Essential Planetary Core Fluid Dynamics...SpinLab Record Player Thomas Gastine (IPGP), in prep....

Essential Planetary Core Fluid Dynamics

Jonathan Aurnou UCLA Earth & Space Sciences

[email protected]

CIDER Meeting, KITP 7/6/16

mailto:[email protected]

The Geodynamo Rotating Fluid Dynamics Primer Core Coupling

Talk Outline

Movies Online

www.youtube.com/user/spinlabucla

Downloadable: spinlab.ess.ucla.edu

Movies Online


Talk Outline

Generates a magnetic fields and then continually regenerate that field

Magnetohydrodynamic (MHD) process

Converts kinetic energy of flowing conductor into magnetic energy

The Geodynamo

Image: Glatzmaier & Olson, SciAm 05

Field changes over relatively short times Only present explanation: field tied to core fluid motions

Core-Mantle Boundary B_r

Movie: Chris Finlay (DTU)

A.D.

Generates a magnetic fields and then continually regenerate that field

Magnetohydrodynamic (MHD) process

Converts kinetic energy of flowing conductor into magnetic energy

The Geodynamo

Image: Glatzmaier & Olson, SciAm 05

z-vorticity

Present PictureGeodynamo driven by axial, helical columnar flows

Soderlund et al. EPSL 2012

g

Ω

Christensen, Enc. Solid Earth Geophys. 2011 z-vorticity

Present PictureGeodynamo driven by axial, helical columnar flows In models, magnetic flux patches often associated with columns



Talk Outline

New Horizons Image

Ro =U

R

Jets

Ro =U

R

JetsNew Horizons Image

Magnetic field

Image: Hao Cao


Talk Outline

g

Ω

Christensen, Enc. Solid Earth Geophys. 2011 z-vorticity

Fluids Primer

Goal: Understand basic fluid dynamics in a rapidly rotating core

“Differencing” Experiments

Step through a set of four related laboratory experiments Discuss relevant dynamics at each step



& build/take apart rotating Navier-Stokes…



& build/take apart rotating Navier-Stokes…

Heuristic approach: shortest time-scale process~ largest acceleration ~ dominates

Jon Bridgeman, Mike Lavell, Steve Tomlinson & Eric King


Isolated droplets/particles (empty tank) 1. Stationary vs. 2. Rotating

Fluid Layer (water-filled tank) 3. Stationary vs. 4. Rotating

Experiment 1Stationary “Empty” Tank

= 0.12 s

Free-Fall Estimates

Experiment 2Rotating “Empty” Tank

Non-inertial ForcesEffective Gravity

Effective Gravity

~ 5.4 Gravity dominates

Experiment 3Stationary Water-Filled Tank

= 0.9 shydrostatic balance

Experiment 4Rotating Water-Filled Tank

Spin-up by viscous & pressure terms (~ 15 minutes)

Ekman,E =rot

visc

7 106

hydrostatic balance: Parabolic equipotential surfaces

H(s)

Image: Jon Cheng

Coriolis dominatesQuasi-Geostrophic Balance

Geostrophic FlowsInvariant along rotation axis

Taylor-ProudmanTheorem

“Quasi-geostrophic”TPTflow!

Columnar convection ‘modestly’ breaks TPT Axial up/down flows + inertial swirlings = helices…

Sam

May

, Dig

iPyR

o

InertialFrameParabolic table

Helical Columns


ri

Sam

May

, Dig

iPyR

o

RotatingFrameParabolic table: gravity balances centrifugal

ri 'u

2

D~u

Dt= ~u 2~

u2

ri 2u

Inertial Circles

ri =u

2

Bit like a gyro-radius

Helical Columns

Inertial circles (+ boundary jets)

NASA’s Perpetual Ocean Data Assimilation

Visualization

Helical Columns


Helical Columns

Columnar convection breaks TPT Axial up/down flows + inertial swirlings = helices…

Movie: Jon Cheng’s phone

Helical Columns

Columnar convection breaks TPT Axial up/down flows + inertial swirlings = helices…

Axial up/down-wellings + inertial swirling = helices…

Movie: my cell phoneE = 2.5e-5

Rotating frame;top view ofdescending dye

Helical Columns

Thomas Gastine (IPGP), in prep.

