IMPACT IMPACT OF WAVESOF WAVES ON THE OCEAN ON THE OCEAN CIRCULATIONCIRCULATION

PHD THESIS DEFENSE, 2004 – 2007 NICOLAS RASCLE

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

Introduction

General concepts

I. Impact of waves on the currents of the surface layer in the open ocean (1D)

II. Impact of waves on the coastal and nearshore currents (3D)

Conclusion

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PHD THESIS DEFENSE, 2004 – 2007 NICOLAS RASCLE

Context of the thesis :interactions Atmosphere / Waves / Ocean

Subject of the thesis :impact of waves on the ocean circulation

Atmosphere

INTRODUCTION

Waves Energy and momentum exchanges

Ocean

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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 ?

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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 ?

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GENERAL

Waves ?

x

z

Short gravity wave :Wavelength = 100 mPeriod = 10 sHeight = 1 m

But the mean length scales for the variations of the wave field are longer : 100 km, a few days…

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Eulerian description of the Stokes drift

Waves (linear) = acos(kx-t)u = acos(kx-t) exp(kz) si z < w = asin(kx-t) exp (kz)

x

z zu

The Stokes transport occurs between crests and throughs.

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GENERAL

Lagrangienne description of the Stokes drift

Waves

x

z

The orbits of particles are not closed :-> Stokes drift

The transport occurs over a depth of the order of a ten of meters.

zu = Us

= acos(kx-t)u = acos(kx-t) exp(kz) si z < w = asin(kx-t) exp (kz)

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GENERAL

2 difficulties to model the current when waves are present :

1. 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)

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GENERAL

Once made a GLM averaging, one obtains :

The free surface is moved back to its mean position. The Stokes drift in agreementwith its Lagrangian description. The mean current described bya quasi-Eulerian mean, and not anEulerian mean. Lagrangian drift = quasi-Eulerian velocity + Stokes drift :

Wave field dynamics <-/-> Quasi-Eulerian current dynamics

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GENERAL

Coriolis Turbulent diffusion

Wind stress

Stokes-Coriolis force :(action of the Coriolis force

on the wave field, momentum then given to the mean flow)

Dynamics of the mean current dynamics of the total Lagrangian drift

Ex : Equilibrium in an horizontaly uniform case (and without stratification)

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GENERAL

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

x

y

Wind stress

Stokes-Coriolisforce

Wind waves

The Stokes-Coriolis force (Hasselmann, 1970)

Ekman transport

Stokes transport

Stokes-Coriolistransport

Case of a wind sea

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GENERAL

Vertically integrated, no net transport induced by waves. But there still might be a net Lagrangian drift :

No net Lagrangian drift

Lagrangiandrift

Stokes transportTransport ofStokes-Coriolis

Stokes-Coriolis force (Hasselmann, 1970)

Mean Current Stokes drift

Case of a long swell Case of a wind sea

+ verticalmixing

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GENERAL

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 ?

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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) :

The Stokes drift

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PART 1 : VELOCITIES IN THE SURFACE LAYER

(Wind : U10=10 m/s)Young wind sea Developed wind seaShort swellLong swell ---

Energie spectra E(f) (=height^2) Spectra f^3 E(f) (Stokes drift at the surface)

Stokes driftsUs=10. cm/sUs=12. cm/sUs=5.2 cm/sUs=1.6 cm/s

Height, PeriodsHs=1.6m, Tp=5.5sHs=2.8m, Tp=8sHs=2.8m, Tp=8sHs=2.8m, Tp=12s

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PART 1 : VELOCITIES IN THE SURFACE LAYER

For a fully-developed wind sea :• at the surface 1.2% of U10 (< 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.

The Stokes drift

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(Wind : U10=10 m/s)Young wind sea Developed wind seaShort swellLong swell ---

PART 1 : VELOCITIES IN THE SURFACE LAYER

Vertical mixing : effect of waves

Mixing length : prescribed

TKE calculation

diffusion production dissipation

Injection of TKE by the dissipation of the wave field :

1D TKE model (Craig et Banner, 1994)

Roughness length

TKE surface flux

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PART 1 : VELOCITIES IN THE SURFACE LAYER

EQUATIONS POUR LE COURANT QUASI-EULERIEN

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

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Vertical mixing : effect of waves

PART 1 : VELOCITIES IN THE SURFACE LAYER

Stokes drift

Mean current

Lagrangian drift

EQUATIONS POUR LE COURANT QUASI-EULERIEN

(Vent : U10=10 m/s)

