Stability, Instability, and "Backwards'' Transport in Accretion Disks"

The stratification of entropy and the stratification of angular momentum are closely analogous. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical turbulence. In both instances we argue that the transport must proceed ``backwards'' relative to the sense one would expect from a simple enhanced diffusion approach. Reversed angular momentum transport has already been seen in numerical simulations; contra-gradient thermal diffusion should be amenable to numerical verification as well. These arguments also bear on the observed nonlinear local stability of isolated Keplerian disks. We also describe a diffusive instability that is the entropy analogue to the magnetorotational instability. It affects thermally stratified layers when Coulomb conduction and a weak magnetic field are present. The criterion for convective instability goes from one of upwardly decreasing entropy to one of upwardly decreasing temperature. The maximum growth rate is of order the inverse sound crossing time, independent of the thermal conductivity. The indifference of the growth rate to the conduction coefficient, its simple dynamical scaling, and the replacement in the stability criterion of a conserved quantity (entropy) gradient by a free energy (temperature) gradient are properties similar to those exhibited by the magnetorotational instability.Comment: 21 pages, 5 figs., AAS LaTEX macros v4.0. Accepted to ApJ, final versio

Anisotropic eddy viscosity models

A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry

Ensemble averaged dynamic modeling

The possibility of using the information from simultaneous equivalent Large Eddy Simulations (LAS) for improving the subgrid scale modeling is investigated. An ensemble average dynamic model is proposed as an alternative to the usual spatial average versions. It is shown to be suitable independently of the existence of any homogeneity directions, and its formulation is thus universal. The ensemble average dynamic model is shown to give very encouraging results for as few as 16 simultaneous LES's

A Lagrangian dynamic subgrid-scale model turbulence

A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space

Reynolds number effects on Rayleigh-Taylor Instability with Implications for Type Ia Supernovae

Spontaneous mixing of materials at unstably stratified interfaces occurs in a wide variety of atmospheric, oceanic, geophysical and astrophysical flows. The Rayleigh-Taylor instability, in particular, plays key roles in the death of stars, planet formation and the quest for controlled thermonuclear fusion. Despite its ubiquity, fundamental questions regarding Rayleigh-Taylor instability persist. Among such questions are: Does the flow forget its initial conditions? Is the flow self-similar? What is the value of the scaling constant? How does mixing influence the growth rate? Here we show results from a 3072{sup 3} grid-point Direct Numerical Simulation in an attempt to answer these and other questions. The data indicate that the scaling constant cannot be found by fitting a curve to the width of the mixing region (as is common practice) but can only be accurately obtained by recourse to the similarity equation for the growth rate. The data further establish that the ratio of kinetic energy to released potential energy is not constant, as has heretofore been assumed. The simulated flow reaches a Reynolds number of 32,000, far exceeding that of all previous simulations. The latter stages of the simulation reveal a weak Reynolds number dependence, which may have profound consequences for modeling Type Ia supernovae as well as other high Reynolds number flows

III. Report of the Committee on Dental Education of the Association of American University: 1926

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66524/2/10.1177_00220345270070041104.pd

Vorticity Budget of Weak Thermal Convection in Keplerian disks

By employing the equations of mean-square vorticity (enstrophy) fluctuations in strong shear flows, we demonstrate that unlike energy production of turbulent vorticity in nonrotating shear flows, the turbulent vorticity of weak convection in Keplerian disks cannot gain energy from vortex stretching/tilting by background shear unless the asscoiated Reynolds stresses are negative. This is because the epicyclic motion is an energy sink of the radial component of mean-square turbulent vorticity in Keplerian disks when Reynolds stresses are positive. Consequently, weak convection cannot be self-sustained in Keplerian flows. This agrees with the results implied from the equations of mean-square velocity fluctuations in strong shear flows. Our analysis also sheds light on the explanation of the simulation result in which positive kinetic helicity is produced by the Balbus-Hawley instability in a vertically stratified Keplerian disk. We also comment on the possibility of outward angular momentum transport by strong convection based on azimuthal pressure perturbations and directions of energy cascade.Comment: 8 pages, 1 figure, emulateapj.sty, revised version in response to referee's comments, accepted by Ap