E = 1e-7

SpinLab Record Player



E = 1e-7


Talk Outline

Effects of CMB TopographyTPT: axially invariant flow around a localized obstacle

www.youtube.com/watch?v=7GGfsW7gOLI

Calkins et al. GJI 2012 Fixed longitude, non-axisymmetric topographic ridge on CMB

Simplified “QG” core convection

Effects of CMB Topography

Calkins et al. GJI 2012 Fixed longitude, topographic ridge on CMB

Simplified “QG” core convection

Effects of CMB Topography

Calkins et al. GJI 2012

Effects of CMB Topographyz-vorticity < t > streamlines




Ridge Ridge

++

--



++

--

Pais & Jault GJI 2008Calkins et al. GJI 2012

Effects of CMB TopographyAssumes QG core flow (aka, “TPT”), as in Calkins et al. 2012

Inverts for flow by assuming fluid is locked to magnetic field on short time scales

Rm =

B-advection

B-di↵usion

1

streamlines

Sumita & Olson 1999

Pais & Jault GJI 2008

streamlines

Effects of CMB Temperature

Sumita & Olson 1999Calkins et al. GJI 2012


streamlines


Sumita & Olson 1999Calkins et al. GJI 2012

Garnero 20??

streamlines


Thermo-topographic “Farallon” anomaly? Why there? One dominant anomaly?

Effects of ICB Anomalies?…

Aubert et al. 2013

May be due to m=1 IC translation anomaly Translation jibes with seismic and geodynamic constraints?



Talk Outline

Small-scale axial, helical convection in Coriolis-dominated systems

Such flows can generate dynamo fields: Dynamo lecture

Large-scale core dynamics may be “sculpted” by boundary anomalies

To what degree? By realistic anomalies? Which ones?

Summary


Talk Outline

THANKS…

Silicate Mantle

LiquidOuter Core

Solid InnerCore

Radius = 6470 km

CMB(core-mantleboundary)

Silicate Mantle

LiquidOuter Core

Solid InnerCore

CMB radius = 3485 km

Inner Core radius = 1220

km

CMB(core-mantleboundary)

Radius = 6470 km

Fe+10%?

Q~45 TW

~15- 5 TW

www.neptune.washington.edu!

q

q

q q

Sufficientsuperheat/

radioactivity to drive

early dynamo?

q

q

q qNO?—

Mechanical dynamo?

q

q

q q

Movie:Alex Grannan

q

q

q q

Movie:Daphne Lemasquerier

& Alex Grannan

q

q

q q

q

q

q q

Pressure (GPa)360330

Tem

pera

ture

(K

) Tmelt

Tad

q

q

q q

Pressure (GPa)360330

Tem

pera

ture

(K

) Tmelt

Tad

Core evolution

Thermal conductivity k?!?!

Thermo?-chemical? convection?

A.D.

Finl

ay &

Jac

kson

200

3

Core-Mantle Boundary B_r

Finlay & Jackson 2003

A.D.

Finl

ay &

Jac

kson

200

3


H(s)

Image: Jon Cheng

Fp

Fg

FpFc


Movie: Jon Cheng

H(s)

Movie: Jon Cheng

Geostrophic Flows

Perpendicular to pressure gradients Invariant along rotation axis

for hydrostatic balance in z

Horizontally non-divergent flow


IC T

ange

nt C

ylin

der

Taylor-Proudman TheoremRequires axially invariant flow around a localized obstacle

www.youtube.com/watch?v=7GGfsW7gOLI

Rotating Convection ColumnsEkman number, E

Scaled viscous force

Image: J. Cheng

Rotating Convection Columns

Rayleigh number, Ra Scaled buoyancy forceOnset Forcing:

Ekman number, E Scaled viscous force

Image: J. Cheng


Rayleigh number, Ra Scaled buoyancy forceOnset Forcing:

Onset column width:

Ekman number, E Scaled viscous force

Image: J. Cheng

O(1

)

Tall

O(E1/3) Skinny


Onset Forcing:mc E1/3


z-vorticity

g

Ω

Christensen, Enc. Solid Earth Geophys. 2011

Models:

E ~ 1e-4; lc ~ 0.1


Onset Forcing:mc E1/3


z-vorticity

g

Ω

Christensen, Enc. Solid Earth Geophys. 2011

Models:

E ~ 1e-4; lc ~ 0.1

Earth’s Core:

E ~ 1e-15; lc ~ 1e-5

10^3 too

wide

(i.e., 104 x smaller than scale of flux patches)

Model E1/3 columns: generate large-scale flux patches

Unobservably small: Cannot explain large-scale core flux patches

Planetary Cores E1/3 columns: ~10 m wide Tall and wafer thin

Columns: Models vs. Cores

MHD Experiments Magnet

Rotating magneto-convection in liquid metal Strong magnetic field can balance Coriolis

Different behaviors predicted

Slow precessing “wall mode” Fast oscillatory convection in bulk

Movie: Guillaume Fabre


Slow precessing “wall mode” Fast oscillatory convection in bulk

Image: Adolfo Ribeiro

Top View: Axial

Velocity

In liquid metal, fast oscillatory columns and slow wall modes Wall modes similar to low latitude waves in observations

Missing in present dynamo models

Lab MHD Experiments

Essential Planetary Core Fluid Dynamics...SpinLab Record Player Thomas Gastine (IPGP), in prep....

Documents

Transcript of Essential Planetary Core Fluid Dynamics...SpinLab Record Player Thomas Gastine (IPGP), in prep....