Double Diffusion in

the Core

Double Diffusion in

the Core

David GubbinsSEE, University of

Leeds

CIDER Community Workshop Marconi Center 2009

David GubbinsSEE, University of

Leeds

CIDER Community Workshop Marconi Center 2009

Double Diffusion in the Oceans

Double Diffusion in the Oceans

In the oceans, solar heating warms the top producing hot (light), salty (heavy) water

Heat diffuses faster than salt This leads to an instability, loss of heat increases the density and carries salty water downwards, producing an instability (salt fountain)

This process can produce “fingering” (salt fingers)

…and establish layering, stratified layers separated by thin zones of turbulent mixing

In the oceans, solar heating warms the top producing hot (light), salty (heavy) water

Heat diffuses faster than salt This leads to an instability, loss of heat increases the density and carries salty water downwards, producing an instability (salt fountain)

This process can produce “fingering” (salt fingers)

…and establish layering, stratified layers separated by thin zones of turbulent mixing

Double Diffusion in the Core

Double Diffusion in the Core

If both heat and composition are unstable, they combine

If a layer is compositionally stratified (e.g. at top or bottom of the core) we have the opposite situation to the oceans

The top is cold (heavy) and high in light elements (light)

This produces an overstability This can also produce a layered structure

The time scale is about 100 Myr

If both heat and composition are unstable, they combine

If a layer is compositionally stratified (e.g. at top or bottom of the core) we have the opposite situation to the oceans

The top is cold (heavy) and high in light elements (light)

This produces an overstability This can also produce a layered structure

The time scale is about 100 Myr

Possible Stratified Layers

Possible Stratified Layers

1991: Souriau & Poupinet find decrease in Vp of 0.1% in bottom 150 km of inner core, deduce density stratification

1992, 1995: Song & Helmberger find similar anomalous structure from amplitudes and waveforms -> PREM2

1995: Similar structure incorporated into model AK135…

…confirmed by others, eg Zou, Koper & Cormier (2008)

At the top: slow diffusion of light elements from the mantle may produce ~100km light layer (Asahara et al, 2007; Hernlund)

1991: Souriau & Poupinet find decrease in Vp of 0.1% in bottom 150 km of inner core, deduce density stratification

1992, 1995: Song & Helmberger find similar anomalous structure from amplitudes and waveforms -> PREM2

1995: Similar structure incorporated into model AK135…

…confirmed by others, eg Zou, Koper & Cormier (2008)

At the top: slow diffusion of light elements from the mantle may produce ~100km light layer (Asahara et al, 2007; Hernlund)

In the oceans, evaporation at the surface leads to hot salty water above cold fresh water, leading to a “perpetual salt fountain”. In the core the solute is light and the gradients are opposite, as on the right, leading to overstable oscillations.

DOUBLY-DIFFUSIVE CONVECTION

Parameters for the Core

Parameters for the Core

Two Rayleigh numbers: Ra, Rs Ra=gTTd3/Ratio Ra/Rs = TT/cxFor compositional stratification x = 0.02

For a layer on the liquidus T = 500 KThen Ra/Rs = 0.02

Two Rayleigh numbers: Ra, Rs Ra=gTTd3/Ratio Ra/Rs = TT/cxFor compositional stratification x = 0.02

For a layer on the liquidus T = 500 KThen Ra/Rs = 0.02

In the oceans double diffusion leads to a stack of stably stratified layers separated by thin, turbulent zones

After J. S. Turner, “Buoyancy in Fluids”, 1979

CONCLUSIONS: DYNAMICAL STABILITY

CONCLUSIONS: DYNAMICAL STABILITY

A partially stratified layer may be subject to doubly-diffusive instabilities

This may lead to layering within the stable zone, as in oceanic double diffusion

Layering could explain the discrepancy between seismic travel times and amplitudes

Worth a look!

A partially stratified layer may be subject to doubly-diffusive instabilities

This may lead to layering within the stable zone, as in oceanic double diffusion

Layering could explain the discrepancy between seismic travel times and amplitudes

Worth a look!