7 research outputs found
A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
We explore some consequences of the ``alpha model,'' also called the
``Lagrangian-averaged'' model, for two-dimensional incompressible
magnetohydrodynamic (MHD) turbulence. This model is an extension of the
smoothing procedure in fluid dynamics which filters velocity fields locally
while leaving their associated vorticities unsmoothed, and has proved useful
for high Reynolds number turbulence computations. We consider several known
effects (selective decay, dynamic alignment, inverse cascades, and the
probability distribution functions of fluctuating turbulent quantities) in
magnetofluid turbulence and compare the results of numerical solutions of the
primitive MHD equations with their alpha-model counterparts' performance for
the same flows, in regimes where available resolution is adequate to explore
both. The hope is to justify the use of the alpha model in regimes that lie
outside currently available resolution, as will be the case in particular in
three-dimensional geometry or for magnetic Prandtl numbers differing
significantly from unity. We focus our investigation, using direct numerical
simulations with a standard and fully parallelized pseudo-spectral method and
periodic boundary conditions in two space dimensions, on the role that such a
modeling of the small scales using the Lagrangian-averaged framework plays in
the large-scale dynamics of MHD turbulence. Several flows are examined, and for
all of them one can conclude that the statistical properties of the large-scale
spectra are recovered, whereas small-scale detailed phase information (such as
e.g. the location of structures) is lost.Comment: 22 pages, 20 figure
Not Much Helicity is Needed to Drive Large Scale Dynamos
Understanding the in situ amplification of large scale magnetic fields in
turbulent astrophysical rotators has been a core subject of dynamo theory. When
turbulent velocities are helical, large scale dynamos that substantially
amplify fields on scales that exceed the turbulent forcing scale arise, but the
minimum sufficient fractional kinetic helicity f_h,C has not been previously
well quantified. Using direct numerical simulations for a simple helical
dynamo, we show that f_h,C decreases as the ratio of forcing to large scale
wave numbers k_F/k_min increases. From the condition that a large scale helical
dynamo must overcome the backreaction from any non-helical field on the large
scales, we develop a theory that can explain the simulations. For k_F/k_min>8
we find f_h,C< 3%, implying that very small helicity fractions strongly
influence magnetic spectra for even moderate scale separation.Comment: 5 pages, 4 figure
Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence
Rapidly rotating turbulent flow is characterized by the emergence of columnar
structures that are representative of quasi-two dimensional behavior of the
flow. It is known that when energy is injected into the fluid at an
intermediate scale , it cascades towards smaller as well as larger scales.
In this paper we analyze the flow in the \textit{inverse cascade} range at a
small but fixed Rossby number, {}. Several
{numerical simulations with} helical and non-helical forcing functions are
considered in periodic boxes with unit aspect ratio. In order to resolve the
inverse cascade range with {reasonably} large Reynolds number, the analysis is
based on large eddy simulations which include the effect of helicity on eddy
viscosity and eddy noise. Thus, we model the small scales and resolve
explicitly the large scales. We show that the large-scale energy spectrum has
at least two solutions: one that is consistent with
Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of
energy in two-dimensional (2D) turbulence with a {}
scaling, and the other that corresponds to a steeper {}
spectrum in which the three-dimensional (3D) modes release a substantial
fraction of their energy per unit time to 2D modes. {The spectrum that} emerges
{depends on} the anisotropy of the forcing function{,} the former solution
prevailing for forcings in which more energy is injected into 2D modes while
the latter prevails for isotropic forcing. {In the case of anisotropic forcing,
whence the energy} goes from the 2D to the 3D modes at low wavenumbers,
large-scale shear is created resulting in another time scale ,
associated with shear, {thereby producing} a spectrum for the
{total energy} with the 2D modes still following a {}
scaling
The essential role of multi-point measurements in investigations of turbulence, three-dimensional structure, and dynamics: the solar wind beyond single scale and the Taylor Hypothesis
Space plasmas are three-dimensional dynamic entities. Except under very
special circumstances, their structure in space and their behavior in time are
not related in any simple way. Therefore, single spacecraft in situ
measurements cannot unambiguously unravel the full space-time structure of the
heliospheric plasmas of interest in the inner heliosphere, in the Geospace
environment, or the outer heliosphere. This shortcoming leaves numerous central
questions incompletely answered. Deficiencies remain in at least two important
subjects, Space Weather and fundamental plasma turbulence theory, due to a lack
of a more complete understanding of the space-time structure of dynamic
plasmas. Only with multispacecraft measurements over suitable spans of spatial
separation and temporal duration can these ambiguities be resolved. We note
that these characterizations apply to turbulence across a wide range of scales,
and also equally well to shocks, flux ropes, magnetic clouds, current sheets,
stream interactions, etc. In the following, we will describe the basic
requirements for resolving space-time structure in general, using turbulence'
as both an example and a principal target or study. Several types of missions
are suggested to resolve space-time structure throughout the Heliosphere.Comment: White Paper submitted to: Decadal Survey for Solar and Space Physics
(Heliophysics) 2024-2033. arXiv admin note: substantial text overlap with
arXiv:1903.0689
Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions
The essential role of multi-point measurements in investigations of heliospheric turbulence, three-dimensional structure, and dynamics
White Paper submitted to: Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. arXiv admin note: substantial text overlap with arXiv:1903.06890Space plasmas are three-dimensional dynamic entities. Except under very special circumstances, their structure in space and their behavior in time are not related in any simple way. Therefore, single spacecraft in situ measurements cannot unambiguously unravel the full space-time structure of the heliospheric plasmas of interest in the inner heliosphere, in the Geospace environment, or the outer heliosphere. This shortcoming leaves numerous central questions incompletely answered. Deficiencies remain in at least two important subjects, Space Weather and fundamental plasma turbulence theory, due to a lack of a more complete understanding of the space-time structure of dynamic plasmas. Only with multispacecraft measurements over suitable spans of spatial separation and temporal duration can these ambiguities be resolved. We note that these characterizations apply to turbulence across a wide range of scales, and also equally well to shocks, flux ropes, magnetic clouds, current sheets, stream interactions, etc. In the following, we will describe the basic requirements for resolving space-time structure in general, using turbulence' as both an example and a principal target or study. Several types of missions are suggested to resolve space-time structure throughout the Heliosphere