71 research outputs found
Stochastic Perturbations in Vortex Tube Dynamics
A dual lattice vortex formulation of homogeneous turbulence is developed,
within the Martin-Siggia-Rose field theoretical approach. It consists of a
generalization of the usual dipole version of the Navier-Stokes equations,
known to hold in the limit of vanishing external forcing. We investigate, as a
straightforward application of our formalism, the dynamics of closed vortex
tubes, randomly stirred at large length scales by gaussian stochastic forces.
We find that besides the usual self-induced propagation, the vortex tube
evolution may be effectively modeled through the introduction of an additional
white-noise correlated velocity field background. The resulting
phenomenological picture is closely related to observations previously reported
from a wavelet decomposition analysis of turbulent flow configurations.Comment: 16 pages + 2 eps figures, REVTeX
Fluctuation-response relation in turbulent systems
We address the problem of measuring time-properties of Response Functions
(Green functions) in Gaussian models (Orszag-McLaughin) and strongly
non-Gaussian models (shell models for turbulence). We introduce the concept of
{\it halving time statistics} to have a statistically stable tool to quantify
the time decay of Response Functions and Generalized Response Functions of high
order. We show numerically that in shell models for three dimensional
turbulence Response Functions are inertial range quantities. This is a strong
indication that the invariant measure describing the shell-velocity
fluctuations is characterized by short range interactions between neighboring
shells
Stabilization of Hydrodynamic Flows by Small Viscosity Variations
Motivated by the large effect of turbulent drag reduction by minute
concentrations of polymers we study the effects of a weakly space-dependent
viscosity on the stability of hydrodynamic flows. In a recent Letter [Phys.
Rev. Lett. {\bf 87}, 174501, (2001)] we exposed the crucial role played by a
localized region where the energy of fluctuations is produced by interactions
with the mean flow (the "critical layer"). We showed that a layer of weakly
space-dependent viscosity placed near the critical layer can have a very large
stabilizing effect on hydrodynamic fluctuations, retarding significantly the
onset of turbulence. In this paper we extend these observation in two
directions: first we show that the strong stabilization of the primary
instability is also obtained when the viscosity profile is realistic (inferred
from simulations of turbulent flows with a small concentration of polymers).
Second, we analyze the secondary instability (around the time-dependent primary
instability) and find similar strong stabilization. Since the secondary
instability develops around a time-dependent solution and is three-dimensional,
this brings us closer to the turbulent case. We reiterate that the large effect
is {\em not} due to a modified dissipation (as is assumed in some theories of
drag reduction), but due to reduced energy intake from the mean flow to the
fluctuations. We propose that similar physics act in turbulent drag reduction.Comment: 10 pages, 17 figs., REVTeX4, PRE, submitte
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and convergence are presented. Comparisons are made between the
present schemes in terms of accuracy and computational efficiency for solving
problems with severe internal and boundary gradients. The present study shows
that the fourth-order compact ADI scheme is stable and efficient
Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box
An efficient semi-implicit second-order-accurate finite-difference method is
described for studying incompressible Rayleigh-Benard convection in a box, with
sidewalls that are periodic, thermally insulated, or thermally conducting.
Operator-splitting and a projection method reduce the algorithm at each time
step to the solution of four Helmholtz equations and one Poisson equation, and
these are are solved by fast direct methods. The method is numerically stable
even though all field values are placed on a single non-staggered mesh
commensurate with the boundaries. The efficiency and accuracy of the method are
characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure
Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear
An effect of a mean velocity shear on a turbulence and on the effective force
which is determined by the gradient of Reynolds stresses is studied. Generation
of a mean vorticity in a homogeneous incompressible turbulent flow with an
imposed mean velocity shear due to an excitation of a large-scale instability
is found. The instability is caused by a combined effect of the large-scale
shear motions (''skew-induced" deflection of equilibrium mean vorticity) and
''Reynolds stress-induced" generation of perturbations of mean vorticity.
Spatial characteristics, such as the minimum size of the growing perturbations
and the size of perturbations with the maximum growth rate, are determined.
This instability and the dynamics of the mean vorticity are associated with the
Prandtl's turbulent secondary flows. This instability is similar to the
mean-field magnetic dynamo instability. Astrophysical applications of the
obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.
Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades
ago, describes the turbulence structure of stable boundary layers in a very
succinct way and is an integral part of numerous local closure-based numerical
weather prediction models. However, the validity of this hypothesis under very
stable conditions is a subject of on-going debate. In this work, we attempt to
address this controversial issue by performing extensive analyses of turbulence
data from several field campaigns, wind-tunnel experiments and large-eddy
simulations. Wide range of stabilities, diverse field conditions and a
comprehensive set of turbulence statistics make this study distinct
Chebyshev Solution of the Nearly-Singular One-Dimensional Helmholtz Equation and Related Singular Perturbation Equations: Multiple Scale Series and the Boundary Layer Rule-of-Thumb
The one-dimensional Helmholtz equation, Δ 2 u xx â u = f ( x ), arises in many applications, often as a component of three-dimensional fluids codes. Unfortunately, it is difficult to solve for ΔâȘ1 because the homogeneous solutions are expâ(± x /Δ), which have boundary layers of thickness O(1/Δ). By analyzing the asymptotic Chebyshev coefficients of exponentials, we rederive the OrszagâIsraeli rule [16] that Chebyshev polynomials are needed to obtain an accuracy of 1% or better for the homogeneous solutions. (Interestingly, this is identical with the boundary layer rule-of-thumb in [5], which was derived for singular functions like tanh([ x â1]/Δ).) Two strategies for small Δ are described. The first is the method of multiple scales, which is very general, and applies to variable coefficient differential equations, too. The second, when f ( x ) is a polynomial, is to compute an exact particular integral of the Helmholtz equation as a polynomial of the same degree in the form of a Chebyshev series by solving triangular pentadiagonal systems. This can be combined with the analytic homogeneous solutions to synthesize the general solution. However, the multiple scales method is more efficient than the Chebyshev algorithm when Δ is very, very tiny.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45436/1/11075_2004_Article_2865.pd
Electromotive Force and Large-Scale Magnetic Dynamo in a Turbulent Flow with a Mean Shear
An effect of sheared large-scale motions on a mean electromotive force in a
nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated
that in a homogeneous divergence-free turbulent flow the alpha-effect does not
exist, however a mean magnetic field can be generated even in a nonrotating
turbulence with an imposed mean velocity shear due to a new ''shear-current"
effect. A contribution to the electromotive force related with the symmetric
parts of the gradient tensor of the mean magnetic field (the kappa-effect) is
found in a nonrotating turbulent flows with a mean shear. The kappa-effect and
turbulent magnetic diffusion reduce the growth rate of the mean magnetic field.
It is shown that a mean magnetic field can be generated when the exponent of
the energy spectrum of the background turbulence (without the mean velocity
shear) is less than 2. The ''shear-current" effect was studied using two
different methods: the Orszag third-order closure procedure and the stochastic
calculus. Astrophysical applications of the obtained results are discussed.Comment: 12 pages, REVTEX4, submitted to Phys. Rev.
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