1. 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

2. lithosphere

3. 1D Flow Instability, Small  (<<1  ) Formulation, Initial Conditions -250-200-150-100-500 2 4 6 8 t = 0 z  -250-200-150-100-500 -0.5 0 0.5 1 z p 11.522.533.544.55 -0.5 0 0.5 1  p  =  d, disaggregation condition 1D Movie? (b1d)

4. 1D Final -350-300-250-200-150-100-500 1 2 3 4 5 t = 70 z  -350-300-250-200-150-100-500 -0.5 0 0.5 1 z p 11.522.533.544.55 -0.5 0 0.5 1  p 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  c, width  d But are they solitary waves?

10. Velocity and Amplitude time /  Blob model amplitude velocity 00.511.522.533.5 0 5 10 15 20 25 30 35 40 time /  Dike model amplitude velocity

11. 1D Quasi-Stationary State 4.555.5 -10 -5 0 5 10 15 20 25 30 35 x/x/ Horizontal Section -60-40-200 -10 -5 0 5 10 15 20 25 30 35 y/y/ Vertical Section 010203040 -6 -4 -2 0 2 4 6 p  Phase Portrait Pressure, Porosity Pressure, Porosity 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 11 11

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  ? 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(  ), Eirik’s talk Viscous bulk rheology with 1D stationary states traveling with phase velocity  (geological formulations ala McKenzie have )

14. Balancing ball

15. H(omega)

16. Phase diagram

17. Sensitivity to Constituitive Relationships