72 research outputs found
Skin friction in zero-pressure-gradient boundary layers
A global approach leading to a self-consistent solution to the
Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is
presented. It is shown that as , the dynamically
defined boundary layer thickness and the
skin friction . Here and are the wall shear stress and
free stream velocity, respectively. The theory is formulated as an expansion in
powers of a small dimensionless parameter
in the limit
Reactive Turbulent Flow in Low-Dimensional, Disordered Media
We analyze the reactions and
occurring in a model of turbulent flow in two dimensions. We find the reactant
concentrations at long times, using a field-theoretic renormalization group
analysis. We find a variety of interesting behavior, including, in the presence
of potential disorder, decay rates faster than that for well-mixed reactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.
Large-Eddy Simulations of Fluid and Magnetohydrodynamic Turbulence Using Renormalized Parameters
In this paper a procedure for large-eddy simulation (LES) has been devised
for fluid and magnetohydrodynamic turbulence in Fourier space using the
renormalized parameters. The parameters calculated using field theory have been
taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We
have carried out LES on grid. These results match quite well with direct
numerical simulations of . We show that proper choice of parameter is
necessary in LES.Comment: 12 pages, 4 figures: Proper figures inserte
Non-Gaussian Distributions in Extended Dynamical Systems
We propose a novel mechanism for the origin of non-Gaussian tails in the
probability distribution functions (PDFs) of local variables in nonlinear,
diffusive, dynamical systems including passive scalars advected by chaotic
velocity fields. Intermittent fluctuations on appropriate time scales in the
amplitude of the (chaotic) noise can lead to exponential tails. We provide
numerical evidence for such behavior in deterministic, discrete-time passive
scalar models. Different possibilities for PDFs are also outlined.Comment: 12 pages and 6 figs obtainable from the authors, LaTex file,
OSU-preprint-
Porous Superhydrophobic Membranes: Hydrodynamic Anomaly in Oscillating Flows
We have fabricated and characterized a novel superhydrophobic system, a
mesh-like porous superhydrophobic membrane with solid area fraction ,
which can maintain intimate contact with outside air and water reservoirs
simultaneously. Oscillatory hydrodynamic measurements on porous
superhydrophobic membranes as a function of reveal surprising effects.
The hydrodynamic mass oscillating in-phase with the membranes stays constant
for , but drops precipitously for . The viscous
friction shows a similar drop after a slow initial decrease proportional to
. We attribute these effects to the percolation of a stable Knudsen
layer of air at the interface.Comment: 5 pages, 3 figure
Passive scalar turbulence in high dimensions
Exploiting a Lagrangian strategy we present a numerical study for both
perturbative and nonperturbative regions of the Kraichnan advection model. The
major result is the numerical assessment of the first-order -expansion by
M. Chertkov, G. Falkovich, I. Kolokolov and V. Lebedev ({\it Phys. Rev. E},
{\bf 52}, 4924 (1995)) for the fourth-order scalar structure function in the
limit of high dimensions 's. %Two values of the velocity scaling exponent
have been considered: % and . In the first case, the
perturbative regime %takes place at , while in the second at , %in agreement with the fact that the relevant small parameter %of the
theory is . In addition to the perturbative results, the
behavior of the anomaly for the sixth-order structure functions {\it vs} the
velocity scaling exponent, , is investigated and the resulting behavior
discussed.Comment: 4 pages, Latex, 4 figure
Active and passive fields face to face
The statistical properties of active and passive scalar fields transported by
the same turbulent flow are investigated. Four examples of active scalar have
been considered: temperature in thermal convection, magnetic potential in
two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman
turbulence and potential temperature in surface flows. In the cases of
temperature and vorticity, it is found that the active scalar behavior is akin
to that of its co-evolving passive counterpart. The two other cases indicate
that this similarity is in fact not generic and differences between passive and
active fields can be striking: in two-dimensional magnetohydrodynamics the
magnetic potential performs an inverse cascade while the passive scalar
cascades toward the small-scales; in surface flows, albeit both perform a
direct cascade, the potential temperature and the passive scalar have different
scaling laws already at the level of low-order statistical objects. These
dramatic differences are rooted in the correlations between the active scalar
input and the particle trajectories. The role of such correlations in the issue
of universality in active scalar transport and the behavior of dissipative
anomalies is addressed.Comment: 36 pages, 20 eps figures, for the published version see
http://www.iop.org/EJ/abstract/1367-2630/6/1/07
Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
Statistical model of strongly anisotropic fully developed turbulence of the
weakly compressible fluid is considered by means of the field theoretic
renormalization group. The corrections due to compressibility to the infrared
form of the kinetic energy spectrum have been calculated in the leading order
in Mach number expansion. Furthermore, in this approximation the validity of
the Kolmogorov hypothesis on the independence of dissipation length of velocity
correlation functions in the inertial range has been proved.Comment: REVTEX file with EPS figure
Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
Field theoretical renormalization group methods are applied to a simple model
of a passive scalar quantity advected by the Gaussian non-solenoidal
(``compressible'') velocity field with the covariance . Convective range anomalous scaling for the structure
functions and various pair correlators is established, and the corresponding
anomalous exponents are calculated to the order of the
expansion. These exponents are non-universal, as a result of the degeneracy of
the RG fixed point. In contrast to the case of a purely solenoidal velocity
field (Obukhov--Kraichnan model), the correlation functions in the case at hand
exhibit nontrivial dependence on both the IR and UV characteristic scales, and
the anomalous scaling appears already at the level of the pair correlator. The
powers of the scalar field without derivatives, whose critical dimensions
determine the anomalous exponents, exhibit multifractal behaviour. The exact
solution for the pair correlator is obtained; it is in agreement with the
result obtained within the expansion. The anomalous exponents for
passively advected magnetic fields are also presented in the first order of the
expansion.Comment: 31 pages, REVTEX file. More detailed discussion of the
one-dimensional case and comparison to the previous paper [20] are given;
references updated. Results and formulas unchange
Particles and fields in fluid turbulence
The understanding of fluid turbulence has considerably progressed in recent
years. The application of the methods of statistical mechanics to the
description of the motion of fluid particles, i.e. to the Lagrangian dynamics,
has led to a new quantitative theory of intermittency in turbulent transport.
The first analytical description of anomalous scaling laws in turbulence has
been obtained. The underlying physical mechanism reveals the role of
statistical integrals of motion in non-equilibrium systems. For turbulent
transport, the statistical conservation laws are hidden in the evolution of
groups of fluid particles and arise from the competition between the expansion
of a group and the change of its geometry. By breaking the scale-invariance
symmetry, the statistically conserved quantities lead to the observed anomalous
scaling of transported fields. Lagrangian methods also shed new light on some
practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy
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