101 research outputs found
Energy Spectra of Superfluid Turbulence in He
In superfluid He turbulence is carried predominantly by the superfluid
component. To explore the statistical properties of this quantum turbulence and
its differences from the classical counterpart we adopt the time-honored
approach of shell models. Using this approach we provide numerical simulations
of a Sabra-shell model that allows us to uncover the nature of the energy
spectrum in the relevant hydrodynamic regimes. These results are in qualitative
agreement with analytical expressions for the superfluid turbulent energy
spectra that were found using a differential approximation for the energy flux
Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence
We consider shell models that display an inverse energy cascade similar to
2-dimensional turbulence (together with a direct cascade of an enstrophy-like
invariant). Previous attempts to construct such models ended negatively,
stating that shell models give rise to a "quasi-equilibrium" situation with
equipartition of the energy among the shells. We show analytically that the
quasi-equilibrium state predicts its own disappearance upon changing the model
parameters in favor of the establishment of an inverse cascade regime with K41
scaling. The latter regime is found where predicted, offering a useful model to
study inverse cascades.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
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
An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
Properties of an infinite system of nonlinearly coupled ordinary differential
equations are discussed. This system models some properties present in the
equations of motion for an inviscid fluid such as the skew symmetry and the
3-dimensional scaling of the quadratic nonlinearity. It is proved that the
system with forcing has a unique equilibrium and that every solution blows up
in finite time in -norm. Onsager's conjecture is confirmed for the
model system
Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results
In a recent paper it was proposed that for some nonlinear shell models of
turbulence one can construct a linear advection model for an auxiliary field
such that the scaling exponents of all the structure functions of the linear
and nonlinear fields coincide.
The argument depended on an assumption of continuity of the solutions as a
function of a parameter. The aim of this paper is to provide a rigorous proof
for the validity of the assumption. In addition we clarify here when the swap
of a nonlinear model by a linear one will not work.Comment: 7 pages, 4 figures, submitted to Nonlinearit
(1+1)-dimensional turbulence
A class of dynamical models of turbulence living on a one-dimensional
dyadic-tree structure is introduced and studied. The models are obtained as a
natural generalization of the popular GOY shell model of turbulence. These
models are found to be chaotic and intermittent. They represent the first
example of (1+1)-dimensional dynamical systems possessing non trivial
multifractal properties. The dyadic structure allows to study spatial and
temporal fluctuations. Energy dissipation statistics and its scaling properties
are studied. Refined Kolmogorov Hypothesis is found to hold.Comment: 18 pages, 9 figures, submitted to Phys.of Fluid
On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence
We propose a new approach to the old-standing problem of the anomaly of the
scaling exponents of nonlinear models of turbulence. We achieve this by
constructing, for any given nonlinear model, a linear model of passive
advection of an auxiliary field whose anomalous scaling exponents are the same
as the scaling exponents of the nonlinear problem. The statistics of the
auxiliary linear model are dominated by `Statistically Preserved Structures'
which are associated with exact conservation laws. The latter can be used for
example to determine the value of the anomalous scaling exponent of the second
order structure function. The approach is equally applicable to shell models
and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq
Scaling and Dissipation in the GOY Shell Model
This is a paper about multi-fractal scaling and dissipation in a shell model
of turbulence, called the GOY model. This set of equations describes a one
dimensional cascade of energy towards higher wave vectors. When the model is
chaotic, the high-wave-vector velocity is a product of roughly independent
multipliers, one for each logarithmic momentum shell. The appropriate tool for
studying the multifractal properties of this model is shown to be the energy
current on each shell rather than the velocity on each shell. Using this
quantity, one can obtain better measurements of the deviations from Kolmogorov
scaling (in the GOY dynamics) than were available up to now. These deviations
are seen to depend upon the details of inertial-range structure of the model
and hence are {\em not} universal. However, once the conserved quantities of
the model are fixed to have the same scaling structure as energy and helicity,
these deviations seem to depend only weakly upon the scale parameter of the
model. We analyze the connection between multifractality in the velocity
distribution and multifractality in the dissipation. Our arguments suggest that
the connection is universal for models of this character, but the model has a
different behavior from that of real turbulence. We also predict the scaling
behavior of time correlations of shell-velocities, of the dissipation,Comment: Revised Versio
Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars
Using a three-dimensional nonlinear hydrodynamic code, we examine the
dynamical stability of more than twenty self-gravitating, compressible,
ellipsoidal fluid configurations that initially have the same velocity
structure as Riemann S-type ellipsoids. Our focus is on ``adjoint''
configurations, in which internal fluid motions dominate over the collective
spin of the ellipsoidal figure; Dedekind-like configurations are among this
group. We find that, although some models are stable and some are moderately
unstable, the majority are violently unstable toward the development of ,
, and higher-order azimuthal distortions that destroy the coherent,
bar-like structure of the initial ellipsoidal configuration on a dynamical time
scale.
The parameter regime over which our models are found to be unstable generally
corresponds with the regime over which incompressible Riemann S-type ellipsoids
have been found to be susceptible to an elliptical strain instability
\citep{LL96}. We therefore suspect that an elliptical instability is
responsible for the destruction of our compressible analogs of Riemann
ellipsoids. The existence of the elliptical instability raises concerns
regarding the final fate of neutron stars that encounter the secular bar-mode
instability and regarding the spectrum of gravitational waves that will be
radiated from such systems.Comment: 28 pages, submitted to ApJ, quicktime movies are available at:
http://www.phys.lsu.edu/~ou/movie/s_type/index.htm
A stochastic model of cascades in 2D turbulence
The dual cascade of energy and enstrophy in 2D turbulence cannot easily be
understood in terms of an analog to the Richardson-Kolmogorov scenario
describing the energy cascade in 3D turbulence. The coherent up- and downscale
fluxes points to non-locality of interactions in spectral space, and thus the
specific spatial structure of the flow could be important. Shell models, which
lack spacial structure and have only local interactions in spectral space,
indeed fail in reproducing the correct scaling for the inverse cascade of
energy. In order to exclude the possibility that non-locality of interactions
in spectral space is crucial for the dual cascade, we introduce a stochastic
spectral model of the cascades which is local in spectral space and which shows
the correct scaling for both the direct enstrophy - and the inverse energy
cascade.Comment: 4 pages, 3 figure
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