Post on 22-Feb-2021
Essential Planetary Core Fluid Dynamics
Jonathan Aurnou UCLA Earth & Space Sciences
aurnou@ucla.edu
CIDER Meeting, KITP 7/6/16
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
Talk Outline
Movies Online
www.youtube.com/user/spinlabucla
Downloadable: spinlab.ess.ucla.edu
Movies Online
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
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
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
Soderlund et al. EPSL 2012
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
Talk Outline
New Horizons Image
Ro =U
R
Jets
Ro =U
R
JetsNew Horizons Image
Magnetic field
Image: Hao Cao
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
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
“Differencing” Experiments
Step through a set of four related laboratory experiments Discuss relevant dynamics at each step
& build/take apart rotating Navier-Stokes…
“Differencing” Experiments
Step through a set of four related laboratory experiments Discuss relevant dynamics at each step
& build/take apart rotating Navier-Stokes…
Heuristic approach: shortest time-scale process~ largest acceleration ~ dominates
Jon Bridgeman, Mike Lavell, Steve Tomlinson & Eric King
“Differencing” Experiments
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
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
Columnar convection ‘modestly’ breaks TPT Axial up/down flows + inertial swirlings = helices…
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
Columnar convection ‘modestly’ breaks TPT Axial up/down flows + inertial swirlings = helices…
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
Thomas Gastine (IPGP), in prep.
Thomas Gastine (IPGP), in prep.
E = 1e-7
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
Talk Outline
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
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
Calkins et al. GJI 2012
Effects of CMB Topographyz-vorticity < t > streamlines
Calkins et al. GJI 2012
Ridge Ridge
++
--
Effects of CMB Topographyz-vorticity < t > streamlines
Calkins et al. GJI 2012
++
--
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 1999
Pais & Jault GJI 2008
streamlines
Effects of CMB Temperature
Sumita & Olson 1999
Pais & Jault GJI 2008
streamlines
Effects of CMB Temperature
Sumita & Olson 1999Calkins et al. GJI 2012
Pais & Jault GJI 2008
streamlines
Effects of CMB Temperature
Sumita & Olson 1999Calkins et al. GJI 2012
Garnero 20??
streamlines
Effects of CMB Temperature
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?
Pais & Jault GJI 2008
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
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
The Geodynamo Rotating Fluid Dynamics Primer Core Coupling
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
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
Core-Mantle Boundary B_r
Finlay & Jackson 2003
A.D.
Finl
ay &
Jac
kson
200
3
hydrostatic balance: Parabolic equipotential surfaces
H(s)
Image: Jon Cheng
Fp
Fg
FpFc
hydrostatic balance: Parabolic equipotential surfaces
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
Thomas Gastine (IPGP), in prep.
IC T
ange
nt C
ylin
der
Thomas Gastine (IPGP), in prep.
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
Rotating Convection Columns
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
Rotating Convection Columns
Onset Forcing:mc E1/3
Soderlund et al. EPSL 2012
z-vorticity
g
Ω
Christensen, Enc. Solid Earth Geophys. 2011
Models:
E ~ 1e-4; lc ~ 0.1
Rotating Convection Columns
Onset Forcing:mc E1/3
Soderlund et al. EPSL 2012
z-vorticity
g
Ω
Christensen, Enc. Solid Earth Geophys. 2011
Models:
E ~ 1e-4; lc ~ 0.1
Rotating Convection Columns
Onset Forcing:mc E1/3
Soderlund et al. EPSL 2012
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
Movie: Guillaume Fabre
Slow precessing “wall mode” Fast oscillatory convection in bulk
Movie: Guillaume Fabre
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