Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session E5: Geophysical Fluid Dynamics: Earths Core & Dynamoes |
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Sponsoring Units: DFD GPC Chair: Daniel Lathrop, University of Maryland Room: B113 |
Sunday, November 20, 2016 5:37PM - 5:50PM |
E5.00001: A liquid sodium model of the Earth's core Daniel Lathrop, Matthew Adams, Douglas Stone, Minh Doan We present results from the three meter liquid sodium spherical Couette experiment at full speed (4 Hz outer sphere rotation rate and a range of inner sphere rates). The experiment is geometrically similar with the earth's core. We study hydrodynamic and hydromagnetic phenomena in rapidly rotating turbulence, as well as magnetic field induction by those flows. Two external electromagnets apply dipole or quadrupole magnetic fields, while an array of 31 external Hall sensors measure the resulting induced magnetic field. This allows us to study dynamo gain (as we yet have no self-generating magnetic dynamo) and broader range of rotating turbulence phenomena. We report substantial magnetic field gain for a variety of flow states. One of these states exhibits bistability in the hydrodynamic flow with magnetic field gain only in one of the two states. Zonal flow shear drives large azimuthal magnetic fields, prompting a need to measure the zonal flows. This has prompted us to develop acoustic mode velocimetry measurements adapted from helioseismology. Prior to measurements in the larger experiment, we develop this technique in our 60 cm diameter spherical Couette experiment in nitrogen gas. There, we compare acoustic mode frequency splittings with theoretical predictions for solid body flow and turbulent flow, and obtain excellent agreement. We also use this technique to estimate the zonal shear in those experiments. [Preview Abstract] |
Sunday, November 20, 2016 5:50PM - 6:03PM |
E5.00002: Experimental Studies of Acoustics in a Spherical Couette Flow Savannah Gowen, Matthew Adams, Douglas Stone, Daniel Lathrop The Earth, like many other astrophysical bodies, contains turbulent flows of conducting fluid which are able to sustain magnetic field. To investigate the hydromagnetic flow in the Earth's outer core, we have created an experiment which generates flows in liquid sodium. However, measuring these flows remains a challenge because liquid sodium is opaque. One possible solution is the use of acoustic waves. Our group has previously used acoustic wave measurements in air to infer azimuthal velocity profiles, but measurements attempted in liquid sodium remain challenging. In the current experiments we measure acoustic modes and their mode splittings in both air and water in a spherical Couette device. The device is comprised of a hollow 30-cm outer sphere which contains a smaller 10-cm rotating inner sphere to drive flow in the fluid in between. We use water because it has material properties that are similar to those of sodium, but is more convenient and less hazardous. Modes are excited and measured using a speaker and microphones. Measured acoustic modes and their mode splittings correspond well with the predicted frequencies in air. However, water modes are more challenging. Further investigation is needed to understand acoustic measurements in the higher density media. [Preview Abstract] |
Sunday, November 20, 2016 6:03PM - 6:16PM |
E5.00003: Magnetostrophic Rotating Magnetoconvection Eric King, Jonathan Aurnou Planetary magnetic fields are generated by turbulent convection within their vast interior liquid metal cores. Although direct observation is not possible, this liquid metal circulation is thought to be dominated by the controlling influences of Coriolis and Lorentz forces. Theory famously predicts that local-scale convection naturally settles into the so-called magnetostrophic state, where the Coriolis and Lorentz forces partially cancel, and convection is optimally efficient. To date, no laboratory experiments have reached the magnetostrophic regime in turbulent liquid metal convection. Furthermore, computational dynamo simulations have as yet failed to produce a globally magnetostrophic dynamo, which has led some to question the existence of the magnetostrophic state. Here, we present results from the first turbulent magnetostrophic rotating magnetoconvection experiments using the liquid metal gallium. We find that turbulent convection in the magnetostrophic regime is, in fact, maximally efficient. The experimental results clarify these previously disparate results, suggesting that the fluid dynamics saturate in magnetostrophic balance within turbulent liquid metal, planetary cores. [Preview Abstract] |
Sunday, November 20, 2016 6:16PM - 6:29PM |
E5.00004: Equatorially trapped convection in a rapidly rotating spherical shell Benjamin Miquel, Keith Julien, Edgar Knobloch Convection plays a preponderant role in driving geophysical flows. Unfortunately, these flows are often characterized by rapid rotation (i.e. small Ekman number $E$) which renders the equations stiff and introduces a scale separation in the system: for example the wavelength of the marginal mode at the onset of convection in a rapidly rotating sphere scales like $E^{1/3}$ and is modulated by a $E^{1/6}$ envelope. These scalings keep the fully nonlinear dynamics of the internal convection in Earth's core ($E\sim 10^{15}$) out of reach from direct numerical simulations, analytical work and experiments on one hand, but advocate for the development of reduced models on the other hand. We present a reduced model derived in a shallow gap spherical shell geometry. As the Rayleigh number is increased, the flow is first destabilized in the equatorial region where the dynamics remains trapped. The linear stability is analyzed and the fully nonlinear dynamics is presented. [Preview Abstract] |
Sunday, November 20, 2016 6:29PM - 6:42PM |
E5.00005: Identification of dominant flow structures in rapidly rotating convection of liquid metals using Dynamic Mode Decomposition Susanne Horn, Jonathan M. Aurnou, Peter J. Schmid We will present results from direct numerical simulations of rapidly rotating convection in a fluid with $Pr \approx 0.025$ in cylindrical containers and Ekman numbers as low as $5 \times 10^{-6}$. In this system, the Coriolis force is the source of two types of inertial modes, the so-called wall modes, that also exist at moderate Prandtl numbers, and cylinder-filling oscillatory modes, that are a unique feature of small Prandtl number convection. The obtained flow fields were analyzed using the Dynamic Mode Decomposition (DMD). This technique allows to extract and identify the structures that govern the dynamics of the system as well as their corresponding frequencies. We have investigated both the regime where the flow is purely oscillatory and the regime where wall modes and oscillatory modes co-exist. In the purely oscillatory regime, high and low frequency oscillatory modes characterize the flow. When both types of modes are present, the DMD reveals that the wall-attached modes dominate the flow dynamics. They precess with a relatively low frequency in retrograde direction. Nonetheless, also in this case, high frequency oscillations have a significant contribution. [Preview Abstract] |
Sunday, November 20, 2016 6:42PM - 6:55PM |
E5.00006: The influence of the magnetic field on the heat transfer rate in rotating spherical shells. Ares Cabello, Ruben Avila Studies of the relationship between natural convection and magnetic field generation in spherical annular geometries with rotation are essential to understand the internal dynamics of the terrestrial planets. In such studies it is important to calculate and analyze the heat transfer rate at the inner and the outer spheres that confine the spherical gap. Previous investigations indicate that the magnetic field has a stabilizing effect on the onset of the natural convection, reduces the intensity of convection and modifies the flow patterns. However so far it is still unclear how the magnetic field change the heat transfer rate behaviour. We investigate the heat transfer rate ($Nu$) in a rotating spherical gap with a self gravity field varying linearly with radius, and its relation with the intensity of the magnetic field induced by the geodynamo effect. The Boussinesq fluid equations are solved by using a spectral element method (SEM). To avoid the singularity at the poles, the cubed-sphere algorithm is used to generate the spherical mesh. Several cases are simulated in which the Rayleigh number, the magnetic Reynolds number and the Taylor number are the variable parameters. The flow patterns, the temperature distribution and the Nusselt numbers at both spheres are calculated. [Preview Abstract] |
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