Physics
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Item Rotating, hydromagnetic laboratory experiment modelling planetary cores(2009) Kelley, Douglas H.; Lathrop, Daniel P.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation describes a series of laboratory experiments motivated by planetary cores and the dynamo effect, the mechanism by which the flow of an electrically conductive fluid can give rise to a spontaneous magnetic field. Our experimental apparatus, meant to be a laboratory model of Earth's core, contains liquid sodium between an inner, solid sphere and an outer, spherical shell. The fluid is driven by the differential rotation of these two boundaries, each of which is connected to a motor. Applying an axial, DC magnetic field, we use a collection of Hall probes to measure the magnetic induction that results from interactions between the applied field and the flowing, conductive fluid. We have observed and identified inertial modes, which are bulk oscillations of the fluid restored by the Coriolis force. Over-reflection at a shear layer is one mechanism capable of exciting such modes, and we have developed predictions of both onset boundaries and mode selection from over-reflection theory which are consistent with our observations. Also, motivated by previous experimental devices that used ferromagnetic boundaries to achieve dynamo action, we have studied the effects of a soft iron (ferromagnetic) inner sphere on our apparatus, again finding inertial waves. We also find that all behaviors are more broadband and generally more nonlinear in the presence of a ferromagnetic boundary. Our results with a soft iron inner sphere have implications for other hydromagnetic experiments with ferromagnetic boundaries, and are appropriate for comparison to numerical simulations as well. From our observations we conclude that inertial modes almost certainly occur in planetary cores and will occur in future rotating experiments. In fact, the predominance of inertial modes in our experiments and in other recent work leads to a new paradigm for rotating turbulence, starkly different from turbulence theories based on assumptions of isotropy and homogeneity, starting instead with inertial modes, which are the linear eigenmodes of any rapidly rotating fluid.Item Problems in Spatiotemporal Chaos(2007-11-26) Cornick, Matthew Tyler; Ott, Edward; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis we consider two problem areas involving spatiotemporally chaotic systems. In Part I we investigate data assimilation techniques applicable to large systems. Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. However, for practical reasons, the high dimensionality of large spatiotemporally chaotic systems prevents the use of classical data assimilation techniques such as the Kalman filter. Here, a recently developed data assimilation method, the local ensemble transform Kalman Filter (LETKF), designed to circumvent this difficulty is applied to \RaBen convection, a prototypical spatiotemporally chaotic laboratory system. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraphs from a Rayleigh-Benard convection experiment. The process of estimating fluid parameters is also investigated. The presented results suggest the potential usefulness of the LETKF technique to a broad class of laboratory experiments in which there is spatiotemporally chaotic behavior. In Part II we study magnetic dynamo action in rotating electrically conducting fluids. In particular, we study how rotation effects the process of magnetic field growth (the dynamo effect) for a externally forced turbulent fluid. We solve the kinematic magnetohydrodynamic (MHD) equations with the addition of a Coriolis force in a periodic domain. Our results suggest that rotation is desirable for producing dynamo flows.Item Liquid sodium model of Earth's outer core(2004-08-27) Shew, Woodrow Lee; Lathrop, Daniel P.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Convective motions in Earth's outer core are responsible for the generation of the geomagnetic field. We present liquid sodium convection experiments in a spherical vessel, designed to model the convective state of Earth's outer core. Heat transfer, zonal fluid velocities, and properties of temperature fluctuations were measured for different rotation rates and temperature drops across the convecting sodium. The small scale fluid motion was highly turbulent, despite the fact that less than half of the total heat transfer was due to convection. Retrograde zonal velocities were measured at speeds up to 0.02 times the tangential speed of the outer wall of the vessel. Power spectra of temperature fluctuations indicate a well defined knee characterizing the convective energy input. This frequency is proportional to the ballistic velocity estimate. In the context of Earth's outer core, our observations imply a thermal Rayleigh number Ra=10^22, a convective velocity near 10^-5 m/s, and length and time scales of convective motions of 100 m and 2 days.