Dynamics of turbulent western boundary currents at low latitude in

a shallow water model (Part I)

Presented by

Cataria Quam Cyrille AKUETEVI

and directed by

Achim Wirth & Bernard Barnier

1

MEIGE

07/06/2013

PLAN

INTRODUCTION : Strong signals in the ocean dynamics

MODELS : Shallow water model, its forcing and numerical implementations

Some RESULTS and AnaLysis: Laminar solutions, Dynamics of western

boundary currents, Coherent structures, Vorticity balance…

CONCLUSIONS

Oceanic

Circulation

Exchange air-sea

Regional

Climate

WHY WE STUDY OCEANIC CIRCULATION AND ITS

VARIABILITY?

GENERAL CONTEXT

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

1) In situ measurement

2) Model

forc

as

tin

g

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

GENERAL CONTEXT

1) In situ measurement

# expensive

# ponctual

2) Model

# cheap but need in situ measurement

# spatial

# forecasting

# Lack of understanding dynamics like: baroclinic

instability, internal waves, western boundary

current and eddy shedding system, …

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

Strong western boundary current (WBC) are a dominant feature of the worlds

oceans

Most energetic regions of World Ocean (Swallow & Bruce, 1966; Schott, 1983; Fischer et al., 1996)

The near western boundary region is the origin of a substantial part of turbulent

kinetic energy production in the domain

It is an area of intense up-welling (Schott & McCreary (2001), Wirth et al. (2001)) and biological

production (Kawamiya and Oschlies, 2003)

SCIENTIFIC CONTEXT

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

Equatorial Atlantic North Brazil Current system with its eddy

(Richardson et al. 1994)

the Trade Winds (TW) are the major force The latitudinal inclinaison of the coast line

is westward

Indian Ocean The Somali Current system with the Great

Whirl (Schott & McCreary 2001)

The seasonally reversing Monsoon Winds (MC) dominate

The latitudinal inclinaison of the coast

line is eastward

SCIENTIFIC CONTEXT

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

Previous works:

To the best of our knowledge there is so far no description or theory of near

wall turbulence in the WBC, that goes beyond the synoptic eddies

In general the quantitative description of WBC and its parameterization are

mainly based on laminar Munk-layer and inertial-layer theory which is in

stark contrast to engineering fluid dynamics where the boundary-layer (BL)

theory is the leading domaine since its birth in the beginning of the 20th

century (Prandtl 1904)

With the exception of the pioneering work of Edwards and Pedlosky (1998a,

1998b) on the deep WBC, low latitude turbulent WBCs have sofar not been

studied extensively

SCIENTIFIC CONTEXT

INTRODUCTION\BACKGROUNGS\MODELS\RESULTS and ANALYSIS\CONCLUSION

INTRODUCTION

The present work focuses on:

the dynamics of low latitude turbulent western boundary currents in a

highly idealized configuration

the determination of the turbulent structures and its dependence on the

Reynold number, by varying the viscosity between experiments, and its

response to two types of wind forcing.

SCIENTIFIC CONTEXT

MODELS

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

MODELS

Eq

3000km

1000km

6000km

Δx=Δy=2.5km (no grid refinement)

Δt=90s (CFL > 10Δt)

No-slip condition

I - Idealize Shallow Water

Trade Winds

Monsoon Winds

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

MODELS

Experiments

Experiments TW1000 TW500 TW400 TW300 TW250 TW150 TW125

ν (m2s-1) 1000 500 400 300 250 150 125

Experiments MW1000 MW500 MW400 MW300

ν (m2s-1) 1000 500 400 300

Eq

Eq

RESULTS

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Laminar solutions

Recall

Munk theory (Munk 1950)

quasi-geostrophic

laminar flow

viscous dissipation balances

planetary vorticity advection:

Layer width

Layer width Analytic solution

Analytic solution

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Inertial theory (Charney 1955, Pedlosky 1979, Vallis 2006)

Quasi-geostrophic

Area where the zonal velocity is westward

relative vorticity advection balances planetary vorticity advection:

