# Influence of a large-scale field on energy dissipation in magnetohydrodynamic turbulence [CL]

In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimension kinetic models, gyrokinetics, etc., which make theoretical calculations easier and numerical computations cheaper. Recently, however, it has become clear that the turbulent energy dissipation is concentrated in the regions of strong magnetic field variations. A significant fraction of the energy dissipation may be localized in very small volumes corresponding to the boundaries between strongly magnetized domains. In these regions the reduced models are not applicable. This has important implications for studies of particle heating and acceleration in magnetic plasma turbulence. The goal of this work is to systematically investigate the relationship between local magnetic field variations and magnetic energy dissipation, and to understand its implications for modeling energy dissipation in realistic turbulent plasmas.

V. Zhdankin, S. Boldyrev and J. Mason
Mon, 13 Mar 17
8/48

Comments: 6 pages, 5 figures, to appear in Monthly Notices of the Royal Astronomical Society

# Hydrodynamic turbulence in quasi-Keplerian rotating flows [CL]

We report a direct-numerical-simulation study of Taylor-Couette flow in the quasi-Keplerian regime at shear Reynolds numbers up to $\mathcal{O}(10^5)$. Quasi-Keplerian rotating flow has been investigated for decades as a simplified model system to study the origin of turbulence in accretion disks that is not fully understood. The flow in this study is axially periodic and thus the experimental end-wall effects on the stability of the flow are avoided. Using optimal linear perturbations as initial conditions, our simulations find no sustained turbulence: the strong initial perturbations distort the velocity profile and trigger turbulence that eventually decays.

L. Shi, B. Hof, M. Rampp, et. al.
Fri, 10 Mar 17
31/52

# Black hole acoustics in the minimal geometric deformation of a de Laval nozzle [CL]

The correspondence between sound waves, in a de Laval propelling nozzle, and quasinormal modes emitted by brane-world black holes deformed by a 5D bulk Weyl fluid are here explored and scrutinised. The analysis of sound waves patterns in a de Laval nozzle at a laboratory, reciprocally, is here shown to provide relevant data about the 5D bulk Weyl fluid and its on-brane projection, comprised by the minimal geometrically deformed compact stellar distribution on the brane. Acoustic perturbations of the gas fluid flow in the de Laval nozzle are proved to coincide to the quasinormal modes of black holes solutions deformed by the 5D Weyl fluid, in the geometric deformation procedure. Hence, in a phenomenological E\”otv\”os-Friedmann fluid brane-world model, the realistic shape of a de Laval nozzle is derived and its consequences studied.

R. Rocha
Tue, 7 Mar 17
32/66

# Comparative statistics of selected subgrid-scale models in large eddy simulations of decaying, supersonic MHD turbulence [CL]

Large eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by direct simulations due to their complexity, for example, in the highly turbulent regime. However, their accuracy and success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in the simulation. We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and the scale-similarity (SS) model, and one recently proposed nonlinear (NL) SGS model in the realm of compressible MHD turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number of ~3) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model and filter, we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore, we compare the temporal evolution of lower and higher order statistical moments of the spatial distributions of kinetic and magnetic energy, vorticity, current density, and dilatation magnitudes. We find no statistical influence on the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. In addition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both EV and NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipation on the smallest scales. We demonstrate that the nonlinear model improves higher order statistics already with a small explicit filter, i.e. a three-point stencil. The results of e.g. the structure functions or the skewness and kurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution. We conclude that the nonlinear model with a small explicit filter is suitable for application in more complex scenarios when higher order statistics are important.

P. Grete, D. Vlaykov, W. Schmidt, et. al.
Fri, 3 Mar 17
36/62

Comments: 13 pages, 8 figures, accepted for publication in PRE

# Detonability of white dwarf plasma: turbulence models at low densities [SSA]

We study the conditions required to produce self-sustained detonations in turbulent, carbon-oxygen degenerate plasma at low densities.
We perform a series of three-dimensional hydrodynamic simulations of turbulence driven with various degrees of compressibility. The average conditions in the simulations are representative of models of merging binary white dwarfs.
We find that material with very short ignition times is abundant in the case that turbulence is driven compressively. This material forms contiguous structures that persist over many ignition times, and that we identify as prospective detonation kernels. Detailed analysis of prospective kernels reveals that these objects are centrally-condensed and their shape is characterized by low curvature, supportive of self-sustained detonations. The key characteristic of the newly proposed detonation mechanism is thus high degree of compressibility of turbulent drive.
The simulated detonation kernels have sizes notably smaller than the spatial resolution of any white dwarf merger simulation performed to date. The resolution required to resolve kernels is 0.1 km. Our results indicate a high probability of detonations in such well-resolved simulations of carbon-oxygen white dwarf mergers. These simulations will likely produce detonations in systems of lower total mass, thus broadening the population of white dwarf binaries capable of producing Type Ia supernovae. Consequently, we expect a downward revision of the lower limit of the total merger mass that is capable of producing a prompt detonation.
We review application of the new detonation mechanism to various explosion scenarios of single, Chandrasekhar-mass white dwarfs.

D. Fenn and T. Plewa
Thu, 2 Mar 17
43/44

Comments: 13 pages, MNRAS in press

# The distribution of density in supersonic turbulence [GA]

We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.

J. Squire and P. Hopkins
Tue, 28 Feb 17
31/69

Symmetries and topology are central to an understanding of physics. Topology explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering by non-magnetic impurities or bumps. Subsequent to the discovery of the quantum spin Hall effect, states of matter with different topological properties were classified according to the discrete symmetries of the system. Recently topologically protected edge excitations have been found in artificial lattice structures that support classical waves of various types. The interplay between discrete symmetries and the topology of fluid waves has so far played no role in the study of the dynamics of oceans and atmospheres. Here we show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorially trapped Kelvin and Yanai waves have a topological origin, manifesting as equatorial edge modes in the rotating shallow water model. These unidirectional edge modes are guaranteed to exist by the non-trivial global structure of the bulk Poincar\’e modes encoded through the first Chern number of value $\pm2$, in agreement with the correspondence between behavior deep in the bulk and edge excitations of a physical system. Thus the oceans and atmospheres of Earth and other rotating planets naturally share fundamental properties with topological insulators, despite the absence of an underlying lattice. As equatorially trapped Kelvin waves are an important component of El Ni\~no Southern Oscillation, and Madden-Julian Oscillation, our results demonstrate the topology plays an unexpected role in Earth’s climate system. These and other geophysical waves of topological origin are protected against static perturbations by time scale separation from other modes that inhibits scattering.