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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).

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initial hydrodynamic results from the princeton mri experiment
Initial Hydrodynamic Results from the Princeton MRI Experiment

M.J. Burin1,3, H. Ji2,3, J. Goodman1,3, E. Schartman2, W. Liu2,3

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



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)

motivation the cause of turbulence in astrophysical accretion disks what instability s are relevant
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; subcriticalshear 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


experimental apparatus overview
Experimental Apparatus: Overview

Roller Bearing

Teflon seal (1/5)

Phenolic gear (1/6)

connects to motor via belt

Inter-nested stainless

steel shaftsaligned by

cam followers.

Shafts are co-supported

with roller/thrust collars

Rotating vessel

components are of cast acrylic except for inner cylinder.

(Tie-rods are used

to reinforce the

outer cylinder)

Roller/Thrust Bearing

Note: this is mechanically nontrivial

experimental apparatus detail of rotating vessel
Experimental Apparatus: Detail of Rotating Vessel

Inner cylinder: R1=7cm, 1 < 4000rpm

Outer cylinder: R2=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 ~ 107

Max Rem ~ 10-100

rotating apparatus design use of intermediary rings to reduce ekman circulation
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.

ideal (pure radial flux)


(from prototype)

It was found numerically that just a couple intermediary rings, rotating at intermediary speeds, can significantly reduce the Ekman effect.

(Kageyama et al. 2004)

use of intermediary rings to reduce ekman circulation initial results
Use of Intermediary Rings to Reduce Ekman Circulation: Initial Results


“PIV” Data:

Re ~ 2 x 105

2D simulation:

Re ~3600

by W. Liu

w/ differential


w/ solid end-caps

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.

Results submitted to Experiments in Fluids, August 2005


Subcritical Shear Instability: Background Comments

  • 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.


* 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 recent observations
Subcritical Shear Instability: Recent Observations (?)



-1 < R  < 0

Also relevant:

Rotation Number R

R = -4/3


w/ shear


Rayleigh stability boundary

R > 0

Cyclonic Case


grey areas of subcritical instability


Example point 

Richard & Zhan 1999, Richard 2001

subcritical shear instability what does the data mean i e what makes for an instability signature x
Subcritical Shear Instability: what does the data mean?I.e.,What makes for an instability signature (“x”)?

The stability boundary data given

(“x”s) do not appear to represent

a sudden subcritical transition

to relatively high fluctuation levels

Not exactly sudden

8 %

Not exactly increasing


Boundary flows

(e.g. Ekman circulation)

are suspect


subcritical shear instability simulations
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 ~ 104)
  • 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)

subcritical shear instability an experimental test
Subcritical Shear Instability: An Experimental Test

From Keplerian-like

conditions to a centrifugally-unstable regime

… and back again

(check for hysteresis).

Rayleigh stability boundary

Note: actual Re #’s used are about two orders of magnitude higher

initial result no significant fluctuation power for high re keplerian like flow
Initial Result: No Significant Fluctuation Power for high Re Keplerian-like Flow

data from midplane

Re ~ 1e6

R ~ -1.05


  • Fluctuations start and return to near-quiescent levels (~1%)
  • Initial evidence for subcritical stability
  • No evidence
  • for hysteresis
  • 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 …

addendum plans for mri study
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 **