THE SURFACE LAYER
The Stokes drift
For a fully-developed wind sea :
at the surface 1.2% of U (< Kenyon, 1969)
up to 30% of the Ekman transport (< McWilliams et Restrepo, 1999)
affect depths of
10-40m
For the swell, small surface Stokes drift.
(Wind : U10=10 m/s)
Young wind sea
Developed wind sea
Short swell
Long swell ---
17 / 38

18. PART 1 : VELOCITIES IN THE SURFACE LAYER
Vertical mixing : effect of waves
1D TKE model (Craig et Banner, 1994)
Mixing length :
prescribed
TKE calculation
Roughness length
diffusion
production
dissipation
Injection of TKE by the dissipation
of the wave field :
TKE surface flux
18 / 38

19. Vertical mixing : effect of waves
PART 1 : VELOCITIES IN THE SURFACE LAYER
EQUATIONS POUR LE COURANT QUASI-EULERIEN
Vertical mixing : effect of waves
Dominant parameter : the roughness length
A dimensional analysis, confirmed by mesurements of dissipation of TKE : (Terray et al., 1996)
-> The surface mixing increases with the wave growth.
Proxy for the scale of the breaking waves
19 / 38

20. Consequence for the Lagrangian drift :
EQUATIONS POUR LE COURANT QUASI-EULERIEN
PART 1 : VELOCITIES IN THE SURFACE LAYER
Consequence for the Lagrangian drift :
The drift at the surface essentially comes from the Stokes
drift when the waves are developed. (Rascle et al., 2006)
(Vent : U10=10 m/s)
Lagrangian drift
Stokes drift
Mean current
20 / 38

21. PART 1 : VELOCITIES IN THE SURFACE LAYER
Validations :
The observations of TKE dissipation
The observations of Lagrangian drifts
The observations of quasi-Eulerian currents
TKE model built from observations of TKE dissipation
z0 tuned in consequence
Still some uncertainties (Gemmrich et Farmer, 1999, 2004)
21 / 38

22. PART 1 : VELOCITIES IN THE SURFACE LAYER
Validations :
The observations of TKE dissipation
The observations of Lagrangian drifts
The observations of quasi-Eulerian currents
Few available (complete) data
Estimation to 2-3% of U10 at the surface (Huang, 1979)
Note the current work of Kudryavtsev et al. on the vertical shears
of drifters observations (Kudryavtsev et al., 2007, submitted)
22 / 38

23. PART 1 : VELOCITIES IN THE SURFACE LAYER
Validations :
The observations of TKE dissipation
The observations of Lagrangian drifts
The observations of quasi-Eulerian currents
2 datasets examined :
SMILE (1989, californian shelf)
(Santala, 1991)
LOTUS 3 (1982, Sargassian sea)
(Price et al., 1987, Polton et al. 2005)
VMCM
Short field experiment (2 days)
Wave follower
Mesurement very close to the surface
Bias corrections
Long field experiment (160 days)
Classical mooring
Minimum depth of measurements : 5m
23 / 38

24. PART 1 : VELOCITIES IN THE SURFACE LAYER
Validations : 3. the observations of quasi-Eulerian currents
Vertical shears close to the surface (SMILE)
1D TKE model with stratification (Noh, 1996, Gaspar et al. 1990)
Small downwind shear -> validates the wave-induced near-surface mixing
Crosswind shear ?
No evidence of the Stokes-Coriolis effect on the crosswind component
24 / 38

25. PART 1 : VELOCITIES IN THE SURFACE LAYER
Validations : 3. the observations of quasi-Eulerian currents
Complete spirales (LOTUS 3)
Very good agreement model / data.
No evidence of the wave-induced mixing (at 5m deep and more)
No evidence of the Stokes-Coriolis transport (contrary to Polton et al., 2005 without stratification). Probably because of a wave-induced bias.
1D TKE model with stratification nudging. (Noh, 1996, Gaspar et al. 1990)
25 / 38

26. PART 1 : VELOCITIES IN THE SURFACE LAYER
Summary - Conclusion
Impact of waves on the currents of the surface layer in the open ocean (1D)
Problematic of surface drift offshore (1D)
re-evaluation of the Stokes drift
evaluation of the mean current by parameterizing the wave-induced mixing
evaluation of the Lagrangian drift at the surface
-> the Stokes drift dominates (Rascle et al., 2006)
comparison with mean currents observations
-> carefull conclusions (Stokes-Coriolis ?) (Rascle et Ardhuin, 2007, soumis)
26 / 38

27. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
Part 2 : Impact of waves on the coastal and nearshore currents (3D)
Coastal zone
Inner-shelf zone
Surf zone
Waves
Shoaling
Breaking
Tide
Wind
Coriolis
Stratification
-10m
Tide
Waves
-50m
Transition ?
Poorly understood dynamics
Importance of radiation stress ?
of (Stokes-) Coriolis ?
Important zone
Radiation stresses 2D
Bousinessq models
Primitive equation
models
2 goals :
understand the inner-shelf dynamics
model : develop a 3D model (primitives equations) to resolve from the offshore to the surf zone
27 / 38

28. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
For the hydrodynamics of that inner-shelf zone, one needs
complete equations (3D) of the forcing of currents by waves :
Mellor > problem in the vertical profile of the radiation stress
(Ardhuin et al., 2007 b)
McWilliams et al., > adiabatic
Ardhuin, Rascle et Belibassakis 2007 (GLM)
Momentum:
Mass:
Tracers:
28 / 38

29. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
My work :
Implement those equations in ROMS to solve the mean circulation forced by waves : extension of a coastal model to the surf zone
2. Tests on an academic case
3. Description of the dynamics with GLM formalism, Comparison to existing descriptions of the surf-zone and inner-shelf zone
29 / 38

30. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
1. Academic case
Waves
Breaking
Straight and infinite
coast
Set-down
Set-up
Jet
Calculation of waves, of Stokes drift
Model of Thornton and Guza
Forcing
Calculation of the mean current
ROMS model, modified primitive equations
(GLM equations)
dt = 3 s
Kz = 0.03 m2/s
40 vertical levels
f = 10-4 s-1
4 km
400 points (dx=10 m)
30 / 38

31. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
2. Implementation in ROMS :
Mom. :
Mass:
Tracers:
Primitives equations model
Sigma coordinates
Just solves the mean current : Stokes drift comes from the wave model
Baroclinic / barotropic time stepping -> complicates the modification of the equations (tracer)
31 / 38

32. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
Momentum :
horizontal and vertical vortex forces (McWilliams et al., 2004)
3. Description of the dynamics in the GLM theory
Littoral jet
Horiz. vortex force : shifts the jet towards the beach
Vertical vortex force : slow down the jet
Vorticity
ω3 < 0
Vorticity
ω3 > 0
32 / 38

33. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
3. Description of the dynamics in the GLM theory
Momentum :
Stokes-Coriolis force
Stokes transport
Transport of the
mean current
Stokes-Coriolis force
-> transition towards the off-shore dynamics
(Lentz et al., 2007, submitted)
Inner-shelf zone
Surf zone
33 / 38

34. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
3. Description of the dynamics in the GLM theory
tracers :
What about the Lagrangian drift ?
Non-linear effects on the Stokes drift in shallow water
The Stokes is important compared to the cross-shore currents (Monismith et Fong, 2004)
And even more if the waves are non-linear.
Can lead to an important Lagrangian drift towards the beach at the surface,even outside the surf zone
34 / 38

35. PART 2 : INNER-SHELF AND SURF ZONE CURRENTS
Summary - Conclusion
Impact of waves on the coastal and nearshore currents (3D)
Goal : link between shelf and surf-zone, through the inner-shelf zone
Equations (recently developed) for the 3D interactions between waves and current (Ardhuin et al., 2007)
Implementation in a coastal model (ROMS)
Academic test
What new on the dynamics with the GLM theory ?
horizontal and vertical vortex forces
(effects partly discussed by Newberg et Allen, 2007)
Stokes-Coriolis effect for the transition towards the offshore dynamics
(observed by Lentz et al., 2007, submitted)
analyse of the Lagrangian drift
(non-linear effects on the Stokes drift in shallow water)
35 / 38

36. Impact on the ocean circulation at global scale ?
GENERAL CONCLUSION
The waves :
Impact on the ocean circulation at global scale ?
Impact on ocean surface drift ?
Impact on the mixing of the near-surface ocean ?
Impact on the currents close to the coast ?
Use of a set of equations which separates waves and currents
(GLM) (Ardhuin et al., 2007)
What do my work bring to answer to those (3 last) questions ?
36 / 38

37. The surface drift offshore : dominated by the waves Stokes drift
GENERAL CONCLUSION
The surface drift offshore :
dominated by the waves Stokes drift
the mean current is weaker at the surface
but note that the surface drift of a swell is small (-> the drift still depends on the wind)
The near-surface mixing :
depends on the waves developement
strong when the waves are developed -> impact on the mixed layer, on the vertical distributions of drifting materials (impact on the Random Walk ?)
one needs waves to get simultaneously realistic (strong) surface mixing and realistic surface drift
The coastal currents :
strong current induced by waves in the surf zone (that’s not new !)
but also a few things new on the dynamics of the surf zone and of the inner-shelf zone
there can be strong cross-shore drifts induced by waves, even in the inner shelf zone
37 / 38

38. Following the present work :
FUTURE WORKS
Following the present work :
Mixing model : Validations of the roughness length with TKE dissipation measurements (Gemmrich and Farmer, 2004) Re-evaluation of the TKE flux at the surface (Phd thesis of J. F. Fillipot)
Model of the offshore surface drift : Validations with the observations of Lagrangian drifts (Kudryavtsev et al., 2007, soumis)
Inner-shelf model : Comparison of the model with the mesurements of Lentz et al., 2007, submitted
Possible future works :
Parameterizations of the Stokes drift and of the radiation stress for non-linear realistic waves
Studies of rip-current and other 3D problems involving the coupling of waves and currents. Impact of the horizontal and vertical vortex force.
Applications to material drifts in coastal and off-shore waters. …
Thank you.
38 / 38