On the Dynamics of Oceanic Gravity Currents · The vertical resolution is key to correctly...

On the Dynamics of Oceanic GravityCurrents

Achim Wirth

LEGI / CNRS

LEGOS, Dec 6, 2011

Ocean Circulation

Gyre“weather”

Overturning“climat”

Ocean Dynamics by Scale

-k

energy injection

(107m)−1 (105m)−1 (10m)−1 (10−2m)−1

energy dissip

Ocean Dynamics by Scale

-k

energy injection

(107m)−1

inverse energy cascade

(105m)−1

bc/bt inst.

geostrophy QG turbulence ? ? ? ? ? strat. rot. turb.

(10m)−1

turb. 3D

(10−2m)−1

energy dissip

? ? ? ? ? ? direct energy cascade

Ocean Dynamics by Scale

-k

energy injection

(107m)−1

inverse energy cascade

(105m)−1

bc/bt inst.

geostrophy QG turbulence ? ? ? ? ? strat. rot. turb.

(10m)−1

turb. 3D

(10−2m)−1

energy dissip

? ? ? ? ? ? direct energy cascade

geophys. fluid dyn. turbulence

Ocean Dynamics by Scale

-k

energy injection

(107m)−1

inverse energy cascade

(105m)−1

bc/bt inst.

geostrophy QG turbulence ? ? ? ? ? strat. rot. turb.

(10m)−1

turb. 3D

(10−2m)−1

energy dissip

? ? ? ? ? ? direct energy cascade

convectiongravity currentinteract topographyfrontfilamentint. waves..........

geophys. fluid dyn. turbulence

small scale processes

Ocean Dynamics by Scale

-k

energy injection

(107m)−1

inverse energy cascade

(105m)−1

bc/bt inst.

geostrophy QG turbulence ? ? ? ? ? strat. rot. turb.

(10m)−1

turb. 3D

(10−2m)−1

energy dissip

? ? ? ? ? ? direct energy cascade

convectiongravity currentinteract topographyfrontfilamentint. waves..........

geophys. fluid dyn. turbulence

small scale processes

Gravity Current

••

•• •

•

••

Geostrophy

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�� F ′

g

F ′

c

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-x

α

⊗-

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Fg

Fc

F ′

gF ′

cF ′

c

u =g′

ftan α

Forced Geostrophy

vein

friction layer

Ekman layer

Forced Geostrophie

veine

friction layer

Ekman layer

Forced Geostrophy

vein

friction layer

Ekman layer

Heat Equation

∂th = −∂xUEk =δ

2∂xvgeo =

δg′

2f∂xxh = ∂x (κH∂xh)

24h 60h

Friction... determines the dynamics of oceanic gravity currents.

The frictional processes can not be explicitely representedin today’s (and tomorrow’s) ocean models

τ + cD|u|

linear Rayleigh friction (τ ) quadratic drag law (cD)

Initial Conditions

Temp Vg

Reference Exp. (2D)

Z σ

Grid σ

Convective Adjustment and Classic (2D)

2+4+3 Levels (2D)

Down-slope transport

2.5D 3D

Conclusions A

◮ The vertical resolution is key to correctly represent oceanicgravity currents.

◮ A few σ (< 6) levels in the bottom layer are sufficient.

◮ The refinement of the vertical resoltuion at the bottom ismore important than at the surface.

◮ These results are NOT restricted to gravity currents.

How do we find REAL bottom-friction

◮ Optimist : Study non-hydorstatic PBL-dynamics.◮ Pessimist : Use data-assimilation to determine friction

parameters from obs. (that we do not have).

Non-hydrostatic simulation :

HAROMOD

Coherent Structures

Coherent Structures

Coherent Structures

?roughness of the ocean floor ?

variability of roughness ?

multiscale roughness (bio) ?

roughness type “k” vrs. “d” ?

orientation of roughness elements ?

suspension of sediments ?

tidal currents ?

waves ?

retroaction of currents on roughness ?

And : “The matter is far from beeing understood” Jiménez, Ann.Rev. Fluid Mech. (2004).

Friction... determines the dynamics of oceanic gravity currents.

The frictional processes can not be explicitely representedin today’s (and tomorrow’s) ocean models

τ + cD|u|

linear Rayleigh friction (τ ) quadratic drag law (cD)

Data Assimilation :Estimation of parameters and friction laws :detetction of transition from linear to quadratic law.

0 500 1000 1500 2000 2500Re

0

5

10

15

C_D

(10

^-4)

c̃D = cD +τ

|u|

cD

Conclusions

Convection

Gravity Current

Conclusions & Perspectives

Convection

Gravity CurrentDWBC

?m

ixin

g?

mixed layer, air-sea interaction