23,419 research outputs found
Inverse cascades in turbulence and the case of rotating flows
We first summarize briefly several properties concerning the dynamics of
two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of
energy to the largest accessible scale of the system. In order to study a
similar phenomenon in three-dimensional (3D) turbulence undergoing strong
solid-body rotation, we test a previously developed Large Eddy Simulation (LES)
model against a high-resolution direct numerical simulation of rotating
turbulence on a grid of points. We then describe new numerical results
on the inverse energy cascade in rotating flows using this LES model and
contrast the case of 2D versus 3D forcing, as well as non-helical forcing
(i.e., with weak overall alignment between velocity and vorticity) versus the
fully helical Beltrami case, both for deterministic and random forcing. The
different scaling of the inverse energy cascade can be attributed to the
dimensionality of the forcing, with, in general, either a or a
energy spectrum of slow modes at large scales, perpendicular
referring to the direction of rotation. We finally invoke the role of shear in
the case of a strongly anisotropic deterministic forcing, using the so-called
ABC flow.Comment: 10 pages, 3 figure
Helicity dynamics in stratified turbulence in the absence of forcing
A numerical study of decaying stably-stratified flows is performed.
Relatively high stratification and moderate Reynolds numbers are considered,
and a particular emphasis is placed on the role of helicity (velocity-vorticity
correlations). The problem is tackled by integrating the Boussinesq equations
in a periodic cubical domain using different initial conditions: a non-helical
Taylor-Green (TG) flow, a fully helical Beltrami (ABC) flow, and random flows
with a tunable helicity. We show that for stratified ABC flows helicity
undergoes a substantially slower decay than for unstratified ABC flows. This
fact is likely associated to the combined effect of stratification and large
scale coherent structures. Indeed, when the latter are missing, as in random
flows, helicity is rapidly destroyed by the onset of gravitational waves. A
type of large-scale dissipative "cyclostrophic" balance can be invoked to
explain this behavior. When helicity survives in the system it strongly affects
the temporal energy decay and the energy distribution among Fourier modes. We
discover in fact that the decay rate of energy for stratified helical flows is
much slower than for stratified non-helical flows and can be considered with a
phenomenological model in a way similar to what is done for unstratified
rotating flows. We also show that helicity, when strong, has a measurable
effect on the Fourier spectra, in particular at scales larger than the buoyancy
scale for which it displays a rather flat scaling associated with vertical
shear
Large-scale anisotropy in stably stratified rotating flows
We present results from direct numerical simulations of the Boussinesq
equations in the presence of rotation and/or stratification, both in the
vertical direction. The runs are forced isotropically and randomly at small
scales and have spatial resolutions of up to grid points and Reynolds
numbers of . We first show that solutions with negative energy
flux and inverse cascades develop in rotating turbulence, whether or not
stratification is present. However, the purely stratified case is characterized
instead by an early-time, highly anisotropic transfer to large scales with
almost zero net isotropic energy flux. This is consistent with previous studies
that observed the development of vertically sheared horizontal winds, although
only at substantially later times. However, and unlike previous works, when
sufficient scale separation is allowed between the forcing scale and the domain
size, the total energy displays a perpendicular (horizontal) spectrum with
power law behavior compatible with , including in the
absence of rotation. In this latter purely stratified case, such a spectrum is
the result of a direct cascade of the energy contained in the large-scale
horizontal wind, as is evidenced by a strong positive flux of energy in the
parallel direction at all scales including the largest resolved scales
Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations
We report results on rotating stratified turbulence in the absence of
forcing, with large-scale isotropic initial conditions, using direct numerical
simulations computed on grids of up to 4096^3 points. The Reynolds and Froude
numbers are respectively equal to Re=5.4 x 10^4 and Fr=0.0242. The ratio of the
Brunt-V\"ais\"al\"a to the inertial wave frequency, N/f, is taken to be equal
to 4.95, a choice appropriate to model the dynamics of the southern abyssal
ocean at mid latitudes. This gives a global buoyancy Reynolds number
R_B=ReFr^2=32, a value sufficient for some isotropy to be recovered in the
small scales beyond the Ozmidov scale, but still moderate enough that the
intermediate scales where waves are prevalent are well resolved. We concentrate
on the large-scale dynamics, for which we find a spectrum compatible with the
Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical
vertical length scale is of order unity, with strong gradients in the vertical.
