1,026 research outputs found
Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
A model of the passive vector field advected by the uncorrelated in time
Gaussian velocity with power-like covariance is studied by means of the
renormalization group and the operator product expansion. The structure
functions of the admixture demonstrate essential power-like dependence on the
external scale in the inertial range (the case of an anomalous scaling). The
method of finding of independent tensor invariants in the cases of two and
three dimensions is proposed to eliminate linear dependencies between the
operators entering into the operator product expansions of the structure
functions. The constructed operator bases, which include the powers of the
dissipation operator and the enstrophy operator, provide the possibility to
calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge
Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection
The anomalous scaling of correlation functions in the turbulent statistics of
active scalars (like temperature in turbulent convection) is understood in
terms of an auxiliary passive scalar which is advected by the same turbulent
velocity field. While the odd-order correlation functions of the active and
passive fields differ, we propose that the even-order correlation functions are
the same to leading order (up to a trivial multiplicative factor). The leading
correlation functions are statistically preserved structures of the passive
scalar decaying problem, and therefore universality of the scaling exponents of
the even-order correlations of the active scalar is demonstrated.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
Observation of intermittency in wave turbulence
We report the observation of intermittency in gravity-capillary wave
turbulence on the surface of mercury. We measure the temporal fluctuations of
surface wave amplitude at a given location. We show that the shape of the
probability density function of the local slope increments of the surface waves
strongly changes across the time scales. The related structure functions and
the flatness are found to be power laws of the time scale on more than one
decade. The exponents of these power laws increase nonlinearly with the order
of the structure function. All these observations show the intermittent nature
of the increments of the local slope in wave turbulence. We discuss the
possible origin of this intermittency.Comment: new version to Phys. Rev. Let
Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach
By employing Hopf's functional method, we find the exact characteristic
functional for a simple nonlinear dynamical system introduced by Orszag.
Steady-state equal-time statistics thus obtained are compared to direct
numerical simulation. The solution is both non-trivial and strongly
non-Gaussian.Comment: 6 pages and 2 figure
Phenomenology of Wall Bounded Newtonian Turbulence
We construct a simple analytic model for wall-bounded turbulence, containing
only four adjustable parameters. Two of these parameters characterize the
viscous dissipation of the components of the Reynolds stress-tensor and other
two parameters characterize their nonlinear relaxation. The model offers an
analytic description of the profiles of the mean velocity and the correlation
functions of velocity fluctuations in the entire boundary region, from the
viscous sub-layer, through the buffer layer and further into the log-layer. As
a first approximation, we employ the traditional return-to-isotropy hypothesis,
which yields a very simple distribution of the turbulent kinetic energy between
the velocity components in the log-layer: the streamwise component contains a
half of the total energy whereas the wall-normal and the cross-stream
components contain a quarter each. In addition, the model predicts a very
simple relation between the von-K\'arm\'an slope and the turbulent
velocity in the log-law region (in wall units): . These
predictions are in excellent agreement with DNS data and with recent laboratory
experiments.Comment: 15 pages, 11 figs, included, PRE, submitte
Intermittency in the large N-limit of a spherical shell model for turbulence
A spherical shell model for turbulence, obtained by coupling replicas of
the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of
energy and of an helicity-like invariant is imposed in the inviscid limit. In
the limit this model is analytically soluble and is remarkably
similar to the random coupling model version of shell dynamics. We have studied
numerically the convergence of the scaling exponents toward the value predicted
by Kolmogorov theory (K41). We have found that the rate of convergence to the
K41 solution is linear in 1/N. The restoring of Kolmogorov law has been related
to the behaviour of the probability distribution functions of the instantaneous
scaling exponent.Comment: 10 pages, Latex, 3 Postscript figures, to be published on Europhys.
Let
Equilibrium solutions of the shallow water equations
A statistical method for calculating equilibrium solutions of the shallow
water equations, a model of essentially 2-d fluid flow with a free surface, is
described. The model contains a competing acoustic turbulent {\it direct}
energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown,
nonetheless that, just as in the corresponding theory of the inviscid Euler
equation, the infinite number of conserved quantities constrain the flow
sufficiently to produce nontrivial large-scale vortex structures which are
solutions to a set of explicitly derived coupled nonlinear partial differential
equations.Comment: 4 pages, no figures. Submitted to Physical Review Letter
Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers
We address the "Additive Equivalence" discovered by Virk and coworkers: drag
reduction affected by flexible and rigid rodlike polymers added to turbulent
wall-bounded flows is limited from above by a very similar Maximum Drag
Reduction (MDR) asymptote. Considering the equations of motion of rodlike
polymers in wall-bounded turbulent ensembles, we show that although the
microscopic mechanism of attaining the MDR is very different, the macroscopic
theory is isomorphic, rationalizing the interesting experimental observations.Comment: 8 pages, PRE, submitte
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
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