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!!!