59 research outputs found
Statistics of mixing in three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood
number and at Prandtl number one is investigated by means of high resolution
direct numerical simulations of the Boussinesq equations. RT turbulence is a
paradigmatic time-dependent turbulent system in which the integral scale grows
in time following the evolution of the mixing region. In order to fully
characterize the statistical properties of the flow, both temporal and spatial
behavior of relevant statistical indicators have been analyzed.
Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds
numbers) and scale dependent observables built in terms of velocity and
temperature fluctuations are considered. We extend the mean-field analysis for
velocity and temperature fluctuations to take into account intermittency, both
in time and space domains. We show that the resulting scaling exponents are
compatible with those of classical Navier--Stokes turbulence advecting a
passive scalar at comparable Reynolds number. Our results support the scenario
of universality of turbulence with respect to both the injection mechanism and
the geometry of the flow
Fronts in passive scalar turbulence
The evolution of scalar fields transported by turbulent flow is characterized
by the presence of fronts, which rule the small-scale statistics of scalar
fluctuations. With the aid of numerical simulations, it is shown that: isotropy
is not recovered, in the classical sense, at small scales; scaling exponents
are universal with respect to the scalar injection mechanisms; high-order
exponents saturate to a constant value; non-mature fronts dominate the
statistics of intense fluctuations. Results on the statistics inside the
plateaux, where fluctuations are weak, are also presented. Finally, we analyze
the statistics of scalar dissipation and scalar fluxes.Comment: 18 pages, 27 figure
Coarse-grained description of a passive scalar
The issue of the parameterization of small-scale dynamics is addressed in the
context of passive-scalar turbulence. The basic idea of our strategy is to
identify dynamical equations for the coarse-grained scalar dynamics starting
from closed equations for two-point statistical indicators. With the aim of
performing a fully-analytical study, the Kraichnan advection model is
considered. The white-in-time character of the latter model indeed leads to
closed equations for the equal-time scalar correlation functions. The classical
closure problem however still arises if a standard filtering procedure is
applied to those equations in the spirit of the large-eddy-simulation strategy.
We show both how to perform exact closures and how to identify the
corresponding coarse-grained scalar evolution.Comment: 22 pages; submitted to Journal of Turbulenc
Large Deviation Approach to the Randomly Forced Navier-Stokes Equation
The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. By virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. Moreover, an explicit
expression of the prefactor of the scaling law is obtained.Comment: 24 page
Pressure and intermittency in passive vector turbulence
We investigate the scaling properties a model of passive vector turbulence
with pressure and in the presence of a large-scale anisotropy. The leading
scaling exponents of the structure functions are proven to be anomalous. The
anisotropic exponents are organized in hierarchical families growing without
bound with the degree of anisotropy. Nonlocality produces poles in the
inertial-range dynamics corresponding to the dimensional scaling solution. The
increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional
ratios signals the persistence of anisotropy effects also in the inertial
range.Comment: 4 pages, 1 figur
Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar quantity advected by a non-Gaussian
velocity field with finite correlation time. The velocity is governed by the
Navier--Stokes equation, subject to an external random stirring force with the
correlation function . It is shown that
the scalar field is intermittent already for small , its structure
functions display anomalous scaling behavior, and the corresponding exponents
can be systematically calculated as series in . The practical
calculation is accomplished to order (two-loop approximation),
including anisotropic sectors. Like for the well-known Kraichnan's rapid-change
model, the anomalous scaling results from the existence in the model of
composite fields (operators) with negative scaling dimensions, identified with
the anomalous exponents. Thus the mechanism of the origin of anomalous scaling
appears similar for the Gaussian model with zero correlation time and
non-Gaussian model with finite correlation time. It should be emphasized that,
in contrast to Gaussian velocity ensembles with finite correlation time, the
model and the perturbation theory discussed here are manifestly Galilean
covariant. The relevance of these results for the real passive advection,
comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur
Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
The first example of a turbulent system where the failure of the hypothesis
of small-scale isotropy restoration is detectable both in the `flattening' of
the inertial-range scaling exponent hierarchy, and in the behavior of odd-order
dimensionless ratios, e.g., skewness and hyperskewness, is presented.
Specifically, within the kinematic approximation in magnetohydrodynamical
turbulence, we show that for compressible flows, the isotropic contribution to
the scaling of magnetic correlation functions and the first anisotropic ones
may become practically indistinguishable. Moreover, skewness factor now
diverges as the P\'eclet number goes to infinity, a further indication of
small-scale anisotropy.Comment: 4 pages Latex, 1 figur
Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.Comment: 15 pages, 18 figure
Low altitude energetic electron lifetimes after enhanced magnetic activity as deduced from SAC-C and DEMETER data
Influence of helicity on scaling regimes in the extended Kraichnan model
We have investigated the advection of a passive scalar quantity by
incompressible helical turbulent flow in the frame of extended Kraichnan model.
Turbulent fluctuations of velocity field are assumed to have the Gaussian
statistics with zero mean and defined noise with finite time-correlation.
Actual calculations have been done up to two-loop approximation in the frame of
field-theoretic renormalization group approach. It turned out that space parity
violation (helicity) of turbulent environment does not affect anomalous scaling
which is peculiar attribute of corresponding model without helicity. However,
stability of asymptotic regimes, where anomalous scaling takes place, strongly
depends on the amount of helicity. Moreover, helicity gives rise to the
turbulent diffusivity, which has been calculated in one-loop approximation.Comment: 16 pages, talk given by M. Hnatich at "Renormalization Group 2005",
Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math.
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