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Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks


The most efficient energy sources known in the Universe are accretion disks. Those around black holes convert 5–40 per cent of rest-mass energy to radiation. Like water circling a drain, inflowing mass must lose angular momentum, presumably by vigorous turbulence in disks, which are essentially inviscid1. The origin of the turbulence is unclear. Hot disks of electrically conducting plasma can become turbulent by way of the linear magnetorotational instability2. Cool disks, such as the planet-forming disks of protostars, may be too poorly ionized for the magnetorotational instability to occur, and therefore essentially unmagnetized and linearly stable. Nonlinear hydrodynamic instability often occurs in linearly stable flows (for example, pipe flows) at sufficiently large Reynolds numbers. Although planet-forming disks have extreme Reynolds numbers, keplerian rotation enhances their linear hydrodynamic stability, so the question of whether they can be turbulent and thereby transport angular momentum effectively is controversial3,4,5,6,7,8,9,10,11,12,13,14,15. Here we report a laboratory experiment, demonstrating that non-magnetic quasi-keplerian flows at Reynolds numbers up to millions are essentially steady. Scaled to accretion disks, rates of angular momentum transport lie far below astrophysical requirements. By ruling out purely hydrodynamic turbulence, our results indirectly support the magnetorotational instability as the likely cause of turbulence, even in cool disks.

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Figure 1: Experimental set-up.
Figure 2: Experimentally studied Taylor-Couette flows.
Figure 3: Experimentally measured Reynolds stress versus height in a quasi-keplerian profile.
Figure 4: Dimensionless Reynolds stress at Reynolds numbers up to 2 × 106.


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We thank S. Balbus for discussions, R. Cutler for technical assistance with the apparatus, P. Heitzenroeder, C. Jun, L. Morris and S. Raftopolous for engineering assistance, as well as Dantec Dynamics for the contracted use of an LDV measurement system. This research was supported by the US Department of Energy, Office of Science – Fusion Energy Sciences Program; the US National Aeronautics and Space Administration, Astronomy and Physics Research and Analysis and Astrophysics Theory Programs; and the US National Science Foundation, Physics and Astronomical Sciences Divisions. Author Contributions H.J., M.B. and E.S. planned and executed the experiments, and analysed data; E.S. and M.B. prepared apparatus and diagnostics; H.J. drafted the paper; and J.G. suggested this subject and assisted in the interpretation of the results and in revising the paper.

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Correspondence to Hantao Ji.

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Ji, H., Burin, M., Schartman, E. et al. Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343–346 (2006).

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