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A transition between “Darcy” and Stokes regimes Geological scenario

Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich. A transition between “Darcy” and Stokes regimes Geological scenario Review of steady flow instabilities => porosity waves Analysis of conditions for disaggregation.

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A transition between “Darcy” and Stokes regimes Geological scenario

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  1. Transition from Pervasive to Segregated Fluid Flow in Ductile RocksJames Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes regimes • Geological scenario • Review of steady flow instabilities => porosity waves • Analysis of conditions for disaggregation

  2. lithosphere

  3. 1D Flow Instability, Small f (<<1-f) Formulation, Initial Conditions t = 0 8 f f = , disaggregation condition 6 d f 4 2 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 f 1D Movie? (b1d)

  4. 1D Final t = 70 5 4 3 f 2 1 -350 -300 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 -350 -300 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 f • Solitary vs periodic solutions • Solitary wave amplitude close to source amplitude • Transient effects lead to mass loss

  5. 2D Instability

  6. Birth of the Blob • Stringent nucleation conditions • Small amplification, low velocities • Dissipative transient effects Bad news for Blob fans:

  7. Is the blob model stupid?A differential compaction model Dike Movie? (z2d)

  8. The details of dike-like waves Comparison movie (y2d2)

  9. Final comparison • Dike-like waves nucleate from essentially nothing • They suck melt out of the matrix • They are bigger and faster • Spacing dc, width dd • But are they solitary waves?

  10. 5.2 5 4.8 4.6 4.4 4.2 4 3.8 3.6 3.4 0 5 10 15 20 25 30 35 Velocity and Amplitude Blob model Dike model 40 amplitude amplitude velocity velocity 35 30 25 20 15 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 t t time / time /

  11. 1D Quasi-Stationary State Horizontal Section Vertical Section Phase Portrait 35 35 Pressure, Porosity Pressure, Porosity 6 30 30 4 25 25 f1 20 20 2 15 15 p 0 10 10 f1 -2 5 5 0 0 -4 -5 -5 -6 -10 -10 4.5 5 5.5 -60 -40 -20 0 0 10 20 30 40 f x/d y/d • Essentially 1D lateral pressure profile • Waves grow by sucking melt from the matrix • The waves establish a new “background”” porosity • Not a true stationary state

  12. So dike-like waves are the ultimate in porosity-wave fashion: They nucleate out of essentially nothing They suck melt out of the matrix They seem to grow inexorably toward disaggregation But Do they really grow inexorably, what about 1-f? Can we predict the conditions (fluxes) for disaggregation? Simple 1D analysis

  13. Mathematical Formulation Incompressible viscous fluid and solid components Darcy’s law with k = f(f), Eirik’s talk Viscous bulk rheology with 1D stationary states traveling with phase velocity w (geological formulations ala McKenzie have )

  14. Balancing ball

  15. H(omega)

  16. Phase diagram

  17. Sensitivity to Constituitive Relationships

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