725 research outputs found
ANOMALOUS SCALING OF THE PASSIVE SCALAR
We establish anomalous inertial range scaling of structure functions for a
model of advection of a passive scalar by a random velocity field. The velocity
statistics is taken gaussian with decorrelation in time and velocity
differences scaling as in space, with . The
scalar is driven by a gaussian forcing acting on spatial scale and
decorrelated in time. The structure functions for the scalar are well defined
as the diffusivity is taken to zero and acquire anomalous scaling behavior for
large pumping scales . The anomalous exponent is calculated explicitly for
the 4^{\m\rm th} structure function and for small and it differs
from previous predictions. For all but the second structure functions the
anomalous exponents are nonvanishing.Comment: 8 pages, late
Lagrangian acceleration statistics in turbulent flows
We show that the probability densities af accelerations of Lagrangian test
particles in turbulent flows as measured by Bodenschatz et al. [Nature 409,
1017 (2001)] are in excellent agreement with the predictions of a stochastic
model introduced in [C. Beck, PRL 87, 180601 (2001)] if the fluctuating
friction parameter is assumed to be log-normally distributed. In a generalized
statistical mechanics setting, this corresponds to a superstatistics of
log-normal type. We analytically evaluate all hyperflatnes factors for this
model and obtain a flatness prediction in good agreement with the experimental
data. There is also good agreement with DNS data of Gotoh et al. We relate the
model to a generalized Sawford model with fluctuating parameters, and discuss a
possible universality of the small-scale statistics.Comment: 10 pages, 2 figure
Fusion Rules in Turbulent Systems with Flux Equilibrium
Fusion rules in turbulence specify the analytic structure of many-point
correlation functions of the turbulent field when a group of coordinates
coalesce. We show that the existence of flux equilibrium in fully developed
turbulent systems combined with a direct cascade induces universal fusion
rules. In certain examples these fusion rules suffice to compute the
multiscaling exponents exactly, and in other examples they give rise to an
infinite number of scaling relations that constrain enormously the structure of
the allowed theory.Comment: Submitted to PRL on July 95, 4 pages, REVTe
Non-universality of the scaling exponents of a passive scalar convected by a random flow
We consider passive scalar convected by multi-scale random velocity field
with short yet finite temporal correlations. Taking Kraichnan's limit of a
white Gaussian velocity as a zero approximation we develop perturbation theory
with respect to a small correlation time and small non-Gaussianity of the
velocity. We derive the renormalization (due to temporal correlations and
non-Gaussianity) of the operator of turbulent diffusion. That allows us to
calculate the respective corrections to the anomalous scaling exponents of the
scalar field and show that they continuously depend on velocity correlation
time and the degree of non-Gaussianity. The scalar exponents are thus non
universal as was predicted by Shraiman and Siggia on a phenomenological ground
(CRAS {\bf 321}, 279, 1995).Comment: 4 pages, RevTex 3.0, Submitted to Phys.Rev.Let
Direct Numerical Simulation Tests of Eddy Viscosity in Two Dimensions
Two-parametric eddy viscosity (TPEV) and other spectral characteristics of
two-dimensional (2D) turbulence in the energy transfer sub-range are calculated
from direct numerical simulation (DNS) with 512 resolution. The DNS-based
TPEV is compared with those calculated from the test field model (TFM) and from
the renormalization group (RG) theory. Very good agreement between all three
results is observed.Comment: 9 pages (RevTeX) and 5 figures, published in Phys. Fluids 6, 2548
(1994
Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
For a delta-correlated velocity field, simultaneous correlation functions of
a passive scalar satisfy closed equations. We analyze the equation for the
four-point function. To describe a solution completely, one has to solve the
matching problems at the scale of the source and at the diffusion scale. We
solve both the matching problems and thus find the dependence of the four-point
correlation function on the diffusion and pumping scale for large space
dimensionality . It is shown that anomalous scaling appears in the first
order of perturbation theory. Anomalous dimensions are found analytically
both for the scalar field and for it's derivatives, in particular, for the
dissipation field.Comment: 19 pages, RevTex 3.0, Submitted to Phys.Rev. E, revised versio
Large eddy simulation of two-dimensional isotropic turbulence
Large eddy simulation (LES) of forced, homogeneous, isotropic,
two-dimensional (2D) turbulence in the energy transfer subrange is the subject
of this paper. A difficulty specific to this LES and its subgrid scale (SGS)
representation is in that the energy source resides in high wave number modes
excluded in simulations. Therefore, the SGS scheme in this case should assume
the function of the energy source. In addition, the controversial requirements
to ensure direct enstrophy transfer and inverse energy transfer make the
conventional scheme of positive and dissipative eddy viscosity inapplicable to
2D turbulence. It is shown that these requirements can be reconciled by
utilizing a two-parametric viscosity introduced by Kraichnan (1976) that
accounts for the energy and enstrophy exchange between the resolved and subgrid
scale modes in a way consistent with the dynamics of 2D turbulence; it is
negative on large scales, positive on small scales and complies with the basic
conservation laws for energy and enstrophy. Different implementations of the
two-parametric viscosity for LES of 2D turbulence were considered. It was found
that if kept constant, this viscosity results in unstable numerical scheme.
Therefore, another scheme was advanced in which the two-parametric viscosity
depends on the flow field. In addition, to extend simulations beyond the limits
imposed by the finiteness of computational domain, a large scale drag was
introduced. The resulting LES exhibited remarkable and fast convergence to the
solution obtained in the preceding direct numerical simulations (DNS) by
Chekhlov et al. (1994) while the flow parameters were in good agreement with
their DNS counterparts. Also, good agreement with the Kolmogorov theory was
found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary
djnlx.tex fil
Anomalous Scaling in the N-Point Functions of Passive Scalar
A recent analysis of the 4-point correlation function of the passive scalar
advected by a time-decorrelated random flow is extended to the N-point case. It
is shown that all stationary-state inertial-range correlations are dominated by
homogeneous zero modes of singular operators describing their evolution. We
compute analytically the zero modes governing the N-point structure functions
and the anomalous dimensions corresponding to them to the linear order in the
scaling exponent of the 2-point function of the advecting velocity field. The
implications of these calculations for the dissipation correlations are
discussed.Comment: 16 pages, latex fil
A Simple Passive Scalar Advection-Diffusion Model
This paper presents a simple, one-dimensional model of a randomly advected
passive scalar. The model exhibits anomalous inertial range scaling for the
structure functions constructed from scalar differences. The model provides a
simple computational test for recent ideas regarding closure and scaling for
randomly advected passive scalars. Results suggest that high order structure
function scaling depends on the largest velocity eddy size, and hence scaling
exponents may be geometry-dependent and non-universal.Comment: 30 pages, 11 figure
Universality and saturation of intermittency in passive scalar turbulence
The statistical properties of a scalar field advected by the non-intermittent
Navier-Stokes flow arising from a two-dimensional inverse energy cascade are
investigated. The universality properties of the scalar field are directly
probed by comparing the results obtained with two different types of injection
mechanisms. Scaling properties are shown to be universal, even though
anisotropies injected at large scales persist down to the smallest scales and
local isotropy is not fully restored. Scalar statistics is strongly
intermittent and scaling exponents saturate to a constant for sufficiently high
orders. This is observed also for the advection by a velocity field rapidly
changing in time, pointing to the genericity of the phenomenon. The persistence
of anisotropies and the saturation are both statistical signatures of the
ramp-and-cliff structures observed in the scalar field.Comment: 4 pages, 8 figure
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