Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session E01: Astrophysical Fluid Dynamics |
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Chair: Pascale Garaud, University of California, Santa Cruz Room: Georgia World Congress Center B201 |
Sunday, November 18, 2018 5:10PM - 5:23PM |
E01.00001: Evolution of baroclinic critical layers Chen Wang, Neil J Balmforth Recent work has suggested that three dimensional rotating stratified shear flows can be the setting of a self-replicating vortex instability (Marcus et al., Phys. Rev. Lett. 2013, 111(8): 084501). Such ``Zombie vortices'' replicate themselves by exciting internal waves that break at a novel type of critical layer. In this study, we examine the evolution of such ``baroclinic critical layers'' in the situation that the waves are directly forced by a steady disturbance. Linear theory predicts that the flow settles down to a steady wave everywhere but near the baroclinic critical levels, where vorticity and density grow linearly with time over a region whose width decreases with time. The critical layer must therefore become nonlinear. By developing a nonlinear baroclinic critical layer theory, we show that the secular linear growth becomes halted. However, at later times, the vorticity begins to grow exponentially over yet smaller regions that are shifted with respect to the original baroclinic critical levels. |
Sunday, November 18, 2018 5:23PM - 5:36PM |
E01.00002: Direct Statistical Simulation and Generalized Quasilinear Approximation of Mean Flows and Convection in the Busse Annulus Jeffrey S Oishi, Steven Tobias, John Bradley Marston Understanding the generation of mean flows from anisotropic turbulence is crucial to developing insight into a number of astrophysical and geophysical problems. The Busse Annulus is a common and simple 2D model for rotating convection. Direct numerical simulation has revealed that the system creates mean flows from the turbulence due to rotation-induced correlations. Here, we discuss the application of direct statistical simulation and the generalized quasilinear approximation to the convection in the Busse Annulus. Direct statistical simulation in the CE2 approximation uses the standard quasilinear approach to solve for the cumulants of the velocities and temperature perturbations, rather than the fields themselves. The generalized quasilinear approximation divides the flow into "low" and "high" wavenumbers, with the "low" modes taking the place of the mean flow. We will demonstrate that even a very small number of "low" modes significantly outperforms the standard quasilinear approximation in predicting mean flows in the Busse Annulus. Finally, we will compare generalized quasilinear results with CE2 direct statistical simulation and discuss the path to constructing a generalized CE2 method combining generalized quaslinear techniques with direct statistical simulation. |
Sunday, November 18, 2018 5:36PM - 5:49PM |
E01.00003: Nonlinear tidal instabilities in compressible atmospheres Keaton Burns, Nevin N Weinberg The amount of dissipation caused by tidal interactions in binary stars and planetary systems is poorly understood but important in determining the orbital evolution of these systems. In particular, it is theorized that dissipation from tidal instabilities may measurably alter the gravitational waves emitted by binary neutron stars, potentially allowing detectors such as LIGO to observationally constrain the unknown interior structure of these objects. As a first step towards studying these effects in fully compressible stellar models, we present a study of the stability of a tidally deformed plane-parallel atmosphere. Using a general-purpose spectral PDE solver, we evaluate the threshold amplitude for the weakly nonlinear instability of the tidal response to coupled collections of p-modes and g-modes over multiple scale heights. We additionally perform fully nonlinear simulations to verify the predicted threshold amplitudes. This work demonstrates the feasibility of using general spectral methods to perform weakly nonlinear analyses of atmospheres with arbitrary background structures and including multiple mode families and non-adiabatic effects. We will also discuss current efforts to extend this work to spherical geometries and more realistic neutron star models. |
Sunday, November 18, 2018 5:49PM - 6:02PM |
E01.00004: Convection with nonlinear conductivities: feedback effects at low and high Mach number Evan H Anders, Benjamin Brown In the interior of stars like the Sun, convection occurs in the presence of a highly nonlinear radiative conductivity. In this work, we study compressible, stratified convection with a nonlinear radiative conductivity which depends on a Kramer's-like opacity. We show that the Mach number of the resultant convection can be controlled by the opacity's dependence on temperature. In these systems, the Reynolds and Peclet numbers are separately controlled by Rayleigh and Prandtl numbers, so turbulent convection can be studied at low and high Mach number. We determine the importance of nonlinear conductive feedback on the convective flows when the Mach number is low [O(0.01)] and when it is high [O(1)]. We discuss implications for convection in the Sun's deep interior. |
Sunday, November 18, 2018 6:02PM - 6:15PM |
E01.00005: The effect of magnetic fields on double-diffusive fingering in astrophysics Peter Harrington, Pascale Garaud Double-diffusive convection at high Prandtl number (Pr ~ O(1) or larger) has been well studied in geophysical contexts, but detailed investigations of the low Prandtl number regimes (Pr << 1) which are relevant to most astrophysical scenarios like stellar or planetary interiors have only recently become feasible. Since most low-Pr fluids in astrophysical scenarios are electrically conducting, it is possible that magnetic fields play a role in either enhancing or suppressing double-diffusive fingering convection, but to date there have been no investigations of such possibilities. Here we study the effects of both vertical (aligned with the gravitational axis) and horizontal background magnetic fields on the linear stability and nonlinear saturation of double-diffusive fingering convection, through a combination of theoretical work and direct numerical simulation (DNS). The possibility of dynamo behavior in the case where the fluid is also rotating is discussed, as well as the potential for magnetic effects to explain discrepancies between theoretical and observed mixing rates in low-mass red giant branch (RGB) stars. |
Sunday, November 18, 2018 6:15PM - 6:28PM |
E01.00006: The effect of shear on fingering convection at low Prandtl number Pascale Garaud, Anuj Kumar, Jayashree Sridhar Fingering convection results from the double-diffusive instability of a stable temperature gradient combined with an unstable compositional gradient. It is thought to play a significant role in the interior of stars, which are intrinsically low Prandtl number fluids. The nonlinear properties of fingering convection as a standalone process are now well understood. However, the effect of other processes such as rotation, shear and magnetic fields for instance remain to be explored and quantified. In this talk I will review what is known about fingering convection, then describe recent linear stability results and DNS results on the effect of shear. We find in particular that moderate shear can strongly suppress transport by fingering convection, which could have important implications in stellar astrophysics. |
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