178 research outputs found
Anisotropic eddy viscosity models
A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry
Relaxation times for Hamiltonian systems
Usually, the relaxation times of a gas are estimated in the frame of the
Boltzmann equation. In this paper, instead, we deal with the relaxation problem
in the frame of the dynamical theory of Hamiltonian systems, in which the
definition itself of a relaxation time is an open question. We introduce a
lower bound for the relaxation time, and give a general theorem for estimating
it. Then we give an application to a concrete model of an interacting gas, in
which the lower bound turns out to be of the order of magnitude of the
relaxation times observed in dilute gases.Comment: 26 page
Dissipation scales of kinetic helicities in turbulence
A systematic study of the influence of the viscous effect on both the spectra
and the nonlinear fluxes of conserved as well as non conserved quantities in
Navier-Stokes turbulence is proposed. This analysis is used to estimate the
helicity dissipation scale which is shown to coincide with the energy
dissipation scale. However, it is shown using the decomposition of helicity
into eigen modes of the curl operator, that viscous effects have to be taken
into account for wave vector smaller than the Kolomogorov wave number in the
evolution of these eigen components of the helicity.Comment: 6 pages, 2 figures, submited to Po
Dynamo Transition in Low-dimensional Models
Two low-dimensional magnetohydrodynamic models containing three velocity and
three magnetic modes are described. One of them (nonhelical model) has zero
kinetic and current helicity, while the other model (helical) has nonzero
kinetic and current helicity. The velocity modes are forced in both these
models. These low-dimensional models exhibit a dynamo transition at a critical
forcing amplitude that depends on the Prandtl number. In the nonhelical model,
dynamo exists only for magnetic Prandtl number beyond 1, while the helical
model exhibits dynamo for all magnetic Prandtl number. Although the model is
far from reproducing all the possible features of dynamo mechanisms, its
simplicity allows a very detailed study and the observed dynamo transition is
shown to bear similarities with recent numerical and experimental results.Comment: 7 page
Ensemble averaged dynamic modeling
The possibility of using the information from simultaneous equivalent Large Eddy Simulations (LAS) for improving the subgrid scale modeling is investigated. An ensemble average dynamic model is proposed as an alternative to the usual spatial average versions. It is shown to be suitable independently of the existence of any homogeneity directions, and its formulation is thus universal. The ensemble average dynamic model is shown to give very encouraging results for as few as 16 simultaneous LES's
Correcting cold wire measurements in isotropic turbulence with a DNS database
We estimate the effect of the finite spatial resolution of a cold wire for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence at low Taylor-microscale Reynolds number (≃ 42) and Schmidt number unity. Correction factors for the scalar variance, scalar mean dissipation rate, and mixed velocity-scalar derivative skewness are evaluated, for a sensor length of up to 15 times the Batchelor length scale. The largest attenuation effect is found on the dissipation rate, followed by the scalar variance. The mixed skewness,which is affected the least, is overestimated
Gyrokinetic Large Eddy Simulations
The Large Eddy Simulation (LES) approach is adapted to the study of plasma
microturbulence in a fully three-dimensional gyrokinetic system. Ion
temperature gradient driven turbulence is studied with the {\sc GENE} code for
both a standard resolution and a reduced resolution with a model for the
sub-grid scale turbulence. A simple dissipative model for representing the
effect of the sub-grid scales on the resolved scales is proposed and tested.
Once calibrated, the model appears to be able to reproduce most of the features
of the free energy spectra for various values of the ion temperature gradient
Boundary effects on the dynamics of chains of coupled oscillators
We study the dynamics of a chain of coupled particles subjected to a
restoring force (Klein-Gordon lattice) in the cases of either periodic or
Dirichlet boundary conditions. Precisely, we prove that, when the initial data
are of small amplitude and have long wavelength, the main part of the solution
is interpolated by a solution of the nonlinear Schr\"odinger equation, which in
turn has the property that its Fourier coefficients decay exponentially. The
first order correction to the solution has Fourier coefficients that decay
exponentially in the periodic case, but only as a power in the Dirichlet case.
In particular our result allows one to explain the numerical computations of
the paper \cite{BMP07}
Free energy cascade in gyrokinetic turbulence
In gyrokinetic theory, the quadratic nonlinearity is known to play an
important role in the dynamics by redistributing (in a conservative fashion)
the free energy between the various active scales. In the present study, the
free energy transfer is analyzed for the case of ion temperature gradient
driven turbulence. It is shown that it shares many properties with the energy
transfer in fluid turbulence. In particular, one finds a forward (from large to
small scales), extremely local, and self-similar cascade of free energy in the
plane perpendicular to the background magnetic field. These findings shed light
on some fundamental properties of plasma turbulence, and encourage the
development of large eddy simulation techniques for gyrokinetics.Comment: 4 pages, 2 Postscript figure
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