Ethan Schartman

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 inviscid. The origin of the turbulence is unclear. Hot disks of electrically conducting plasma can become turbulent by way of the linear magnetorotational instability. 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 controversial. 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.

Observation of Magnetocoriolis Waves in a Liquid Metal Taylor-Couette Experiment

The first observation of fast and slow magnetocoriolis (MC) waves in a laboratory experiment is reported. Rotating nonaxisymmetric modes arising from a magnetized turbulent Taylor-Couette flow of liquid metal are identified as the fast and slow MC waves by the dependence of the rotation frequency on the applied field strength. The observed slow MC wave is damped but the observation provides a means for predicting the onset of the magnetorotational instability.

Development of a Couette–Taylor flow device with active minimization of secondary circulation

A novel Taylor-Couette experiment has been developed to produce rotating shear flows for the study of hydrodynamic and magnetohydrodynamic instabilities which are believed to drive angular momentum transport in astrophysical accretion disks. High speed, concentric, corotating cylinders generate the flow where the height of the cylinders is twice the radial gap width. Ekman pumping is controlled and minimized by splitting the vertical boundaries into pairs of nested, differentially rotating rings. The end rings and cylinders comprise four independently driven rotating components which provide flexibility in developing flow profiles. The working fluids of the experiment are water, a water-glycerol mix, or a liquid gallium alloy. The mechanical complexity of the apparatus and large dynamic pressures generated by high speed operation with the gallium alloy presented unique challenges. The mechanical implementation of the experiment and some representative results obtained with laser Doppler velocimetry in water are discussed.

Magnetorotational Instability in a Short Couette Flow of Liquid Gallium

A concise review is given of an experimental project to study magnetorotational instability (MRI) in a short Couette geometry using liquid gallium. Motivated by the astrophysical importance and lack of direct observation of MRI in nature and in the laboratory, a theoretical stability analysis was performed to predict the required experimental parameters. Despite the long‐wavelength nature of MRI, local analysis agrees excellently with global eigenmode calculations when periodic boundary conditions are used in the axial direction. To explore the effects of rigidly rotating vertical boundaries (endcaps), a prototype water experiment was conducted using dimensions and rotation rates favored by the above analysis. Significant deviations from the expected Couette flow profiles were found. The cause of the discrepancy was investigated by nonlinear hydrodynamic simulations using realistic boundary conditions. It was found that Ekman circulation driven by the endcaps transports angular momentum and qualitatively ...

Studies of turbulent angular momentum transport in Taylor-Couette flow via 2D LDV

The turbulent (i.e., fluctuation-driven) transport of angular momentum in Taylor-Couette flow may be observed locally and directly with second order velocity fluctuation correlations obtained by dual beam (2D) Laser Doppler Velocimetry (LDV). This method is complementary to torque measurements, and initial results are commensurate with earlier torque studies performed in turbulent regimes. Other results utilizing this technique with centrifugally-stable high Reynolds number (Re) flows indicate that the fluid is quiescent and devoid of significant angular momentum transport, even up to Re ~ 106. This latter result is thought to bear upon the hydrodynamic properties of cool astrophysical accretion disks.