323 research outputs found
Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence
The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation time-scale and forcing strength. Numerical tests show that the same (universal) anomalous relative scaling exponents are obtained for the three model variants. It is also found that transverse velocity gradients are more intermittent than longitudinal ones, whereas dissipation and enstrophy scale with the same exponents. The results are consistent with the universality of intermittency and relative scaling exponents, and suggest that these are dictated by the self-stretching terms that are the same in each variant of the model
Matrix exponential-based closures for the turbulent subgrid-scale stress tensor
Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy
Gaussian multiplicative Chaos for symmetric isotropic matrices
Motivated by isotropic fully developed turbulence, we define a theory of
symmetric matrix valued isotropic Gaussian multiplicative chaos. Our
construction extends the scalar theory developed by J.P. Kahane in 1985
Lagrangian dynamics and statistical geometric structure of turbulence
The local statistical and geometric structure of three-dimensional turbulent
flow can be described by properties of the velocity gradient tensor. A
stochastic model is developed for the Lagrangian time evolution of this tensor,
in which the exact nonlinear self-stretching term accounts for the development
of well-known non-Gaussian statistics and geometric alignment trends. The
non-local pressure and viscous effects are accounted for by a closure that
models the material deformation history of fluid elements. The resulting
stochastic system reproduces many statistical and geometric trends observed in
numerical and experimental 3D turbulent flows, including anomalous relative
scaling.Comment: 5 pages, 5 figures, final version, publishe
Probing quantum and classical turbulence analogy through global bifurcations in a von K\'arm\'an liquid Helium experiment
We report measurements of the dissipation in the Superfluid Helium high
REynold number von Karman flow (SHREK) experiment for different forcing
conditions, through a regime of global hysteretic bifurcation. Our
macroscopical measurements indicate no noticeable difference between the
classical fluid and the superfluid regimes, thereby providing evidence of the
same dissipative anomaly and response to asymmetry in fluid and superfluid
regime. %In the latter case, A detailed study of the variations of the
hysteretic cycle with Reynolds number supports the idea that (i) the stability
of the bifurcated states of classical turbulence in this closed flow is partly
governed by the dissipative scales and (ii) the normal and the superfluid
component at these temperatures (1.6K) are locked down to the dissipative
length scale.Comment: 5 pages, 5 figure
On the origin of intermittency in wave turbulence
Using standard signal processing tools, we experimentally report that
intermittency of wave turbulence on the surface of a fluid occurs even when two
typical large-scale coherent structures (gravity wave breakings and bursts of
capillary waves on steep gravity waves) are not taken into account. We also
show that intermittency depends on the power injected into the waves. The
dependence of the power-law exponent of the gravity-wave spectrum on the
forcing amplitude cannot be also ascribed to these coherent structures.
Statistics of these both events are studied.Comment: To be published in EP
Fully developed turbulence and the multifractal conjecture
We review the Parisi-Frisch MultiFractal formalism for
Navier--Stokes turbulence with particular emphasis on the issue of
statistical fluctuations of the dissipative scale. We do it for both Eulerian
and Lagrangian Turbulence. We also show new results concerning the application
of the formalism to the case of Shell Models for turbulence. The latter case
will allow us to discuss the issue of Reynolds number dependence and the role
played by vorticity and vortex filaments in real turbulent flows.Comment: Special Issue dedicated to E. Brezin and G. Paris
Acceleration and vortex filaments in turbulence
We report recent results from a high resolution numerical study of fluid
particles transported by a fully developed turbulent flow. Single particle
trajectories were followed for a time range spanning more than three decades,
from less than a tenth of the Kolmogorov time-scale up to one large-eddy
turnover time. We present some results concerning acceleration statistics and
the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure
Links between dissipation, intermittency, and helicity in the GOY model revisited
High-resolution simulations within the GOY shell model are used to study
various scaling relations for turbulence. A power-law relation between the
second-order intermittency correction and the crossover from the inertial to
the dissipation range is confirmed. Evidence is found for the intermediate
viscous dissipation range proposed by Frisch and Vergassola. It is emphasized
that insufficient dissipation-range resolution systematically drives the energy
spectrum towards statistical-mechanical equipartition. In fully resolved
simulations the inertial-range scaling exponents depend on both model
parameters; in particular, there is no evidence that the conservation of a
helicity-like quantity leads to universal exponents.Comment: 24 pages, 13 figures; submitted to Physica
Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
Modeling the velocity gradient tensor A along Lagrangian trajectories in
turbulent flow requires closures for the pressure Hessian and viscous Laplacian
of A. Based on an Eulerian-Lagrangian change of variables and the so-called
Recent Fluid Deformation closure, such models were proposed recently. The
resulting stochastic model was shown to reproduce many geometric and anomalous
scaling properties of turbulence. In this work, direct comparisons between
model predictions and Direct Numerical Simulation (DNS) data are presented.
First, statistical properties of A are described using conditional averages of
strain skewness, enstrophy production, energy transfer and vorticity
alignments, conditioned upon invariants of A. These conditionally averaged
quantities are found to be described accurately by the stochastic model. More
detailed comparisons that focus directly on the terms being modeled in the
closures are also presented. Specifically, conditional statistics associated
with the pressure Hessian and the viscous Laplacian are measured from the model
and are compared with DNS. Good agreement is found in strain-dominated regions.
However, some features of the pressure Hessian linked to rotation dominated
regions are not reproduced accurately by the model. Geometric properties such
as vorticity alignment with respect to principal axes of the pressure Hessian
are mostly predicted well. In particular, the model predicts that an
eigenvector of the rate-of-strain will be also an eigenvector of the pressure
Hessian, in accord to basic properties of the Euler equations. The analysis
identifies under what conditions the Eulerian-Lagrangian change of variables
with the Recent Fluid Deformation closure works well, and in which flow regimes
it requires further improvements.Comment: 16 pages, 10 figures, minor revisions, final version published in
Phys. Fluid
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