2. Future Bubbledrive Model Layout

3. Current Bubbledrive Model Layout

4. Computational Chart of the Bubbledrive Model

5. Hydrodynamics of Magma in the Conduit 1.Homogenous approximation of two phase flow (low relative velocity between melt and bubbles) 2.Continuity equation (non-steady state) where j=  v and  is bulk magma density. In cylindrical coordinates – Reduction to one-dimensional form – yields

6. Hydrodynamics of Magma in the Conduit 3.Momentum equation (non-steady state) In one dimension along gravity field it becomes – where f is a friction factor as a function of Reynolds number such that 4.Density is calculated from full scale interactive bubble growth model.

7. Interactive Diffusive-Decompressive Bubble Growth Model

9. Input Parameters for Model Runs Trigger # 1 Landslide and “instant” decompression Example of Mount St. Helens eruption  Trigger # 2 Recharge from below (at constant rate)

10. Table of Model Parameters ParameterValueRefs/Relations Volatile CompositionH2OH2OAnderson, 1991 Melt CompositionRhyolitespecified Initial Melt Temperature1000 o Cspecified Melt Density2200 kg/m 3 Clark et al., 1987 Initial Viscosity at Vent2.64*10 7 Pa sec Hess and Dingwell, 1996 Initial Viscosity at 1000 m9.91*10 5 Pa sec Initial Diffusion Coefficient at Vent1.04*10 -11 m 2 /sec Zhang, 1999 Initial Diffusion Coefficient at 1000 m1.97*10 -11 m 2 /sec Henry Constant (Solubility)1.6*10 -11 1/PaBurnham, 1975 Temperature Conductivity1.42*10 -7 m 2 /secSnyder et al., 1994 Melt Heat Capacity1350 J/(kg K)Neuville et at., 1993 Gas Heat Capacity2500 J/(kg K)Perry et al., 1984 Latent Heat of VC7150 J/kgNeuville et at., 1993 VC Temperature802 o CBacon, 1977 VC Interval50 Kspecified Initial Heat of Evaporation9676 J/moleSahagian et al., 1996 * VC - vitrification or crystallization

11. Table of Model Runs ## CodeShapeDepth, mVent D, m Recharge*, m/sec Decompression*, MPa Composition Set #1 1r1-0Glass1000200080Rhyolitic 2r1-1Glass1000200180Rhyolitic 3r1-2Glass1000200280Rhyolitic 4r1-5Glass1000200580Rhyolitic 5r1-10Glass10002001080Rhyolitic Set #2 6r1-0-0Cylinder1000100080Rhyolitic 7r1-0-2Cylinder1000100280Rhyolitic Set #3 8r2-0-0Cylinder2000100080Rhyolitic Set #4 9r2-2-0Bottle2000200080Rhyolitic 10r2-2-01Bottle20002000.180Rhyolitic Set #5 11r4-0-0Cylinder4000100080Rhyolitic 12r4-0-2Cylinder4000100280Rhyolitic Set #6 13r4-2-0Chamber4000300080Rhyolitic 14r4-2-0Chamber4000300280Rhyolitic *Triggers

12. Model Run “r1-0” Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. No recharge from below.

13. Model Run “r1-0” Key Results Fast eruption start in about 2 minutes. Steady discharge for the most eruption period. Accelerating exit velocity. Abrupt eruption finish. Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. No recharge from below.

14. Model Run “r1-1” Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 1 m/s.

15. Model Run “r1-1” Key Results Eruption spike in about 10 minutes. Steady discharge reached in about 20 min. Gradually accelerating exit velocity. Supersaturation curve corresponds to exit velocity. Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 1 m/s.

16. Model Run “r1-2” Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 2 m/s.

17. Model Run “r1-2” Key Results Eruption spike in about 7 minutes. Steady discharge is reached in about 15 min. Gradually accelerating exit velocity to its max. Supersaturation curve corresponds to exit velocity. Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 2 m/s.

18. Model Run “r1-5” Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 5 m/s.

19. Model Run “r1-5” Key Results Eruption spike in about 4 minutes. Steady discharge is reached in about 6 min. Gradually accelerating exit velocity to its spike. Supersaturation curve corresponds to discharge. Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 5 m/s.

20. Model Run “r1-10” Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 10 m/s.

21. Model Run “r1-10” Key Results Eruption spike in about 2 minutes. Steady discharge is reached in about 3 min. Gradually accelerating exit velocity. Key Characteristics Pilsner glass conduit shape. 200 m vent diameter. 1 km conduit depth. Recharge from below at 10 m/s.

