1. Double Diffusion in the Core David Gubbins SEE, University of Leeds CIDER Community Workshop Marconi Center 2009 David Gubbins SEE, University of Leeds CIDER Community Workshop Marconi Center 2009

2. 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

3. 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

4. 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)

5. 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

6. Parameters for the Core Two Rayleigh numbers: Ra, Rs Ra=g  T  Td 3 /  Ratio Ra/Rs =  T  T/  c  x For compositional stratification  x = 0.02 For a layer on the liquidus  T = 500 K Then Ra/Rs = 0.02 Two Rayleigh numbers: Ra, Rs Ra=g  T  Td 3 /  Ratio Ra/Rs =  T  T/  c  x For compositional stratification  x = 0.02 For a layer on the liquidus  T = 500 K Then Ra/Rs = 0.02

8. 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

9. 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!