Simulation Strategies for Shock-Turbulence Interactions

The computational challenge of predicting shock-turbulence interactions stems from the fundamentally different physics at play. Shock waves are microscopically thin regions wherein flow properties change rapidly over a distance roughly equal to the molecular mean free path; hence, they are essentially strong discontinuities in the flow field. Turbulence, on the other hand, is a chaotic phenomenon with broadband spatial and temporal scales of motion. Most shock-capturing methods rely on strong numerical dissipation to artificially smooth the discontinuity, such that it can be resolved on the computational grid. Unfortunately, the artificial dissipation necessary for capturing shocks has a deleterious effect on turbulence. An additional problem is the fact that shock-capturing schemes are typically based on one-dimensional Riemann solutions that are not strictly valid in multiple dimensions. This can lead to anisotropy errors and grid-seeded perturbations. Other complications arising from upwinding, flux limiting, operator splitting etc., can seriously degrade performance and generate significant errors, especially in multiple dimensions. The purpose of this work is to design improved algorithms, capable of capturing both shocks and turbulence, which also scale to tens of thousands of processors. We have evaluated two new hydrodynamic algorithms, in relation to the widely used WENO method, on a suite of test cases. The new methods, referred to as the 'Compact' and 'Hybrid' schemes, show very promising results

Atoms in the Surf: Molecular Dynamics Simulation of the Kelvin-Helmholtz Instability using 9 Billion Atoms

We present a fluid dynamics video showing the results of a 9-billion atom molecular dynamics simulation of complex fluid flow in molten copper and aluminum. Starting with an atomically flat interface, a shear is imposed along the copper-aluminum interface and random atomic fluctuations seed the formation of vortices. These vortices grow due to the Kelvin-Helmholtz instability. The resulting vortical structures are beautifully intricate, decorated with secondary instabilities and complex mixing phenomena. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.Comment: Description of video submitted to APS DFD Gallery of Fluid Motion 200

Analgesic treatment of ciguatoxin-induced cold allodynia

Ciguatera, the most common form of nonbacterial ichthyosarcotoxism, is caused by consumption of fish that have bioaccumulated the polyether sodium channel activator ciguatoxin. The neurological symptoms of ciguatera include distressing, often persistent sensory disturbances such as paraesthesias and the pathognomonic symptom of cold allodynia. We show that intracutaneous administration of ciguatoxin in humans elicits a pronounced axon-reflex flare and replicates cold allodynia. To identify compounds able to inhibit ciguatoxin-induced Na-v responses, we developed a novel in vitro ciguatoxin assay using the human neuroblastoma cell line SH-SY5Y. Pharmacological characterisation of this assay demonstrated a major contribution of Na(v)1.2 and Na(v)1.3, but not Na(v)1.7, to ciguatoxin-induced Ca2+ responses. Clinically available Nav inhibitors, as well as the K(v)7 agonist flupirtine, inhibited tetrodotoxin-sensitive ciguatoxin-evoked responses. To establish their in vivo efficacy, we used a novel animal model of ciguatoxin-induced cold allodynia. However, differences in the efficacy of these compounds to reverse ciguatoxin-induced cold allodynia did not correlate with their potency to inhibit ciguatoxin-induced responses in SH-SY5Y cells or at heterologously expressed Nav1.3, Na(v)1.6, Na(v)1.7, or Na(v)1.8, indicating cold allodynia might be more complex than simple activation of Na-v channels. These findings highlight the need for suitable animal models to guide the empiric choice of analgesics, and suggest that lamotrigine and flupirtine could be potentially useful for the treatment of ciguatera. (C) 2013 International Association for the Study of Pain. Published by Elsevier B. V. All rights reserved