Two characteristic scales emerge from this computation, and are identified from
sharp variations in the spectral distribution of either total energy or
helicity. A spectral break is also observed at a scale at which the partition
of energy between the kinetic and potential modes changes abruptly, and beyond
which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous
in the flow in the velocity and temperature fields, with local overturning
events indicated by small Richardson numbers, and a small large-scale
enhancement of energy directly attributable to the effect of rotation is also
observed.Comment: 19 pages, 9 figures (including compound figures
Isotropisation at small scales of rotating helically-driven turbulence
We present numerical evidence of how three-dimensionalization occurs at small
scale in rotating turbulence with Beltrami (ABC) forcing, creating helical
flow. The Zeman scale at which the inertial and eddy turn-over
times are equal is more than one order of magnitude larger than the dissipation
scale, with the relevant domains (large-scale inverse cascade of energy, dual
regime in the direct cascade of energy and helicity , and dissipation)
each moderately resolved. These results stem from the analysis of a large
direct numerical simulation on a grid of points, with Rossby and
Reynolds numbers respectively equal to 0.07 and . At scales
smaller than the forcing, a helical wave-modulated inertial law for the energy
and helicity spectra is followed beyond by Kolmogorov spectra
for and . Looking at the two-dimensional slow manifold, we also show
that the helicity spectrum breaks down at , a clear sign of
recovery of three-dimensionality in the small scales.Comment: 13 pages, 6 figure
A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets
We propose two sets of initial conditions for magnetohydrodynamics (MHD) in
which both the velocity and the magnetic fields have spatial symmetries that
are preserved by the dynamical equations as the system evolves. When
implemented numerically they allow for substantial savings in CPU time and
memory storage requirements for a given resolved scale separation. Basic
properties of these Taylor-Green flows generalized to MHD are given, and the
ideal non-dissipative case is studied up to the equivalent of 2048^3 grid
points for one of these flows. The temporal evolution of the logarithmic
decrements, delta, of the energy spectrum remains exponential at the highest
spatial resolution considered, for which an acceleration is observed briefly
before the grid resolution is reached. Up to the end of the exponential decay
of delta, the behavior is consistent with a regular flow with no appearance of
a singularity. The subsequent short acceleration in the formation of small
magnetic scales can be associated with a near collision of two current sheets
driven together by magnetic pressure. It leads to strong gradients with a fast
rotation of the direction of the magnetic field, a feature also observed in the
solar wind.Comment: 8 pages, 4 figure
Conformal invariance in three-dimensional rotating turbulence
We examine three--dimensional turbulent flows in the presence of solid-body
rotation and helical forcing in the framework of stochastic Schramm-L\"owner
evolution curves (SLE). The data stems from a run on a grid of points,
with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the
parallel component of the vorticity in the direction parallel to that of
rotation, and examine the resulting field for
scaling properties of its zero-value contours. We find for the first time for
three-dimensional fluid turbulence evidence of nodal curves being conformal
invariant, belonging to a SLE class with associated Brownian diffusivity
. SLE behavior is related to the self-similarity of the
direct cascade of energy to small scales in this flow, and to the partial
bi-dimensionalization of the flow because of rotation. We recover the value of
with a heuristic argument and show that this value is consistent with
several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR
A comparison of spectral element and finite difference methods using statically refined nonconforming grids for the MHD island coalescence instability problem
A recently developed spectral-element adaptive refinement incompressible
magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp.
Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island
coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD
process that can produce sharp current layers and subsequent reconnection and
heating in a high-Lundquist number plasma such as the solar corona [Ng and
Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin
current layers, it is highly desirable to use adaptively or statically refined
grids to resolve them, and to maintain accuracy at the same time. The output of
the spectral-element static adaptive refinement simulations are compared with
simulations using a finite difference method on the same refinement grids, and
both methods are compared to pseudo-spectral simulations with uniform grids as
baselines. It is shown that with the statically refined grids roughly scaling
linearly with effective resolution, spectral element runs can maintain accuracy
significantly higher than that of the finite difference runs, in some cases
achieving close to full spectral accuracy.Comment: 19 pages, 17 figures, submitted to Astrophys. J. Supp
Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR at weak coupling
We consider a semi-classical treatment, in the regime of weak gauge coupling,
of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with
SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we
consider the theories obtained as power series expansions around a certain
class of normalizable vacua of the classical theory, corresponding to isolated
points in the moduli space of flat connections, and the perturbative
corrections to the free energy eigenstates and eigenvalues in the weakly
interacting theory. The perturbation theory construction of the interacting
Hilbert space is complicated by the divergence of the norm of the interacting
states. Consequently, the free and interacting Hilbert furnish unitarily
inequivalent representation of the algebra of creation and annihilation
operators of the quantum theory. We discuss a consistent redefinition of the
Hilbert space norm to obtain the interacting Hilbert space and the properties
of the interacting representation. In particular, we consider the lowest
non-vanishing corrections to the free energy spectrum and discuss the crucial
importance of supersymmetry for these corrections to be finite.Comment: 31 pages, 1 figure, v4 Minor changes, references correcte
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