279 research outputs found
Inverse cascade behavior in freely decaying two-dimensional fluid turbulence
We present results from an ensemble of 50 runs of two-dimensional
hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from
an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have
random initial conditions with same initial integral scale, energy, enstrophy,
and Reynolds number. When both ensemble- and time-averaged, inverse energy
cascade behavior is observed, even in the absence of external mechanical
forcing: the energy spectrum at scales larger than the characteristic scale of
the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law
at smaller scales, and a positive flux of enstrophy. The source of energy for
this behavior comes from the modal energy around the energy containing scale at
t=0. The results shed some light into connections between decaying and forced
turbulence, and into recent controversies in experimental studies of
two-dimensional and magnetohydrodynamic turbulent flows.Comment: 7 pages, 6 figure
Long-time properties of MHD turbulence and the role of symmetries
We investigate long-time properties of three-dimensional MHD turbulence in
the absence of forcing and examine in particular the role played by the
quadratic invariants of the system and by the symmetries of the initial
configurations. We observe that, when sufficient accuracy is used, initial
conditions with a high degree of symmetries, as in the absence of helicity, do
not travel through parameter space over time whereas by perturbing these
solutions either explicitly or implicitly using for example single precision
for long times, the flows depart from their original behavior and can become
either strongly helical, or have a strong alignment between the velocity and
the magnetic field. When the symmetries are broken, the flows evolve towards
different end states, as predicted by statistical arguments for non-dissipative
systems with the addition of an energy minimization principle, as already
analyzed in \cite{stribling_90} for random initial conditions using a moderate
number of Fourier modes. Furthermore, the alignment properties of these flows,
between velocity, vorticity, magnetic potential, induction and current,
correspond to the dominance of two main regimes, one helically dominated and
one in quasi-equipartition of kinetic and magnetic energy. We also contrast the
scaling of the ratio of magnetic energy to kinetic energy as a function of
wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function
of wavenumber. We find that the former ratio is constant with an approximate
equipartition for scales smaller than the largest scale of the flow whereas the
ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure
A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation
We present results from two-dimensional numerical simulations of a supersonic
turbulent flow in the plane of the galactic disk, incorporating shear,
thresholded and discrete star formation (SF), self-gravity, rotation and
magnetic fields. A test of the model in the linear regime supports the results
of the linear theory of Elmegreen (1991). In the fully nonlinear turbulent
regime, while some results of the linear theory persist, new effects also
emerge. Some exclusively nonlinear effects are: a) Even though there is no
dynamo in 2D, the simulations are able to maintain or increase their net
magnetic energy in the presence of a seed uniform azimuthal component. b) A
well-defined power-law magnetic spectrum and an inverse magnetic cascade are
observed in the simulations, indicating full MHD turbulence. Thus, magnetic
field energy is generated in regions of SF and cascades up to the largest
scales. c) The field has a slight but noticeable tendency to be aligned with
density features. d) The magnetic field prevents HII regions from expanding
freely, as in the recent results of Slavin \& Cox (1993). e) A tendency to
exhibit {\it less} filamentary structures at stronger values of the uniform
component of the magnetic field is present in several magnetic runs. f) For
fiducial values of the parameters, the flow in general appears to be in rough
equipartition between magnetic and kinetic energy. There is no clear domination
of either the magnetic or the inertial forces. g) A median value of the
magnetic field strength within clouds is G, while for the
intercloud medium a value of G is found. Maximum contrasts of up to
a factor of are observed.Comment: Plain TeX file, 25 pages. Gzipped, tarred set of Tex file plus 17
figures and 3 tables (Postscript) available at
ftp://kepler.astroscu.unam.mx/incoming/enro/papers/mhdgturb.tar.g
Turbulence comes in bursts in stably stratified flows
There is a clear distinction between simple laminar and complex turbulent
fluids. But in some cases, as for the nocturnal planetary boundary layer, a
stable and well-ordered flow can develop intense and sporadic bursts of
turbulent activity which disappear slowly in time. This phenomenon is
ill-understood and poorly modeled; and yet, it is central to our understanding
of weather and climate dynamics. We present here a simple model which shows
that in stably stratified turbulence, the stronger bursts can occur when the
flow is expected to be more stable. The bursts are generated by a rapid
non-linear amplification of energy stored in waves, and are associated with
energetic interchanges between vertical velocity and temperature (or density)
fluctuations. Direct numerical simulations on grids of 2048^3 points confirm
this somewhat paradoxical result of measurably stronger events for more stable
flows, displayed not only in the temperature and vertical velocity derivatives,
but also in the amplitude of the fields themselves
Generation of turbulence through frontogenesis in sheared stratified flows
The large-scale structures in the ocean and the atmosphere are in geostrophic
balance, and a conduit must be found to channel the energy to the small scales
where it can be dissipated. In turbulence this takes the form of an energy
cascade, whereas one possible mechanism in a balanced flow at large scales is
through the formation of fronts, a common occurrence in geophysical dynamics.
We show in this paper that an iconic configuration in laboratory and numerical
experiments for the study of turbulence, that of the Taylor-Green or von
K\'arm\'an swirling flow, can be suitably adapted to the case of fluids with
large aspect ratios, leading to the creation of an imposed large-scale vertical
shear. To this effect we use direct numerical simulations of the Boussinesq
equations without net rotation and with no small-scale modeling, and with this
idealized Taylor-Green set-up. Various grid spacings are used, up to
spatial points. The grids are always isotropic, with box
aspect ratios of either or . We find that when shear and
stratification are comparable, the imposed shear layer resulting from the
forcing leads to the formation of multiple fronts and filaments which
destabilize and further evolve into a turbulent flow in the bulk, with a
sizable amount of dissipation and mixing, and with a cycle of front creation,
instability, and development of turbulence. The results depend on the vertical
length scales for shear and for stratification, with stronger large-scale
gradients being generated when the two length scales are comparable.Comment: 19 pages, 15 figures, several simulations added in this new versio
Highly Compressible MHD Turbulence and Gravitational Collapse
We investigate the properties of highly compressible turbulence and its
ability to produce self-gravitating structures. The compressibility is
parameterized by an effective polytropic exponent gama-eff. In the limit of
small gama-eff, the density jump at shocks is shown to be of the order of
e^{M^2}, and the production of vorticity by the nonlinear terms appears to be
negligible. In the presence of self-gravity, we suggest that turbulence can
produce bound structures for gama-eff < 2(1-1/n), where 'n' is the typical
dimensionality of the turbulent compressions. We show, by means of numerical
simulations, that, for sufficiently small gama-eff, small-scale turbulent
density fluctuations eventually collapse even though the medium is globally
stable. This result is preserved in the presence of a magnetic field for
supercritical mass-to-flux ratios.Comment: 4 pages, 3 postscript figures. Latex, uses aipproc.sty Contribution
to the Conference Proc. of the 7th Annual Astrophysics Conference in
Maryland, STAR FORMATION, NEAR AND FAR, eds. Stephen S. Holt and Lee G. Mund
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