Hydromagnetic Turbulent Instability in Liquid Sodium Experiments

Title of dissertation: HYDROMAGNETIC TURBULENT INSTABILITY IN LIQUID SODIUM EXPERIMENTS Daniel R. Sisan, Doctor of Philosophy, 2004 Dissertation directed by: Professor Daniel P. Lathrop Department of Physics This dissertation describes the observation of magnetically-induced instabilities that occur from a preexisting hydrodynamically turbulent background. We claim these instabilities are the first direct observation of the magneto-rotational instability (MRI). An extensive body of theoretical and numerical research has established the MRI is important in the theory of accretion disks: magnetic fields destabilize otherwise stable astrophysical flows, causing turbulence and an increased angular momentum transport needed for accretion. Our instabilities occur in liquid sodium between differentially rotating concentric spheres (spherical Couette flow) where an external field is applied parallel to the axis of rotation. Our experiments are also the first known spherical Couette flow in an electrically conducting fluid, and only the second experiment, in any fluid, at an aspect ratio of β = 2, the same of the Earth’s core. We describe the development of a Hall probe array that measures the field at 30 points outside the sphere and is used to perform a spherical harmonic decomposition (up to l = 4) of the induced field. We present measurements taken with this array, along with measurements of torque needed to spin the inner sphere and of the flow velocity using ultrasound doppler velocimetry. Our experiment is consistent with prior theory, even though our instabilities occur in the presence of preexisting hydrodynamic turbulence (the theory starts with an initially laminar flow). This result may be particularly relevant in light of an ongoing debate on whether accretion disks are hydrodynamically unstable independent of external fields. The most important contribution of our experiments, however, may be in providing data with which to benchmark the many numerical and theoretical studies of the MRI and the codes used to simulate the Earth’s core. HYDROMAGNETIC TURBULENT INSTABILITY IN LIQUID SODIUM EXPERIMENTS