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A bound on heat flow below a double crossing of the pv-ppv transition

A bound on heat flow below a double crossing of the pv-ppv transition. (van der Hilst et al. 2007). Two recent seismic studies infer CMB heat flow. (Lay et al., 2006; van der Hilst et al., 2007). A Double Crossing. Hernlund et al. (2005). A Double Crossing. Hernlund et al. (2005).

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A bound on heat flow below a double crossing of the pv-ppv transition

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  1. A bound on heat flow below a double crossing of the pv-ppv transition (van der Hilst et al. 2007) Two recent seismic studies infer CMB heat flow (Lay et al., 2006; van der Hilst et al., 2007)

  2. A Double Crossing Hernlund et al. (2005)

  3. A Double Crossing Hernlund et al. (2005)

  4. A Complication ppv phase is 1-2% denser than pv flow across lower transition absorbs latent heat

  5. Objective Can we place bounds on the CMB heat flow?

  6. Control Volume 1. Mass Integrate over volume V

  7. Control Volume 2. Energy where surface integral gives a term

  8. Control Volume 2. Energy where

  9. Latent Heat Sharp Transition Broad Transition

  10. Minimum Bound Latent heat condition Minimum Gradient at z = -d

  11. Minimum Bound (Con’t) From control volume For a double crossing We obtain

  12. Example Transition parameters Other parameters  = 9 MPa/K Cp = 1300 J/kg  = 1.5% = 5500 kg/m3 T(-d) = 3400 K  = 10-6 m2/s L = TV = 0.8 x 105 J/kg k = Cp  = 7.1 W K-1 m-1 Using vz = 1 mm/yr gives dT/dz > 23 K/km -> local heat flow at CMB is greater than 160 mW/m2

  13. Global Heat Flow at CMB? ppv lens may be absent from areas of return flow

  14. Dependence on Velocity

  15. Estimate Vertical Velocity Balance buoyancy flux with viscous dissipation in pv layer gives Typical dimensions give vz = 1 mm/yr when  ~ 1022 Pas

  16. Conclusions 1. Dynamics of ppv layer can substantially alter local heat flux - probably small changes in global heat flow - large lateral variations in q over CMB 2. Extrapolation of temperature to CMB strongly affected by flow - flows greater than 1 mm/yr yield unrealistic Tcmb • bound on q may constrain geometry of ppv layer and/or viscosity of lowermost mantle

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