Pacific Secular VariationA result of hot lower mantle

David Gubbins

School of Earth Sciences

University of Leeds

Thermal Core-Mantle Interaction

(hot)

(cold)

Lateral variations in heat flux boundary condition on spherical rotating convection

can:

• Drive thermal winds

• “lock” core convection…

• …and delay drift of convection rolls

• Produce resonance of length scales…

• …and secondary resonances

• Force a lateral scale on the convection

• Indirectly produce similar scales on the magnetic field

The effect of lateral variations is weakened by:

• Low Prandtl number (inertia)• Disparity of length scales between convection and

boundary conditions• High Rayleigh number (time dependence)

Geophysical Input for Core Heat Flux

• Mantle convection studies suggest large variations in lateral heat flow (100%)

• …and thermal boundary layer at the base of the mantle (D”)

• Seismology suggests a boundary layer 250 km thick

• …with temperature variations of 500 K

Observational Evidence of Lateral Variations

• Modern geomagnetic field• Time-average of paleomagnetic field• Persistent reversal paths• Non-axisymmetric variations in secular variation• Low secular variation in Pacific

OVERVIEW

• Evidence for low secular variation in the Pacific -historical and paleomagnetic

• Lateral heat variations on the core-mantle boundary

• Simple thermal convection influenced by the boundary

• Relationship with numerical dynamo simulations and application to the Earth’s core

• Implications for the thermal state of the core

Declination AD 1650

Declination AD 1990

Declination at Hawaii and Greenwich Meridian

Inclination Hawaii and Greenwich meridian

Looking for weak Secular Variation

• Historical record shows little SV in Pacific

• 400 years is not long enough to be definitive

• We need 5-50 kyr

• Big Island, Hawaii, offers 35 kyr with dating

Volcanoes of Big Island, Hawaii

Mean residual -2.8o +/- 0.3o

D from flows dated by C14, Big Island, Hawaii

I from flows dated by C14, Big Island, Hawaii

Kilauea East Rift Zone Drilling

Hawaiian data last 50 kyr from borehole data and surface flows

The Cylinder

Convection with laterally varying heat flux depends on 3 important parameters

1. Ekman number 22 dE

2. Vertical Rayleigh number

where h is the mean surface heat flux

k

ghdRv

5

3. Horizontal Rayleigh number

where q is the lateral variation of

heat flux, average zero

k

gqdRh

5

3 LIMITING CASES

• Rv=0: thermal wind

• Rh=0: convection with uniform boundaries

• Rh=0.3Rv: convection heated from below

and influenced by the boundary variations

“Thermal Wind”, Rv=0, E=2x10-4

Uniform boundariesE=2x10-4, Rh=0, Rv=1.1 Rv

c

Uniform boundaries, equatorial slice

Inhomogeneous boundary conditions (periodic solution) surface flow and temperature

Rh=0.3 Rv, E=2x10-4, Rv=1.1 Rvc

Inhomogeneous boundary conditionsRh=0.3 Rv, E=2x10-4, Rv=1.1 Rv

c

SUMMARY

• Boundary heat flux based on shear wave anomalies can inhibit convection at the top of the core below the hot region corresponding to the Pacific…

• …because the anomaly there is longitudinally broader than in the Atlantic/Africa

• This convective flow does not generate a magnetic field

COMPARISON WITH A GEODYNAMO SIMULATION

• This convective flow does not generate a magnetic field

• Bloxham’s geodynamo simulation exhibits a time average that reflects the boundary conditions…

• …but does not give low Pacific SV or a field that resembles the time average at any instant of time

• The principle difference is not the magnetic field…

• It is probably the higher Rv in the dynamo simulation

APPLICATION TO THE EARTH

• Resonance with the boundary arises because of similarity in length scales of convection and boundary anomalies

• Small E (10-9) in the core implies a small scale but magnetic forces increase it

• A higher supercritical Rv is needed for dynamo action, but this produces magnetic fields that are too complex, both spatially and temporally

• Again, the in the low E regime dynamo action may occur at lower supercritical Rv because of its organising effect on the flow

IMPLICATIONS FOR CORE HEAT FLUX

D’’

slowfas

t

low heat fluxhigh heat flux

Difference in Vs implies temperature difference 500 K in 250 km

HORIZONTAL VS VERTICAL HEAT FLUX

•

Lateral temperature difference 500 K

• Within D’’ thickness 200 km• Thermal conductivity 10 W/m/K• Gives heat flux variation 1 TW =…• 20% of conventional estimate of vertical

heat flux• May be larger locally

CONCLUSIONS

• The evidence for weak secular variation in the Pacific is quite strong

• Simple thermal convection calculations show this can come about from lateral variations in heat flux through the boundary

• These flows are too simple to generate a magnetic field, and numerical dynamo simulations give magnetic fields that appear more complex than is observed

• Lateral heat flux variations in D’’ appear to be large enough to cause this effect, provided large scale flow is maintained in the core