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Laminar solutions

Strong WBCs with a recirculation in the rest of the domaine

MW1000

Single gyre extending over the entire

domaine with the WBC crossing the

equator in northward direction

Zonal velocity vanishes almost

completely except near the southern

and northern boundaries of domaine

TW1000

Two gyres with poleward WBCs in

both hemispheres. The northern

WBC is centre of interest

Zonal velocity is westward at low

latitudes up to y=1300km and

eastward above

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Low latitude

TW-forcing

Fair agreement: Inertial theory and TW

uTW

< 0 leading to an inertial boundary layer

(Charney 1955, see also Vallis 2006)

MW-forcing

Fair agreement: Munk-layer theory and MW

uMW

~ 0

High latitude

Fair agreement: Munk-layer theory and MW

& TW where inertial effect vanishes

Difference between the two forcing is due to

the inertial effect

Laminar solutions and dynamics of the two forcings Munk-layer theory solution

(Munk (1950), Pedlosky (1990))

Inertial boundary layer solution

(Charney (1955), Pedlosky (1990))

INTRODUCTION\BACKGROUND\MODEL\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Coherent structures

TW-forcing: PV(m-1s-1)

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

MW-forcing : PV(m-1s-1)

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Intermittent and violent detachments of

the viscous sub-layer just north of the

eddy center

Analog to bursts or ejections in the

classical boundary layer (Robinson

1991) and are thus given the same

name

Initiated by anticyclones, bursts are

always followed by the formation of

dipole away from te boundary

Burst needs fine resolution in both

horizontal directions, not only in the

vicinity of the boundary layer

EDDY, BURST and DIPOLE

PV(m-1s-1)

Scales of motion

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

RESULTS

Taylor scale

Extended Boundary Layer (EBL): plateau at around of a scale of 60km

MW300 TW125

Vorticity balance

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\

RESULTS

The conservative form of the equation of vorticity is:

where S is the curl of the forcing.

Separating the variables into

The equation for the average vorticity balance then reads :

Vorticity fluxes

Vorticity fluxes

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\

RESULTS

Area where FRIC dominates : δν viscous sublayer (VSL)

Area of large average meridional velocity: δV

advective boundary layer (ABL)

MW: TRVA balances FRIC (turbulent terms

transport the vorticity at all latitudes)

TW: RVA balances FRIC at low latitudes

TRVA balances FRIC at high latitudes

Difference between MW- and TW-forcing

Scaling

Scaling of boundary layers width

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\

RESULTS

In the Munk-layer theory δν = δM = δV While the viscosity decreases δν < δM < δV

For the lower viscosity δν < δM < δV < δEBL

δν (MW) < δν (TW) for the same viscosity, explain the result that

simulations of the MW were only possible down to ν = 300m2s-1

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\

RESULTS

The gap between δEBL and δν is a measure of the complexity of the numerical calculations as δν has to be resolved througout δEBL in both horizontal directions

N=(δEBL / δν)2 can be taken as a measure for the involved degrees of freedom in the

calculations : N α Re2.4 in the low latitude MW and up to N α Re2.9 for the high latitude TW while the Munk-layer thickness leads to N α Re2/3

Scaling of boundary layers width

Conclusions

Prove that the inertial overshoot is not the origin of the eddies shedding hence the

non-importance of the equator Different eddy dynamics for TW- and MW-forcing are due to inertial effects

Inertial theory teach that small westward velocities can stabilize the

WBC. Velocity components in other directions have no such effect. A

parameterization of the turbulence must therefore reflect this anisotropy Three boundary layers are identified: - viscous sublayer (δν ) - advective boundary layer (δV ) - extended boundary layer (δEBL )

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

CONCLUSION

Concerning numerical simulation of turbulent boundary layers The thickness of the viscous sub-layer δν decreases faster than the prominent 1/3

scaling from Munk-layer theory prove that todays simulations of the ocean dynamics have resolution which is far from being sufficient

Grid refinement near the boundary has no place in simulations of the turbulent

boundary layer as: (i) the structures are isotropic and (ii) the small scales extend far from the boundary

N=(δEBL / δν)2 can be taken as a measure for the involved degrees of freedom in the calculations : N α Re2.4 in the low latitude MW and up to N α Re2.9 for the high latitude TW while the Munk-layer thickness leads to N α Re2/3

INTRODUCTION\BACKGROUND\MODELS\RESULTS and ANALYSIS\CONCLUSION

CONCLUSION

THANKS!!!