95 research outputs found
A Kolmogorov-Like Exact Relation for Compressible Polytropic Turbulence
Compressible hydrodynamic turbulence is studied under the assumption of a
polytropic closure. Following Kolmogorov, we derive an exact relation for some
two-point correlation functions in the asymptotic limit of a high Reynolds
number
Nonlinear diffusion equations for anisotropic MHD turbulence with cross-helicity
Nonlinear diffusion equations of spectral transfer are systematically derived
for anisotropic magnetohydrodynamics in the regime of wave turbulence. The
background of the analysis is the asymptotic Alfv\'en wave turbulence equations
from which a differential limit is taken. The result is a universal
diffusion-type equation in -space which describes in a simple way and
without free parameter the energy transport perpendicular to the external
magnetic field for transverse and parallel fluctuations. These
equations are compatible with both the thermodynamic equilibrium and the finite
flux spectra derived by Galtier et al. (2000); it improves therefore the model
built heuristically by Litwick \& Goldreich (2003) for which only the second
solution was recovered. This new system offers a powerful description of a wide
class of astrophysical plasmas with non-zero cross-helicity.Comment: 20 pages, 3 figure
Third-order Els\"asser moments in axisymmetric MHD turbulence
Incompressible MHD turbulence is investigated under the presence of a uniform
magnetic field \bb0. Such a situation is described in the correlation space
by a divergence relation which expresses the statistical conservation of the
Els\"asser energy flux through the inertial range. The ansatz is made that the
development of anisotropy, observed when is strong enough, implies a
foliation of space correlation. A direct consequence is the possibility to
derive a vectorial law for third-order Els\"asser moments which is parametrized
by the intensity of anisotropy. We use the so-called critical balance
assumption to fix this parameter and find a unique expression.Comment: 10 pages, 2 figures, will appea
Locality of triad interaction and Kolmogorov constant in inertial wave turbulence
Using the theory of wave turbulence for rapidly rotating incompressible
fluids derived by Galtier (2003), we find the locality conditions that the
solutions of the kinetic equation must satisfy. We show that the exact
anisotropic Kolmogorov-Zakharov (KZ) spectrum satisfies these conditions, which
justifies the existence of this constant (positive) energy flux solution.
Although a direct cascade is predicted in the transverse () and parallel
() directions to the rotation axis, we show numerically that in the
latter case some triadic interactions can have a negative contribution to the
energy flux, while in the former case all interactions contribute to a positive
flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant
at . These results provide theoretical support for recent
numerical and experimental studies.Comment: 10 pages, 4 figure
On the two-dimensional state in driven magnetohydrodynamic turbulence
The dynamics of the two-dimensional (2D) state in driven tridimensional (3D)
incompressible magnetohydrodynamic turbulence is investigated through
high-resolution direct numerical simulations and in the presence of an external
magnetic field at various intensities. For such a flow the 2D state (or slow
mode) and the 3D modes correspond respectively to spectral fluctuations in the
plan and in the area . It is shown that if
initially the 2D state is set to zero it becomes non negligible in few turnover
times particularly when the external magnetic field is strong. The maintenance
of a large scale driving leads to a break for the energy spectra of 3D modes;
when the driving is stopped the previous break is removed and a decay phase
emerges with alfv\'enic fluctuations. For a strong external magnetic field the
energy at large perpendicular scales lies mainly in the 2D state and in all
situations a pinning effect is observed at small scales.Comment: 11 pages, 11 figure
Shortest Paths and Probabilities on Time-Dependent Graphs - Applications to Transport Networks
International audienceIn this paper, we focus on time-dependent graphs which seem to be a good way to model transport Networks. In the first part, we remind some notations and techniques related to time-dependent graphs. In the second one, we introduce new algorithms to take into account the notion of probability related to paths in order to guarantee travelling times with a certain accuracy. We also discuss different probabilistic models and show the links between them
On the von Karman-Howarth equations for Hall MHD flows
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall
magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic
turbulence. From these equations, we derive exact scaling laws for the
third-order correlation tensors. We show how these relations are compatible
with previous heuristic and numerical results. These multi-scale laws provide a
relevant tool to investigate the non-linear nature of the high frequency
magnetic field fluctuations in the solar wind or, more generally, in any plasma
where the Hall effect is important.Comment: 11 page
Anomalous spectral laws in differential models of turbulence
International audienceDifferential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the -space were analysed.Both types of models predict formation an anomalous transient power-law spectra.The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation.Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system
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