153 research outputs found
Turbulence in a localized puff in a pipe
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this recordWe have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about two pipe diameters long
An improved \eps expansion for three-dimensional turbulence: summation of nearest dimensional singularities
An improved \eps expansion in the -dimensional () stochastic
theory of turbulence is constructed by taking into account pole singularities
at in coefficients of the \eps expansion of universal quantities.
Effectiveness of the method is illustrated by a two-loop calculation of the
Kolmogorov constant in three dimensions.Comment: 4 page
Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence
Two conditional averages for the longitudinal velocity increment u_r of the
simulated turbulence are calculated: h(u_r) is the average of the increment of
the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the
corresponding one of the square of the difference of the gradient of the
velocity field. Based on the physical argument, we suggest the formulae for h
and g, which are quite satisfactorily fitted to the 512^3 DNS data. The
predicted PDF is characterized as
(1) the Gaussian distribution for the small amplitudes,
(2) the exponential distribution for the large ones, and (3) a prefactor
before the exponential function for the intermediate ones.Comment: 4 pages, 4 figures, using RevTeX3.
Large eddy simulation of two-dimensional isotropic turbulence
Large eddy simulation (LES) of forced, homogeneous, isotropic,
two-dimensional (2D) turbulence in the energy transfer subrange is the subject
of this paper. A difficulty specific to this LES and its subgrid scale (SGS)
representation is in that the energy source resides in high wave number modes
excluded in simulations. Therefore, the SGS scheme in this case should assume
the function of the energy source. In addition, the controversial requirements
to ensure direct enstrophy transfer and inverse energy transfer make the
conventional scheme of positive and dissipative eddy viscosity inapplicable to
2D turbulence. It is shown that these requirements can be reconciled by
utilizing a two-parametric viscosity introduced by Kraichnan (1976) that
accounts for the energy and enstrophy exchange between the resolved and subgrid
scale modes in a way consistent with the dynamics of 2D turbulence; it is
negative on large scales, positive on small scales and complies with the basic
conservation laws for energy and enstrophy. Different implementations of the
two-parametric viscosity for LES of 2D turbulence were considered. It was found
that if kept constant, this viscosity results in unstable numerical scheme.
Therefore, another scheme was advanced in which the two-parametric viscosity
depends on the flow field. In addition, to extend simulations beyond the limits
imposed by the finiteness of computational domain, a large scale drag was
introduced. The resulting LES exhibited remarkable and fast convergence to the
solution obtained in the preceding direct numerical simulations (DNS) by
Chekhlov et al. (1994) while the flow parameters were in good agreement with
their DNS counterparts. Also, good agreement with the Kolmogorov theory was
found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary
djnlx.tex fil
Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation
We present an extensive pseudospectral study of the randomly forced
Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and
a variance , where is the wavevector and the dimension . We present the first evidence for multiscaling of velocity structure
functions in this model for . We extract the multiscaling exponent
ratios by using extended self similarity (ESS), examine their
dependence on , and show that, if , they are in agreement with those
obtained for the deterministically forced Navier-Stokes equation (NSE). We
also show that well-defined vortex filaments, which appear clearly in studies
of the NSE, are absent in the RFNSE.Comment: 4 pages (revtex), 6 figures (postscript
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
Biscale Chaos in Propagating Fronts
The propagating chemical fronts found in cubic autocatalytic
reaction-diffusion processes are studied. Simulations of the reaction-diffusion
equation near to and far from the onset of the front instability are performed
and the structure and dynamics of chemical fronts are studied. Qualitatively
different front dynamics are observed in these two regimes. Close to onset the
front dynamics can be characterized by a single length scale and described by
the Kuramoto-Sivashinsky equation. Far from onset the front dynamics exhibits
two characteristic lengths and cannot be modeled by this amplitude equation. An
amplitude equation is proposed for this biscale chaos. The reduction of the
cubic autocatalysis reaction-diffusion equation to the Kuramoto-Sivashinsky
equation is explicitly carried out. The critical diffusion ratio delta, where
the planar front loses its stability to transverse perturbations, is determined
and found to be delta=2.300.Comment: Typeset using RevTeX, fig.1 and fig.4 are not available, mpeg
simulations are at
http://www.chem.utoronto.ca/staff/REK/Videos/front/front.htm
Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows
G-equations are well-known front propagation models in turbulent combustion
and describe the front motion law in the form of local normal velocity equal to
a constant (laminar speed) plus the normal projection of fluid velocity. In
level set formulation, G-equations are Hamilton-Jacobi equations with convex
( type) but non-coercive Hamiltonians. Viscous G-equations arise from
either numerical approximations or regularizations by small diffusion. The
nonlinear eigenvalue from the cell problem of the viscous G-equation
can be viewed as an approximation of the inviscid turbulent flame speed .
An important problem in turbulent combustion theory is to study properties of
, in particular how depends on the flow amplitude . In this
paper, we will study the behavior of as at
any fixed diffusion constant . For the cellular flow, we show that
Compared with the inviscid G-equation (), the diffusion dramatically slows
down the front propagation. For the shear flow, the limit
\nit where
is strictly decreasing in , and has zero derivative at .
The linear growth law is also valid for of the curvature dependent
G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square
root of log growt
Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
The large scale properties of spatiotemporal chaos in the 2d
Kuramoto-Sivashinsky equation are studied using an explicit coarse graining
scheme. A set of intermediate equations are obtained. They describe
interactions between the small scale (e.g., cellular) structures and the
hydrodynamic degrees of freedom. Possible forms of the effective large scale
hydrodynamics are constructed and examined. Although a number of different
universality classes are allowed by symmetry, numerical results support the
simplest scenario, that being the KPZ universality class.Comment: 4 pages, 3 figure
Dynamics and statistics of heavy particles in turbulent flows
We present the results of Direct Numerical Simulations (DNS) of turbulent
flows seeded with millions of passive inertial particles. The maximum Taylor's
Reynolds number is around 200. We consider particles much heavier than the
carrier flow in the limit when the Stokes drag force dominates their dynamical
evolution. We discuss both the transient and the stationary regimes. In the
transient regime, we study the growt of inhomogeneities in the particle spatial
distribution driven by the preferential concentration out of intense vortex
filaments. In the stationary regime, we study the acceleration fluctuations as
a function of the Stokes number in the range [0.16:3.3]. We also compare our
results with those of pure fluid tracers (St=0) and we find a critical behavior
of inertia for small Stokes values. Starting from the pure monodisperse
statistics we also characterize polydisperse suspensions with a given mean
Stokes.Comment: 13 pages, 10 figures, 2 table
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