Pacific Secular VariationA result of hot lower mantle
David Gubbins
School of Earth Sciences
University of Leeds
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
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
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
Inhomogeneous boundary conditions (periodic solution) surface flow and temperature
Rh=0.3 Rv, E=2x10-4, Rv=1.1 Rvc
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