1. Initial Hydrodynamic Results from the Princeton MRI Experiment M.J. Burin 1,3, H. Ji 2,3, J. Goodman 1,3, E. Schartman 2, W. Liu 2,3 1. Princeton University Department of Astrophysical Sciences 2. Princeton Plasma Physics Laboratory 3. Center for Magnetic Self-Organization (CMSO) CMSO general meeting Oct. 5-7 2005

2. Outline Motivation and background Brief description of apparatus Result I. obtaining a Keplerian-like* flow Result II. on subcritical hydrodynamic shear instability Progress report on Gallium use (towards MRI)

3. Motivation: The Cause of Turbulence in Astrophysical Accretion Disks: What Instability(s) are Relevant? If sufficiently ionized and magnetized MRI probably responsible, but perhaps not solely If not? (e.g. some protostellar disks). The presence and relevance of various hydrodynamic instabilities is uncertain; subcritical shear instabilities are possible, but simulations and experiments so far appear to disagree. Hope: that a laboratory experiment which can create suitable velocity/shear profiles with sufficient Re/Rm can simulate accretion disk type instabilities in a controlled and repeatable environment. ? Taylor-Couette Flow

4. Experimental Apparatus: Overview Rotating vessel components are of cast acrylic except for inner cylinder. Phenolic gear (1/6) connects to motor via belt Teflon seal (1/5) (Tie-rods are used to reinforce the outer cylinder) Inter-nested stainless steel shafts aligned by cam followers. Shafts are co-supported with roller/thrust collars Roller/Thrust Bearing Roller Bearing Note: this is mechanically nontrivial

5. Inner cylinder: R 1 =7cm, 1 < 4000rpm Outer cylinder: R 2 =21cm, 2 < 500rpm Chamber height: H=28cm; Aspect Ratio ~ 2; wide-gap Unique: Independently-Driven Intermediate Rings as End-Caps Fluids: water, Gallium alloy (soon) When we operate at full speeds: Max Re ~ 10 7 Max Re m ~ 10-100 Experimental Apparatus: Detail of Rotating Vessel

6. Rotating Apparatus Design: Use of Intermediary Rings to Reduce Ekman Circulation In most experiments the end caps rotate as a solid body with the outer cylinder. A resulting pressure imbalance drives a circulation, which efficiently (and undesirably) transports angular momentum radially. data (from prototype) ideal (pure radial flux) It was found numerically that just a couple intermediary rings, rotating at intermediary speeds, can significantly reduce the Ekman effect. (Kageyama et al. 2004)

7. Use of Intermediary Rings to Reduce Ekman Circulation: Initial Results Use of differentially rotating end rings successfully reduces Ekman circulation, allowing the ideal profile to be approached, which in turn allows for Keplerian-like profiles to be realized. w/ solid end-caps w/ differential end-caps Low-Speed PIV Data: Re ~ 2 x 10 5 2D simulation: Re ~3600 by W. Liu Results submitted to Experiments in Fluids, August 2005

8. Being able to establish a high-Re Keplerian-like shear flow, we ask: * what instabilities/fluctuations may now be observed? * what sort/amount of transport results from them? in the absence of magnetic, kinetic, and stratification effects. This is a very reduced but fundamental question, with a sparse and debatable history… It needs to be addressed first. Because: * The question is relevant for (at least) cool unmagnetized disks * The question is relevant to a laboratory study of MRI: E.g., Is the background state is already turbulent? Subcritical Shear Instability: Background Comments

9. Subcritical Shear Instability: Recent Observations (?) Centrifugally Unstable -1 < R < 0 Keplerian R > 0 Cyclonic Case Richard & Zhan 1999, Richard 2001 Also relevant: Rotation Number R w/ shear ? grey areas of subcritical instability Rayleigh stability boundary ? ? Example point R = -4/3

10. Subcritical Shear Instability: what does the data mean? I.e., What makes for an instability signature (x)? The stability boundary data given (xs) do not appear to represent a sudden subcritical transition to relatively high fluctuation levels Unconvincing. Boundary flows (e.g. Ekman circulation) are suspect Not exactly sudden Not exactly increasing Re 0 8 %

11. Subcritical Shear Instability: Simulations Shearing-box simulations by Balbus, Hawley, and Stone/Winters (1996/1999) conclude hydrodynamic stability even for slightly centrifugally stable flows. (Re ~ 10 4 ) New numerical work by Lesur & Longaretti (2005) give a similar claim. New work also ongoing by J. Stone and collaborators … Rg = Critical Re for transition Lesur & Longaretti (2005)

12. Subcritical Shear Instability: An Experimental Test Rayleigh stability boundary From Keplerian-like conditions to a centrifugally-unstable regime … and back again (check for hysteresis). Note: actual Re #s used are about two orders of magnitude higher

13. Fluctuations start and return to near-quiescent levels (~1%) Initial evidence for subcritical stability No evidence for hysteresis Re ~ 1e6 R ~ -1.05 Initial Result: No Significant Fluctuation Power for high Re Keplerian-like Flow V data from midplane

14. Conclusions Ekman circulation can be significantly reduced in a wide-gap rotating flow, allowing for Keplerian-like profiles to be obtained. There is no significant hydrodynamic turbulence in a Keplerian- like flow up to Re ~ 1e6. This is in accord with simulations and in tentative disagreement with the experimental data of Richard & Zahn. More thorough experiments are planned. And then onto MHD and MRI …

15. Addendum: Plans for MRI study Replacement of vessel with stainless steel version to withstand large rotation pressures (~25 atm.) Creation of axial B field (~ 6000 G) via 6 electromagnets Diagnostics: pickup coils for magnetic fluctuations and motor torque (via load cells) for gross radial angular momentum transport. Possible use of ultrasound and acoustics to assess the interior flow state. An invasive fin featuring pressure and Hall probes may be used as well. Some initial Gallium data may be seen later this month at APS-DPP. ** Go on Lab Tour ** See Poster by E. Schartman **