Alexandros Alexakis

Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence

We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional magnetohydrodynamics (MHD) turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from large scales to kinetic energy at smaller scales and the transfer of magnetic energy from large scales to magnetic energy at smaller scales are local, as is also found in the case of neutral fluids and in a way that is compatible with the Kolmogorov theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly nonlocal process in Fourier space. Energy from the velocity field at large scales can be transferred directly into small-scale magnetic fields without the participation of intermediate scales. Some implications of our results to MHD turbulence modeling are also discussed.

On heavy element enrichment in classical novae

Many classical nova ejecta are enriched in CNO and Ne. Rosner and coworkers recently suggested that the enrichment might originate in the resonant interaction between large-scale shear flows in the accreted H/He envelope and gravity waves at the interface between the envelope and the underlying C/O white dwarf (WD). The shear flow amplifies the waves, which eventually form cusps and break. This wave breaking injects a spray of C/O into the superincumbent H/He. Using two-dimensional simulations, we formulate a quantitative expression for the amount of C/O per unit area that can be entrained, at saturation, into the H/He. The fraction of the envelope that is enriched depends on the horizontal distribution of shear velocity and the density contrast between the C/O WD and the H/He layer but is roughly independent of the vertical shape of the shear profile. Using this parameterization for the mixed mass, we then perform several one-dimensional Lagrangian calculations of an accreting WD envelope and consider two scenarios: that the wave breaking and mixing is driven by the convective flows and that the mixing occurs prior to the onset of convection. In the absence of enrichment prior to ignition, the base of the convective zone, as calculated from mixing-length theory with the Ledoux instability criterion, does not reach the C/O interface. As a result, there is no additional mixing, and the runaway is slow. In contrast, the formation of a mixed layer during the accretion of H/He, prior to ignition, causes a more violent runaway. The envelope can be enriched by 25% of C/O by mass (consistent with that observed in some ejecta) for shear velocities, over the surface, with Mach numbers 0.4.

Energy transfer in Hall-MHD turbulence: cascades, backscatter, and dynamo action

Abstract. Scale interactions in Hall MHD are studied using both the mean fieldtheory derivation of transport coefficients, and direct numerical simulations in threespace dimensions. In the magnetically dominated regime, the eddy resistivity isfound to be negative definite, leading to large scale instabilities. A direct cascade ofthe total energyisobserved,althoughasthe amplitude ofthe Hall effect is increased,backscatterofmagneticenergytolargescalesis found, afeature notpresentin MHDflows. The coupling between the magnetic and velocity fields is different than in theMHD case, and backscatter of energy from small scale magnetic fields to large scaleflows is also observed. For the magnetic helicity, a strong quenching of its transferis found. We also discuss non-helical magnetically forced Hall-MHD simulationswhere growth of a large scale magnetic field is observed. 1. Introduction The relevance of two fluid effects has recently been pointed out in several stud-ies of astrophysical and laboratory plasmas (Balbus and Terquem, 2001; Sano andStone, 2002; Mirnov et al., 2003; Ding et al., 2004). The effect of adding the Hallcurrent to the dynamics of the flow was studied in several scenarios, particularly dy-namo action (Helmis, 1968; Galanti et al., 1995; Mininni et al., 2002, 2003a, 2005b)and reconnection (Birn et al., 2001; Shay et al., 2001; Wang et al., 2001; Moraleset al., 2005). Several of these works showed that the Hall currents increase the re-connection rate of magnetic field lines. However, most of the studies of magneticreconnection were done for particular configurations of current sheets. It was shownin particular by Smith et al. (2004) that when a turbulent background is present thereconnection rate is dominated by the amplitude of the turbulent fluctuations. Theprocess of magnetic reconnection is relevant in several astrophysical and geophys-ical scenarios, such as the magnetopause, the magnetotail, the solar atmosphere,or the interplanetary and interstellar medium. Reconnection can also play a rolein the generation of large scale magnetic fields by dynamo action Zeldovich et al.(1983).Some of the works in Hall-magnetohydrodynamics (Hall-MHD) present conflict-ing results, indicating in some cases that the Hall effect can help the growth of a

On the inverse cascade of magnetic helicity

We study the inverse cascade of magnetic helicity in conducting fluids, as pertinent to the generation and dynamics of magnetic fields as observed, e.g., in the solar corona, by investigating the detailed transfer of helicity between different spherical shells in Fourier space in direct numerical simulations of three-dimensional magnetohydrodynamics (MHD). Two different numerical simulations are used, one in which the system is forced with an electromotive force in the induction equation and one in which the system is forced mechanically with an ABC flow and the magnetic field is solely sustained by a dynamo action. The magnetic helicity cascade at the initial stages of both simulations is observed to be inverse and local (in scale space) at large scales and direct and local at small scales. When saturation is approached, most of the helicity is concentrated at large scales and the cascade is nonlocal. Helicity is transferred directly from the forced scales to the largest scales. At the same time, a smaller in amplitude direct cascade is observed from the largest scale to small scales.

Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo.

We study the transfer of energy between different scales for forced three-dimensional magnetohydrodynamics turbulent flows in the kinematic dynamo regime. Two different forces are examined: a nonhelical Taylor-Green flow with magnetic Prandtl number P(M) = 0.4 and a helical ABC flow with P(M) = 1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations in the inertial range are responsible for the magnetic field amplification at small scales (small-scale dynamo) while the large-scale field is amplified mostly due to the large-scale flow. A direct cascade of the magnetic field energy from large to small scales is also presented and is a complementary mechanism for the increase of the magnetic field at small scales. The input of energy from the inertial range velocity field into the small magnetic scales dominates over the energy cascade up to the wave number where the magnetic energy spectrum peaks. At even smaller scales, most of the magnetic energy input is from the cascading process.

On Holmboe’s instability for smooth shear and density profiles

The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin–Helmholtz and Holmboe instabilities are present. For a fixed Richardson number the unstable modes are confined to finite bands between a smallest and a largest marginally unstable wavenumber. The results in this paper indicate that the stability boundary for small wavenumbers is comprised of neutral modes with phase velocity equal to the maximum/minimum wind velocity whereas the other stability boundary, for large wavenumbers, is comprised of singular neutral modes with phase velocity in the range of the velocity shear. We show how these stability boundaries can be evaluated without solving for the growth rate over the entire parameter space as was previously done. The results indicate further that there is a new instability domain that has not been previously noted in the literature. The unstable modes, in this new instability do...

On the C/O Enrichment of Nova Ejecta

Using the results of recent work in shear instabilities in stratified fluids, we show that the resonant interaction between large-scale flows in the accreted H/He envelope of white dwarf stars and interfacial gravity waves can mix the stars envelope with the white dwarfs surface material, leading to the enhancement of the envelopes C/O abundance to levels required by extant models for nova outbursts.

Imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024(3) points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their nonlocal components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed.

Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics

The nature of the interactions between different scales in magneto- hydrodynamic (MHD) turbulence is important for the understanding of the behaviour of magnetized astrophysical, geophysical and industrial flows in a turbulent state. In this paper, we review some recent results in the study of locality of interactions in turbulent flows and we address some of the questions that arise. We examine the cascade of ideal invariants in turbulent MHD flows by examining the transfer functions. We show new results indicating that the nonlocal behaviour of the energy transfer in MHD is the result of a correlation between the velocity and magnetic fields. This nonlocality disappears if we randomize the phases of the two fields keeping the hydrodynamic and magnetic helicities fixed. The cascade of magnetic helicity is also investigated, with special focus on the fate of the small-scale helicity and its coupling with the large-scale flow. These results have implications for dynamo action, in particular for the commonly used distinction between large- and small-scale dynamos. The long-range interactions that exist in MHD flows also raise the question of the existence of universality in MHD, both in the kinematic dynamo regime as well as in the turbulent steady state.

Energy and enstrophy dissipation in steady state 2d turbulence

Abstract Upper bounds on the bulk energy dissipation rate ϵ and enstrophy dissipation rate χ are derived for the statistical steady state of body forced two-dimensional (2d) turbulence in a periodic domain. For a broad class of externally imposed body forces it is shown that ϵ ⩽ k f U 3 Re − 1 / 2 ( C 1 + C 2 Re −1 ) 1 / 2 and χ ⩽ k f 3 U 3 ( C 1 + C 2 Re −1 ) where U is the root-mean-square velocity, k f is a wavenumber (inverse length scale) related with the forcing function, and Re = U / ν k f . The positive coefficients C 1 and C 2 are uniform in the kinematic viscosity ν, the amplitude of the driving force, and the system size. We compare these results with previously obtained bounds for body forces involving only a single length scale, or for velocity dependent constant-energy-flux forces acting at finite wavenumbers. Implications of our results are discussed.