Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R30: Astrophysical Fluid Dynamics |
Hide Abstracts |
Sponsoring Units: DFD Chair: Philip Marcus, UC Berkeley Room: 311 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R30.00001: A New Generalized Thermal Wind Equation and its Application to Zonal Flows on the Gas Giant Planets Philip Marcus, Joshua Tollefson, Imke de Pater For baroclinic, rapidly-rotating flows, the Thermal Wind Equation (TWE) describes how the flow varies along the rotation axis as a function of temperature gradients. The TWE works well for many laboratory and atmospheric flows on Earth. We show that the TWE also works well for the zonal (west-to-east) flows $u$ on Jupiter. However, our recent observations of Neptune's zonal flows not only do not fit the TWE, but also have the incorrect ``sign.'' When an atmosphere's longitudinally-averaged temperature is warmer at the equator than at the mid-latitudes, the TWE indicates that $u$ increases with height in the atmosphere. The change in $u$ as a function of height on Neptune has the opposite sign. Here, we show that the high-velocities of $u$ on Neptune make the cyclostrophic terms (i.e., some of the nonlinear terms proportional to $u^2$) large, and these terms are dropped in the standard derivation of the TWE. When the cyclostrophic terms are retained, a more generalized TWE is obtained that both qualitatively and quantitatively agrees with the observations of the change in $u$ as a function of height in Neptune's atmosphere. We show that both the standard and generalized TWE for zonal flows can be extended to the equator despite the fact that the Coriolis force vanishes there. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R30.00002: Zombie Vortex Instability: Effects of Non-uniform Stratification {\&} Thermal Cooling Joseph Barranco, Suyang Pei, Phil Marcus, Chung-Hsiang Jiang The Zombie Vortex Instability (ZVI) is a nonlinear instability in rotating, stratified, shear flows, such as in protoplanetary disks (PPD) of gas and dust orbiting new stars. The instability mechanism is the excitation of baroclinic critical layers, leading to vorticity amplification and nonlinear evolution into anticyclonic vortices and cyclonic sheets. ZVI is most robust when the Coriolis frequency, shear rate, and Brunt\textbf{--}V\"{a}is\"{a}l\"{a} (BV) frequency are of the same order. Previously, we investigated ZVI with uniform stratification and without thermal cooling. Here, we explore the role of non-uniform stratification as would be found in PPDs in which the BV frequency is zero in the disk midplane, and increases away from the midplane. We find that ZVI is vigorous 1-3 pressure scale heights away from the midplane, but the non-isotropic turbulence generated by ZVI can penetrate into the midplane. We also explore the effect of thermal cooling and find that ZVI is still robust for cooling times as short as 5 orbital periods. ZVI may play important roles in transporting angular momentum in PPDs, and in trapping dust grains, which may trigger gravitational clumping into planetesimals [Preview Abstract] |
Tuesday, November 24, 2015 1:16PM - 1:29PM |
R30.00003: Experimental Simulation of Buoyancy-Driven Vortical Flow in Jupiter Great Red Spot Hady Makhmalbaf, Tianshu Liu, Parviz Merati This new experimental study on Geophysical Buoyancy-Driven Vortical Flow presents a new approach to model the Great Red Spot (GRS) that explains some feature of this phenomena that other classic approaches such as shallow layer model and deep layer model do not. The low velocity region at the center and the counter rotating system at the core that recently were observed by high resolution image processing methods, have never been justified before. This setup generates flow structures similar to the GRS’s in the test zone and compares the results and suggests that a counter rotating flow structure at the lower altitude is the source of the GRS formation. [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R30.00004: ABSTRACT WITHDRAWN |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R30.00005: Laboratory Observation of Instabilities in Stratified Taylor-Couette Flow Bruce Rodenborn, Ruy Ibanez, Harry L. Swinney In 2001 Molemaker et al. (\textit{J. Fluid. Mech.} {\bf 448}, 1) predicted a new class of instabilities in a system of concentric rotating cylinders that contains a fluid with a vertically varying density. Dubrulle et al. (\textit{Astron. Astrophys}. {\bf 429}, 1, 2005) then showed that this phenomenon, which they named stratorotational instability (SRI), could be a source of instability and angular momentum transport in astrophysical accretion disks. Subsequent work by Shalybkov and R\"udiger (\textit{Astron. Astrophys.} {\bf 438}, 411, 2005) hypothesized that such stratified flow is stable when the ratio of outer and inner cylinder rotation rates $\mu$ is less than the ratio of the inner and outer cylinder radii $\eta$. Previous laboratory measurements by Le Bars and Le Gal (\textit{Phys. Rev. Lett.