22. Model Run “r1-0-0” Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 1 km conduit depth. No recharge from below.

23. Model Run “r1-0-0” Key Results Eruption spike in about 25 minutes. Steady discharge for the most eruption period. Accelerating exit velocity. Steady supersaturation at its initial value. Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 1 km conduit depth. No recharge from below.

24. Model Run “r1-0-2” Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 1 km conduit depth. Recharge from below at 2 m/s.

25. Model Run “r1-0-2” Key Results Almost no eruption spike. Steady discharge is reached in about 10 min. Accelerating exit velocity. Supersaturation increases and corresponds to discharge. Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 1 km conduit depth. Recharge from below at 2 m/s.

26. Model Run “r2-0-0” Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 2 km conduit depth. No recharge from below.

27. Model Run “r2-0-0” Key Results Eruption spike in about 40 minutes. Increasing discharge for the most eruption period. Accelerating exit velocity. Steady supersaturation at its initial value. Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 2 km conduit depth. No recharge from below.

28. Model Run “r2-2-0” Key Characteristics Bottle conduit shape. 200 m vent diameter. 2 km conduit depth. No recharge from below.

29. Model Run “r2-2-0” Key Results Eruption spike in about 1 hour. Steady discharge for the most eruption period. Accelerating exit velocity. Complex supersaturation behavior. Key Characteristics Bottle conduit shape. 200 m vent diameter. 2 km conduit depth. No recharge from below.

30. Model Run “r2-2-01” Key Characteristics Bottle conduit shape. 200 m vent diameter. 2 km conduit depth. Recharge from below at 0.1 m/s.

31. Model Run “r2-2-01” Key Results No eruption spike. Steady state eruption after about 10 min. Key Characteristics Bottle conduit shape. 200 m vent diameter. 2 km conduit depth. Recharge from below at 0.1 m/s.

32. Model Run “r4-0-0” Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 4 km conduit depth. No recharge from below.

33. Model Run “r4-0-0” Key Results Eruption spike in about 1 hour. Increasing discharge for the most eruption period. Accelerating exit velocity. Steady supersaturation at its initial value. Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 4 km conduit depth. No recharge from below.

34. Model Run “r4-0-2” Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 4 km conduit depth. Recharge from below at 2 m/s.

35. Model Run “r4-0-2” Key Results Double eruption spike in about 20 minutes. Steady discharge for the most eruption period. Accelerating exit velocity. Complex supersaturation behavior. Key Characteristics Cylindrical conduit shape. 100 m vent diameter. 4 km conduit depth. Recharge from below at 2 m/s.

36. Model Run “r4-2-0” Key Characteristics Chamber conduit shape. 300 m vent diameter. 4 km conduit depth. No recharge from below.

37. Model Run “r4-2-0” Key Results Eruption spike in about 1 hour. Steady discharge for the most eruption period. Steady velocity for the most eruption period. Complex supersaturation behavior. Key Characteristics Chamber conduit shape. 300 m vent diameter. 4 km conduit depth. No recharge from below.

38. Model Run “r4-2-2” Key Characteristics Chamber conduit shape. 300 m vent diameter. 4 km conduit depth. Recharge from below at 2 m/s.

39. Model Run “r4-2-2” Key Results Eruption spike in about 1.5 hours. Steady discharge for the most eruption period. Steady velocity for the most eruption period. Complex supersaturation behavior. Cycling eruptions. Key Characteristics Chamber conduit shape. 300 m vent diameter. 4 km conduit depth. Recharge from below at 2 m/s.

40. Conclusions Conduit geometries – Cylindrical and glass conduit shapes have smooth and quiet eruption styles. Conduit shapes with magma chamber (“bottle” and “chamber”) have long steady state eruption ended by extreme, violent explosion at the end. Violent explosion is attributed to formation of foam layer at the top of magma chamber during steady state eruption. Discharge and vent velocity are proportional to the conduit/chamber depth and is controlled by amount of dissolved volatiles. Eruption cycle – Eruption initialization was fast (about 2 min) for all model runs with instant decompression trigger of 80 MPa (1 wt % H 2 O). Initialization is followed by quasi-steady state eruption of different intensity over extended time (about 80 % of eruption cycle). Eruption spike (explosion) ends steady state part of eruption. Cessation occurs after the spike quickly ending eruption cycle. Volatiles – Maximum supersaturation is observed right under fragmentation level of the magma column. Supersaturation at the vent corresponds to discharge rates and exit velocities. The faster recharge from below the faster steady state eruption is reached and it does not necessarily increases the eruption violence. Key factors – Magma composition (affects viscosity and volatile diffusivity). Conduit shape and trigger. Volatile saturation/supersaturation level.