Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F34: Geophysical Fluid Dynamics: Rotating FlowsGeophysical

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Chair: Hussein Aluie, University of Rochester Room: 102 
Monday, November 20, 2017 8:00AM  8:13AM 
F34.00001: Energy Transfer in Turbulence under Rotation Hussein Aluie, Michele Buzzicotti, Luca Biferale, Moritz Linkmann It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous direct and inverse energy cascades. However, the organization of interactions which leads to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow: (i) 2dimensional interactions amongst triads lying on the 2D3C (or slow) manifold, and (ii) purely 3dimensional interactions between a subset of triads with the same sign of helicity (homochiral). Here, we perform a numerical study of high Reynolds rotating flows by means of direct numerical simulations (DNS), in different parameter regimes to highlight both forward and inverse cascade regimes. We find that the inverse cascade at wavenumbers close to the forcing scale is generated by the dominance of homochiral interactions which couple the 3dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wavenumbers thanks to a 2dimensional mechanism. We further analyze the energy transfer that occurs in different regions in the realspace domain. In particular we distinguish high strain from high vorticity regions and quantify their contributions to the cascade. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F34.00002: The impact of domain aspect ratio on the inverse cascade in rotationally constrained convection Keith Julien, Edgar Knobloch, Meredith Plumley 
Monday, November 20, 2017 8:26AM  8:39AM 
F34.00003: Abstract Withdrawn A fundamental tool of GFD is the Thermal Wind Equation (TWE), which relates the vertical shear of the horizontal wind to the horizontal temperature gradient. Unfortunately, the TWE is invalid at and near the equator because the Coriolis force goes to zero and the Rossby number becomes large. Moreover, at some latitudes, even if the Rossby number is small, the TWE is illconditioned because it requires division by a small number. We have derived a wellconditioned ``Equatorial Thermal Wind Equation'' (EQTWE) that relates the vertical derivative of the eastwest velocity to the secondderivative of the temperature in the northsouth direction that is valid at the equator and up to latitudes of $18^{\circ}$ and whose validity is independent of the traditional Rossby number. We apply the EQTWE to the Jovian wind measured by the Galileo probe Doppler wind experiment to reveal thermal anomalies at the Jovian equator at altitudes below 1~bar and show that they imply a Jovian global circulation model with two layers of Hadley cells, with an upper layer like the one on Earth, and the lower has cells with the opposite rotation. At altitudes above 1~bar we use IR temperatures and the EQTWE to determine velocities and show that there is a fast 205 m/s stratospheric jet at 3~mbar. 
Monday, November 20, 2017 8:39AM  8:52AM 
F34.00004: Equatorially localized convection in a rapidly rotating shallow spherical shell Ben Miquel, Keith Julien, Nick Featherstone, Philippe Marti, JinHan Xie, Edgar Knobloch We study the convective flow in a rapidly rotating spherical shell that models planet cores or stellar convective zones. Flows in these astrophysical objects are often in a strongly rotationally constrained regime (low Ekman number) which is out of reach of current analytical, numerical, and experimental studies. Rotationally constrained flows tend to develop anisotropic, vertically invariant Taylor columns. In the case of shallow spherical shells, this anisotropy results in the localization of the convective motion around the equator. We present an asymptotically reduced model that captures the non linear dynamics of equatorially localized convection in a rapidly rotating shallow shell. Such an approach is instrumental in investigating low Ekman number regimes that pertains to planets or moons with a shallow fluid layer (such as Jupiter's moon, Europa). We present predictions for the heat flux as a function of the latitude. In the case of conducting fluids, implications for the dynamo effect are discussed. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F34.00005: Increasing helicity to achieve a dynamo state on the ThreeMeter system Ruben Rojas, Artur Perevalov, Till Zurner, Daniel Lathrop Dynamo theory describes the generation of magnetic fields in the flows of conducting fluids, for example, in stars and planetary cores. Spherical Couette flows, which are flows between two concentric and independently rotating spheres, is one of the experimental models for achieving this task in the laboratory. We have performed dynamo state search in our threemeter sphericalCouette model reaching up to $Re \sim 10^8$ with amplifications of the field between 1030% but without a selfsustained dynamo magnetic field. A recent numerical work [K. Finke and A. Tilgner. Phys. Rev. E, 86:016310, Jul 2012] suggested that a roughened inner core reduces the threshold for dynamo action. The mean flow would have more poloidal component than the one we are generating with our current smooth sphere setup. With baffles flow would be expelled radially outward on the equatorial plane and returned at the poles, with opposite helicities in the two hemispheres. Baffles welded on our smooth inner sphere are proposed to achieve this task. We are working to perform experiments on a scaled water model of our experimental setup with $Re \sim 10^5$ to measure the helicity improvements of different baffle designs in support of upcoming ThreeMeter modifications. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F34.00006: Reservoir computer predictions for the Three Meter magnetic field time evolution Artur Perevalov, Ruben Rojas, itamar Shani, Brian Hunt, Daniel Lathrop The source of the Earth's magnetic field is the turbulent flow of liquid metal in the outer core. Our experiment’s goal is to create Earthlike dynamo, to explore the mechanisms and to understand the dynamics of the magnetic and velocity fields. Since it is a complicated system, predictions of the magnetic field is a challenging problem. The experiment is a threemeter diameter outer sphere and a onemeter diameter inner sphere with the gap filled with liquid sodium. The spheres can rotate up to 4 and 14 Hz respectively, giving a Reynolds number up to $ 1.5*10^8 $. Two external electromagnets apply magnetic fields, while an array of 31 external and 2 internal Hall sensors measure the resulting induced fields. We use this magnetic probe data to train a reservoir computer to predict the 3M time evolution and mimic waves in the experiment. Surprisingly accurate predictions can be made for several magnetic dipole time scales. This shows that such a complicated MHD system’s behavior can be predicted. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F34.00007: On the Reinterpretation of Magnetostrophic Dynamo Action Jon Aurnou, Keith Julien The generation of planetary magnetic fields has long been argued to be the product of magnetostrophic dynamo action, in which the leadingorder force balance exists between Lorentz, Coriolis, pressure and buoyancy forces. A number of recent planetary dynamo simulations claim to be operating in this purported ultimate dynamo regime. Here we will argue that the recent simulations are in leadingorder quasigeostrophic (QG) balance, with magnetostrophy occurring only in the subdominant balances. Presenting these simulations as examples of classical, leadingorder magnetostrophic balance is a reinterpretation of the very definition of this regime. Our arguments imply that planetary dynamo models continue to operate in the QG dynamo regime. Whether or not magnetostrophic dynamo action can actually occur in planetary settings remains an open, unanswered question. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F34.00008: A single mode study of a quasigeostrophic convectiondriven dynamo model Meredith Plumley, Michael Calkins, Keith Julien, Steven Tobias Planetary magnetic fields are thought to be the product of hydromagnetic dynamo action. For Earth, this process occurs within the convecting, turbulent and rapidly rotating outer core, where the dynamics are characterized by low Rossby, low magnetic Prandtl and high Rayleigh numbers. Progress in studying dynamos has been limited by current computing capabilities and the difficulties in replicating the extreme values that define this setting. Asymptotic models that embrace these extreme parameter values and enforce the dominant balance of geostrophy provide an option for the study of convective flows with actual relevance to geophysics. The quasigeostrophic dynamo model (QGDM) is a multiscale, fullynonlinear Cartesian dynamo model that is valid in the asymptotic limit of low Rossby number. We investigate the QGDM using a simplified class of solutions that consist of a single horizontal wavenumber which enforces a horizontal structure on the solutions. This single mode study is used to explore multiscale time stepping techniques and analyze the influence of the magnetic field on convection. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F34.00009: Multiscale Analysis of Rapidly Rotating Dynamo Simulations Ryan Orvedahl, Michael Calkins, Nicholas Featherstone The magnetic field of the planets and stars are generated by dynamo action in their electrically conducting fluid interiors. Numerical models of this process solve the fundamental equations of magnetohydrodynamics driven by convection in a rotating spherical shell. Rotation plays an important role in modifying the resulting convective flows and the selfgenerated magnetic field. We present results of simulating rapidly rotating systems that are unstable to dynamo action. We use the pseudospectral code {\sf Rayleigh} to generate a suite of direct numerical simulations. Each simulation uses the Boussinesq approximation and is characterized by an Ekman number ($\mathrm{Ek}=\nu/\Omega L^2$) of $10^{5}$. We vary the degree of convective forcing to obtain a range of convective Rossby numbers. The resulting flows and magnetic structures are analyzed using a Reynolds decomposition. We determine the relative importance of each term in the scaleseparated governing equations and estimate the relevant spatial scales responsible for generating the mean magnetic field. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F34.00010: Multiscale numerical simulations of magnetoconvection at low magnetic Prandtl and Rossby numbers Stefano Maffei, Michael Calkins, Keith Julien, Philippe Marti The dynamics of the Earth’s outer core is characterized by low values of the Rossby (Ro), Ekman and magnetic Prandtl numbers. These values indicate the large spectra of temporal and spatial scales that need to be accounted for in realistic numerical simulations of the system. Current direct numerical simulation are not capable of reaching this extreme regime, suggesting that a new class of models is required to account for the rich dynamics expected in the natural system. Here we present results from a quasigeostrophic, multiscale model based on the scale separation implied by the low Ro typical of rapidly rotating systems. We investigate a plane layer geometry where convection is driven by an imposed temperature gradient and the hydrodynamic equations are modified by a large scale magnetic field. Analytical investigation shows that at values of thermal and magnetic Prandtl numbers relevant for liquid metals, the energetic requirements for the onset of convection is not significantly altered even in the presence of strong magnetic fields. Results from strongly forced nonlinear numerical simulations show the presence of an inverse cascade, typical of 2D turbulence, when no or weak magnetic field is applied. For higher values of the magnetic field the inverse cascade is quenched. [Preview Abstract] 
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