} \textbf{99}, 064502, 2007) confirmed this prediction for $Re<1200$ with $Re\equiv (r_o-r_i)\Omega_i r_i/\nu$. However, we find SRI exists for $\mu>\eta$ when the density gradient is large. We also find that the onset of SRI is suppressed for Reynolds numbers $Re>4000$, a region previously unexplored in experiments. For $Re>8000$, we find that the fluid does not exhibit SRI but transitions to a previously unreported chaotic state that mixes the fluid. [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R30.00006: A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection Keith Julien, Michael Calkins, Steve Tobias, Jonathan Aurnou A convection-driven multiscale dynamo model is discussed for the plane layer geometry in the limit of low Rossby number. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic diffusion timescale, and the large-scale thermal diffusion timescale. It is shown that in limit of low magnetic Prandtl number the model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large-scales. For the order one magnetic Prandtl number model the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large-scales. For both cases the Elsasser number is small. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress and Soward. These models may be useful for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to simulations of the full set of governing equations. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R30.00007: Numerical and Statistical Simulations of an Idealized Model Tachocline Abigail Plummer, Steve Tobias, Brad Marston Solar-type stars with outer convective envelopes and stable interiors are believed to have tachoclines. As in the Sun, the tachocline is a thin shear layer thought to play an important role in the magnetic activity of these stars. We use an idealized two-dimensional model tachocline to investigate a joint instability in which the differential rotation is only stable in the absence of a magnetic field. A set of parameters are identified using Direct Numerical Simulations (DNS) that produce a cycle in which energy is transferred abruptly between kinetic and magnetic potential energy reservoirs. Elements of this cyclic behavior are replicated using Direct Statistical Simulations (DSS). Insight is thus gained into the physics prompting these sharp transitions, suggesting that they are the result of eddies interacting to form new eddies. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R30.00008: The Non-linear Saturation of the Goldreich-Schubert-Fricke Instability Jeffrey Oishi, Keaton Burns, Ben Brown, Daniel Lecoanet, Geoffrey Vasil The Goldreich-Schubert-Fricke (GSF) instability is an important process in stellar interiors and possibly in exoplanetary atmospheres. While the linear phase of the instability has been explored for nearly fifty years, its non-linear saturation has not been explored in detail. The GSF is a double-diffusive instability in which Rayleigh unstable perturbations are robbed of buoyant stability by thermal diffusion. Here, we will present results from a suite of direct numerical simulations using the Spiegel-Veronis Boussinesq equations in the Dedalus framework. These DNS are designed to explore the behavior of the GSF over a range of Prandtl numbers. In stellar interiors, $\mathrm{Pr} \simeq 10^{-6}$, but we are limited by computational resources to much higher values, so instead we will discuss the $\mathrm{Pr}$ scaling of transport and mixing. We will also discuss the impact of the Boussinesq approximation in the case where large aspect ration perturbations exceed a scale height. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R30.00009: Hydromagnetic Dynamics and Magnetic Field Enhancement in a Turbulent Spherical Couette Experiment Douglas Stone, Matthew Adams, Onur Kara, Daniel Lathrop The University of Maryland Three Meter Geodynamo, a spherical Couette experiment filled with liquid sodium and geometrically similar to the earth's core, is used to study hydrodynamic and hydromagnetic phenomena in rapidly rotating turbulence. An external coil applies a magnetic field in order to study hydromagnetic effects relevant to the earth's outer core such as dynamo action, while an array of 31 external Hall sensors measures the Gauss coefficients of the resulting magnetic field. The flow state is strongly dependent on Rossby number, $Ro = (\Omega_I - \Omega_O)/\Omega_O$, where $\Omega_I$ and $\Omega_O$ are the inner and outer sphere rotation frequencies. The flow state is inferred from the torque required to drive the inner sphere. The generation of internal toroidal magnetic field through the $\Omega$-effect is measured by a Hall probe inserted into the sodium. A self-sustaining dynamo has not yet been observed at rotation speeds up to $\Omega_O$=3 Hz, which is three-fourths of the design maximum of the experiment. However, continuous dipole amplification up to 12\% of a small applied field has been observed at Ro=?17.7 while bursts of dipole field have been observed up to 15\% of a large external applied field at Ro=+6.0 and up to 20\% of a small applied field at Ro=+2.15. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R30.00010: Elastorotational instability in Taylor-Couette flow with Keplerian ratio as analog of the Magnetorotational Instability Innocent Mutabazi, Yang Bai, Olivier Crumeyrolle The analogy between viscoelastic instability in the Taylor-Couette flow and the magnetorotational instability (MRI) has been found by Ogilvie \& Potter $\left[1\right]$. It relies on the similarity between the governing equations of viscoelastic flows of constant viscosity (Oldroyd-B model equations)and those of Magnetohydrodynamics (MHD). We have performed linear stability analysis of the Taylor-Couette flow with a polymer solution obeying the Oldroyd-B model. A diagram of critical states shows the existence of stationary and helicoidal modes depending on the elasticity of the polymer solution. A generalized Rayleigh criterion determines the potentially unstable zone to pure elasticity-driven perturbations. Experimental results yield four type of modes : one pure elasticity mode and three elastorotational modes that are the MRI-analog modes. Anti-Keplerian case has also been investigated. There is a good agreement between experimental and theoretical results $\left[2\right]$. \\[4pt] [1] G.I. Ogilvie \& A.T. Potter, \textit{Phys. Rev. Lett.} \textbf{100}, 074503 (2008).\\[0pt] [2] Y. Bai, O. Crumeyrolle \& I. Mutabazi, Phys. Rev. E.(2015) [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R30.00011: Stability of an accretion disk: nonlinear small-scale analysis of a quasi-Keplerian shear flow Benjamin Miquel, Edgar Knobloch, Keith Julien We model the background flow in the equatorial plane of an accretion disk with a radially stratified, non-magnetic zonal flow in a quasi-Keplerian balance (i.e. small pressure corrections are taken into account in the radial balance). The dynamics of the perturbations around this background flow obey a set of equations which main ingredients are: (i) a radial shear, (ii) a radial stratification, and (iii) a coupling between the flow and the background entropy gradient. The inviscid linear stability of this set of equation is first discussed: perturbations are decomposed into Kelvin modes (also known as the shearing sheet approximation) which amplitudes are determined analytically as a function of the radial stratification. Then, using as well a Kelvin modes decomposition, the viscous linear problem exhibits potentially transient growth, yet features unconditional stability as $t\rightarrow \infty$. Finally, we demonstrate with 2D simulations of the viscous nonlinear problem that nonlinearities provide an energy transfer mechanism through modes that compensates the transfer induced by the linear shear. This mechanism allows for a sustained instability scenario despite the stability of the linear viscous problem. [Preview Abstract] |
Tuesday, November 24, 2015 3:13PM - 3:26PM |
R30.00012: Microwaves from Extra Galactic Radio Pulsars are found to deflect at Impact Parameters corresponding to the Plasma Limbs of the Sun and Stars Edward Dowdye Findings show that the microwaves from the extra galactic radio pulsars appear to deflect at impact parameters corresponding to the plasma limbs of the sun and the stars. The past century of astrophysical observations show that the bulk of gravitational light bending effects has been observed primarily at the plasma limb of the sun. The gravitational light bending rule of General Relativity predicts that gravitational bending of all waves in vacuum as well as in plasma. With current technical means in Astrophysics, the gravitation light bending effect should be an easily detectable effect for impact parameters corresponding to several solar radii above the plasma limb of the sun. Findings show that the gravitational bending in the plasma atmosphere of the sun appears to represent an indirect interaction that takes place between the gravitational gradient field of the sun and the microwaves from the radio pulsar sources. A minimum energy path calculation, supporting this argument, leads to a derivation of the very same light bending equation obtained from the assumptions of General Relativity. This was confirmed by a measurement on the gravitational deflection of microwaves at the Solar plasma limb by Lebach et al. (1995), who used a very-long-baseline-interferometer (VLBI) technique to determine the value of 0.9998 $+$/- 0.0008 times that of General Relativity. The reason Einstein rings are not abundantly observed in the star-filled night skies is due primarily to the low impact parameter deflections within the plasma limb of the lensing stars. [Preview Abstract] |
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