The drift at the surface essentially comes from the Stokes drift when the waves are developed. (Rascle et al., 2006)

Consequence for the Lagrangian drift :

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PART 1 : VELOCITIES IN THE SURFACE LAYER

Validations :1. The observations of TKE dissipation2. The observations of Lagrangian drifts3. 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)

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PART 1 : VELOCITIES IN THE SURFACE LAYER

• 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)

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Validations :1. The observations of TKE dissipation2. The observations of Lagrangian drifts3. The observations of quasi-Eulerian currents

PART 1 : VELOCITIES IN THE SURFACE LAYER

SMILE (1989, californian shelf)(Santala, 1991)

LOTUS 3 (1982, Sargassian sea)(Price et al., 1987, Polton et al. 2005)

Short field experiment (2 days)Wave followerMesurement very close to the surfaceBias corrections

Long field experiment (160 days)Classical mooringMinimum depth of measurements : 5m

VMCM

2 datasets examined :

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Validations :1. The observations of TKE dissipation2. The observations of Lagrangian drifts3. The observations of quasi-Eulerian currents

PART 1 : VELOCITIES IN THE SURFACE LAYER

Validations : 3. the observations of quasi-Eulerian currents

Vertical shears close to the surface (SMILE)

Small downwind shear -> validates the wave-induced near-surface mixing Crosswind shear ? No evidence of the Stokes-Coriolis effect on the crosswind component

1D TKE model with stratification (Noh, 1996, Gaspar et al. 1990)

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PART 1 : VELOCITIES IN THE SURFACE LAYER

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)

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Validations : 3. the observations of quasi-Eulerian currents

PART 1 : VELOCITIES IN THE SURFACE LAYER

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)

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PART 1 : VELOCITIES IN THE SURFACE LAYERSummary - Conclusion

PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

Coastal zone

Transition ?Poorly understood dynamicsImportance of radiation stress ? of (Stokes-) Coriolis ?Important zone

TideWaves

Part 2 : Impact of waves on the coastal and nearshore currents (3D)

Surf zone

-50m

-10m

Inner-shelf zone

TideWindCoriolisStratification

WavesShoaling Breaking

Primitive equationmodels

Radiation stresses 2DBousinessq models

2 goals : understand the inner-shelf dynamics model : develop a 3D model (primitives equations) to resolve from the offshore to the surf zone

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For the hydrodynamics of that inner-shelf zone, one needscomplete equations (3D) of the forcing of currents by waves :

• Mellor 2003 -> problem in the vertical profile of the radiation stress (Ardhuin et al., 2007 b) • McWilliams et al., 2004 -> adiabatic• Ardhuin, Rascle et Belibassakis 2007 (GLM)

• Momentum:

• Mass:

• Tracers:

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

My work :1. Implement those equations in ROMS to solve the mean circulation

forced by waves : extension of a coastal model to the surf zone2. 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

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

Calculation of waves, of Stokes driftModel of Thornton and Guza

Waves Straight and infinitecoast

Calculation of the mean currentROMS model, modified primitive equations (GLM equations)

Breaking

Jet

Set-upSet-down

Forcing

1. Academic case

4 km

400 points (dx=10 m)

dt = 3 sKz = 0.03 m2/s40 vertical levelsf = 10-4 s-1

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

• Mom. :

• Mass:

• Tracers:

2. Implementation in ROMS :

• 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)

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

Momentum :

• horizontal and vertical vortex forces (McWilliams et al., 2004)

Horiz. vortex force : shifts the jet towards the beachVertical vortex force : slow down the jet

Littoral jet

Vorticityω3 < 0

Vorticityω3 > 0

3. Description of the dynamics in the GLM theory

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

Momentum :

• Stokes-Coriolis force

Stokes-Coriolis force -> transition towards the off-shore dynamics(Lentz et al., 2007, submitted)

Stokes transportTransport of themean current

Surf zoneInner-shelf zone

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3. Description of the dynamics in the GLM theory

PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

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

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3. Description of the dynamics in the GLM theory

PART 2 : INNER-SHELF AND SURF ZONE CURRENTS

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)

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PART 2 : INNER-SHELF AND SURF ZONE CURRENTSSummary - Conclusion

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 ?

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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 driftThe 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

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GENERAL CONCLUSION

FUTURE WORKS

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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.