Physics
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Item TURBULENCE AND SUPERFLUIDITY IN THE ATOMIC BOSE-EINSTEIN CONDENSATE(2024) Zhao, Mingshu; Spielman, Ian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation I investigate turbulence in atomic Bose-Einstein condensates (BECs), focusing on the challenge of quantifying velocity field measurements in quantum fluids. Turbulence, a universal phenomenon observed across various scales and mediums – from classical systems like Earth's oceans and atmosphere to quantum fluids including neutron stars, superfluid helium, and atomic BECs – exhibits complex fluid motion patterns spanning a wide range of length scales. While classical turbulence has been extensively studied, quantum systems present many open questions, particularly regarding the existence of an inertial scale and the applicability of Kolmogorov scaling laws. I introduce a novel velocimetry technique, analogous to particle image velocimetry (PIV), using spinor impurities as tracer particles. This method enables the direct measurement of the velocity field and thereby the velocity structure functions (VSFs) in turbulent atomic BECs. The technique overcomes limitations of existing experimental approaches that rely on time of flight (TOF) measurements, offering a clearer connection to VSFs and enabling a more direct comparison of turbulence in atomic gases with other fluids. The cold-atom PIV technique enables directly measuring the velocity field, leading to a detailed analysis of both VSFs and the velocity increment probability density functions (VI-PDF). Key findings include the observation of superfluid turbulence conforming to Kolmogorov theory from VSFs, and intermittency from high order of VSFs and the non-Gaussian fat tail in the VI-PDF.Item Increasing Helicity towards Dynamo Action with Rough Boundary Spherical Couette Flows(2022) Rojas, Ruben; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The dynamo action is the process through which a magnetic field is amplified and sustained by electrically conductive flows. Galaxies, stars and planets, all exhibit magnetic field amplification by their conductive constituents. For the Earth in particular, the magnetic field is generated due to flows of conductive material in its outer core. At the University of Maryland, our Three-meter diameter spherical Couette experiment uses liquid sodium between concentric spheres to mimic some of these dynamics, giving insight into these natural phenomena. Numerical studies of Finke and Tilgner (Phys. Rev. E, 86:016310, 2012) suggest a reduction in the threshold for dynamo action when a rough inner sphere was modeled by increasing the poloidal flows with respect to the zonal flows and hence increasing helicity. The baffles change the nature of the boundary layer from a shear dominated to a pressure dominated one, having effects on the angular momentum injection. We present results on a hydrodynamics model of 40-cm diameter spherical Couette flow filled with water, where torque and velocimetry measurements were performed to test the effects of different baffle configurations. The selected design was then installed in the 3-m experiment. In order to do that, the biggest liquid sodium draining operation in the history of the lab was executed. Twelve tons of liquid sodium were safely drained in a 2 hours operation. With the experiment assembled back and fully operational, we performed magnetic field amplification measurements as a function of the different experimental parameters including Reynolds and Rossby numbers. Thanks to recent studies in the hydrodynamic scale model, we can bring a better insight into these results. Torque limitations in the inner motor allowed us to inject only 4 times the available power; however, amplifications of more than 2 times the internal and external magnetic fields with respect to the no-baffle case was registered. These results, together with time-dependent analysis, suggest that a dynamo action is closer than before; showing the effect of the new baffles design in generating more efficient flows for magnetic field amplification. We are optimistic about new short-term measurement in new locations of the parameter space, and about the rich variety of unexplored dynamics that this novel experiment has the potential to reach. These setups constitute the first experimental explorations, in both hydrodynamics and magnetohydrodynamics, of rough boundary spherical Couette flows as laboratory candidates for successful Earth-like dynamo action.Item Analysis of models of superfluidity(2022) Jayanti, Pranava Chaitanya; Trivisa, Konstantina; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis deals with the rigorous analysis of two models of superfluidity. One of them is a macro-scale description of the interacting dynamics of a mixture of superfluid Helium and normal Helium. The equations used are modifications of the incompressible Navier-Stokes equations in 2D, with a nonlinear \textit{mutual friction} that couples the two fluids. We show global well-posedness of strong solutions (with high-regularity data) to this model, by proving a Beale-Kato-Majda-type condition. This work has been published in the Journal of Nonlinear Science. \\ Next, we study a micro-scale model (the ``Pitaevskii’’ model) of superfluid-normal fluid interactions, derived by Lev Pitaevskii in 1959. This involves the nonlinear Schr\"odinger equation and incompressible inhomogeneous Navier-Stokes equations. Mass and momentum exchange between the two fluids is mediated through a nonlinear and bidirectional coupling. We establish the existence of local solutions (strong in wavefunction and velocity, weak in density) that satisfy an energy equality. The analysis of this model has been published in the Journal of Mathematical Fluid Mechanics. \\ Finally, we prove a weak-strong type uniqueness theorem for the solutions of the Pitaevskii model. We begin by arguing that the standard weak-strong uniqueness argument does not seem to work in the case of weak solutions whose regularity is governed purely by the energy balance equation, even if the strong solution is as smooth as one wishes. Thus, we are forced to consider slightly less weak solutions obtained from a higher-order energy bound. Owing to their better regularity, we can compare them to \textit{moderate} solutions $-$ which are rougher than conventional strong solutions used for this purpose $-$ and establish a \textit{weak-moderate uniqueness} theorem. Relative to the solutions actually constructed in the earlier part of this thesis, only some of the regularity properties are used, allowing room for improved existence theorems in the future, while maintaining compatible uniqueness results. The uniqueness results have been accepted for publication in Nonlinearity.