1,233 research outputs found
Chaos and predictability of homogeneous-isotropic turbulence
We study the chaoticity and the predictability of a turbulent flow on the
basis of high-resolution direct numerical simulations at different Reynolds
numbers. We find that the Lyapunov exponent of turbulence, which measures the
exponential separation of two initially close solution of the Navier-Stokes
equations, grows with the Reynolds number of the flow, with an anomalous
scaling exponent, larger than the one obtained on dimensional grounds. For
large perturbations, the error is transferred to larger, slower scales where it
grows algebraically generating an "inverse cascade" of perturbations in the
inertial range. In this regime our simulations confirm the classical
predictions based on closure models of turbulence. We show how to link
chaoticity and predictability of a turbulent flow in terms of a finite size
extension of the Lyapunov exponent.Comment: 5 pages, 5 figure
Turbulent channel without boundaries: The periodic Kolmogorov flow
The Kolmogorov flow provides an ideal instance of a virtual channel flow: It
has no boundaries, but nevertheless it possesses well defined mean flow in each
half-wavelength. We exploit this remarkable feature for the purpose of
investigating the interplay between the mean flow and the turbulent drag of the
bulk flow. By means of a set of direct numerical simulations at increasing
Reynolds number we show the dependence of the bulk turbulent drag on the
amplitude of the mean flow. Further, we present a detailed analysis of the
scale-by-scale energy balance, which describes how kinetic energy is
redistributed among different regions of the flow while being transported
toward small dissipative scales. Our results allow us to obtain an accurate
prediction for the spatial energy transport at large scales.Comment: 7 pages, 8 figure
Predictability of the energy cascade in 2D turbulence
The predictability problem in the inverse energy cascade of two-dimensional
turbulence is addressed by means of direct numerical simulations. The growth
rate as a function of the error level is determined by means of a finite size
extension of the Lyapunov exponent. For error within the inertial range, the
linear growth of the error energy, predicted by dimensional argument, is
verified with great accuracy. Our numerical findings are in close agreement
with the result of TFM closure approximation.Comment: 3 pages, 3 figure
Multiple-scale analysis and renormalization for pre-asymptotic scalar transport
Pre-asymptotic transport of a scalar quantity passively advected by a
velocity field formed by a large-scale component superimposed to a small-scale
fluctuation is investigated both analytically and by means of numerical
simulations. Exploiting the multiple-scale expansion one arrives at a
Fokker--Planck equation which describes the pre-asymptotic scalar dynamics.
Such equation is associated to a Langevin equation involving a multiplicative
noise and an effective (compressible) drift. For the general case, no explicit
expression for both the effective drift and the effective diffusivity (actually
a tensorial field) can be obtained. We discuss an approximation under which an
explicit expression for the diffusivity (and thus for the drift) can be
obtained. Its expression permits to highlight the important fact that the
diffusivity explicitly depends on the large-scale advecting velocity. Finally,
the robustness of the aforementioned approximation is checked numerically by
means of direct numerical simulations.Comment: revtex4, 12 twocolumn pages, 3 eps figure
An update on the double cascade scenario in two-dimensional turbulence
Statistical features of homogeneous, isotropic, two-dimensional turbulence is
discussed on the basis of a set of direct numerical simulations up to the
unprecedented resolution . By forcing the system at intermediate
scales, narrow but clear inertial ranges develop both for the inverse and for
direct cascades where the two Kolmogorov laws for structure functions are, for
the first time, simultaneously observed. The inverse cascade spectrum is found
to be consistent with Kolmogorov-Kraichnan prediction and is robust with
respect the presence of an enstrophy flux. The direct cascade is found to be
more sensible to finite size effects: the exponent of the spectrum has a
correction with respect theoretical prediction which vanishes by increasing the
resolution
Inverse cascade in Charney-Hasegawa-Mima turbulence
The inverse energy cascade in Charney-Hasegawa-Mima turbulence is
investigated. Kolmogorov law for the third order velocity structure function is
shown to be independent on the Rossby number, at variance with the energy
spectrum, as shown by high resolution direct numerical simulations. In the
asymptotic limit of strong rotation, coherent vortices are observed to form at
a dynamical scale which slowly grows with time. These vortices form an almost
quenched pattern and induce strong deviation form Gaussianity in the velocity
field.Comment: 4 pages, 5 figure
Large-scale effects on meso-scale modeling for scalar transport
The transport of scalar quantities passively advected by velocity fields with
a small-scale component can be modeled at meso-scale level by means of an
effective drift and an effective diffusivity, which can be determined by means
of multiple-scale techniques. We show that the presence of a weak large-scale
flow induces interesting effects on the meso-scale scalar transport. In
particular, it gives rise to non-isotropic and non-homogeneous corrections to
the meso-scale drift and diffusivity. We discuss an approximation that allows
us to retain the second-order effects caused by the large-scale flow. This
provides a rather accurate meso-scale modeling for both asymptotic and
pre-asymptotic scalar transport properties. Numerical simulations in model
flows are used to illustrate the importance of such large-scale effects.Comment: 19 pages, 8 figure
Large-scale confinement and small-scale clustering of floating particles in stratified turbulence
We study the motion of small inertial particles in stratified turbulence. We
derive a simplified model, valid within the Boussinesq approximation, for the
dynamics of small particles in presence of a mean linear density profile. By
means of extensive direct numerical simulations, we investigate the statistical
distribution of particles as a function of the two dimensionless parameters of
the problem. We find that vertical confinement of particles is mainly ruled by
the degree of stratification, with a weak dependency on the particle
properties. Conversely, small scale fractal clustering, typical of inertial
particles in turbulence, depends on the particle relaxation time and is almost
independent on the flow stratification. The implications of our findings for
the formation of thin phytoplankton layers are discussed.Comment: 5 pages, 6 figure
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