740 research outputs found
Numerical simulation of super-square patterns in Faraday waves
We report the first simulations of the Faraday instability using the full
three-dimensional Navier-Stokes equations in domains much larger than the
characteristic wavelength of the pattern. We use a massively parallel code
based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of
arbitrarily deformable phase interfaces. Simulations performed in rectangular
and cylindrical domains yield complex patterns. In particular, a
superlattice-like pattern similar to those of [Douady & Fauve, Europhys. Lett.
6, 221-226 (1988); Douady, J. Fluid Mech. 221, 383-409 (1990)] is observed. The
pattern consists of the superposition of two square superlattices. We
conjecture that such patterns are widespread if the square container is large
compared to the critical wavelength. In the cylinder, pentagonal cells near the
outer wall allow a square-wave pattern to be accommodated in the center
Extreme multiplicity in cylindrical Rayleigh-Benard convection: II. Bifurcation diagram and symmetry classification
A large number of flows with distinctive patterns have been observed in
experiments and simulations of Rayleigh-Benard convection in a water-filled
cylinder whose radius is twice the height. We have adapted a time-dependent
pseudospectral code, first, to carry out Newton's method and branch
continuation and, second, to carry out the exponential power method and Arnoldi
iteration to calculate leading eigenpairs and determine the stability of the
steady states. The resulting bifurcation diagram represents a compromise
between the tendency in the bulk towards parallel rolls, and the requirement
imposed by the boundary conditions that primary bifurcations be towards states
whose azimuthal dependence is trigonometric. The diagram contains 17 branches
of stable and unstable steady states. These can be classified geometrically as
roll states containing two, three, and four rolls; axisymmetric patterns with
one or two tori; three-fold symmetric patterns called mercedes, mitubishi,
marigold and cloverleaf; trigonometric patterns called dipole and pizza; and
less symmetric patterns called CO and asymmetric three-rolls. The convective
branches are connected to the conductive state and to each other by 16 primary
and secondary pitchfork bifurcations and turning points. In order to better
understand this complicated bifurcation diagram, we have partitioned it
according to azimuthal symmetry. We have been able to determine the
bifurcation-theoretic origin from the conductive state of all the branches
observed at high Rayleigh number
Patterns in transitional shear flows. Part 2: Nucleation and optimal spacing
Low Reynolds number turbulence in wall-bounded shear flows \emph{en route} to
laminar flow takes the form of oblique, spatially-intermittent turbulent
structures. In plane Couette flow, these emerge from uniform turbulence via a
spatiotemporal intermittent process in which localised quasi-laminar gaps
randomly nucleate and disappear. For slightly lower Reynolds numbers, spatially
periodic and approximately stationary turbulent-laminar patterns predominate.
The statistics of quasi-laminar regions, including the distributions of space
and time scales and their Reynolds number dependence, are analysed. A smooth,
but marked transition is observed between uniform turbulence and flow with
intermittent quasi-laminar gaps, whereas the transition from gaps to regular
patterns is more gradual. Wavelength selection in these patterns is analysed
via numerical simulations in oblique domains of various sizes. Via lifetime
measurements in minimal domains, and a wavelet-based analysis of wavelength
predominance in a large domain, we quantify the existence and non-linear
stability of a pattern as a function of wavelength and Reynolds number. We
report that the preferred wavelength maximises the energy and dissipation of
the large-scale flow along laminar-turbulent interfaces. This optimal behaviour
is primarily due to the advective nature of the large-scale flow, with
turbulent fluctuations playing only a secondary role.Comment: 27 pages, 14 figure
Patterns in transitional shear flows. Part 1. Energy transfers and mean-flow interaction
Low Reynolds number turbulence in wall-bounded shear flows en route to
laminar flow takes the form of localised turbulent structures. In plane shear
flows, these appear as a regular alternation of turbulent and quasi-laminar
flow. Both the physical and the spectral energy balance of a turbulent-laminar
pattern are computed and compared to those of uniform turbulence at low .
In the patterned state, the mean flow is strongly modulated and is fuelled by
two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via
mean advection), and, secondly, the extraction of energy from turbulent
fluctuations (via negative production, associated to a strong energy transfer
from small to large scales). These processes are surveyed as uniform turbulence
loses its stability. Inverse energy transfers and negative production are also
found in the uniformly turbulent state.Comment: 29 pages, 15 figure
The Pack Method for Compressive Tests of Thin Specimens of Materials Used in Thin-Wall Structures
The strength of modern lightweight thin-wall structures is generally limited by the strength of the compression members. An adequate design of these members requires a knowledge of the compressive stress-strain graph of the thin-wall material. The "pack" method was developed at the National Bureau of Standards with the support of the National Advisory Committee for Aeronautics to make possible a determination of compressive stress-strain graphs for such material. In the pack test an odd number of specimens are assembled into a relatively stable pack, like a "pack of cards." Additional lateral stability is obtained from lateral supports between the external sheet faces of the pack and outside reactions. The tests seems adequate for many problems in structural research
Extreme multiplicity in cylindrical Rayleigh-B\'enard convection: I. Time-dependence and oscillations
Rayleigh-Benard convection in a cylindrical container can take on many
different spatial forms. Motivated by the results of Hof, Lucas and Mullin
[Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable
states at a single set of parameter values, we have carried out simulations at
the same Prandtl number, that of water, and radius-to-height aspect ratio of
two. We have used two kinds of thermal boundary conditions: perfectly
insulating sidewalls and perfectly conducting sidewalls. In both cases we
obtain a wide variety of coexisting steady and time-dependent flows
On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess
We propose two techniques aimed at improving the convergence rate of steady
state and eigenvalue solvers preconditioned by the inverse Stokes operator and
realized via time-stepping. First, we suggest a generalization of the Stokes
operator so that the resulting preconditioner operator depends on several
parameters and whose action preserves zero divergence and boundary conditions.
The parameters can be tuned for each problem to speed up the convergence of a
Krylov-subspace-based linear algebra solver. This operator can be inverted by
the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose
to generate an initial guess of steady flow, leading eigenvalue and eigenvector
using orthogonal projection on a divergence-free basis satisfying all boundary
conditions. The approach, including the two proposed techniques, is illustrated
on the solution of the linear stability problem for laterally heated square and
cubic cavities
Colored-noise thermostats \`a la carte
Recently, we have shown how a colored-noise Langevin equation can be used in
the context of molecular dynamics as a tool to obtain dynamical trajectories
whose properties are tailored to display desired sampling features. In the
present paper, after having reviewed some analytical results for the stochastic
differential equations forming the basis of our approach, we describe in detail
the implementation of the generalized Langevin equation thermostat and the
fitting procedure used to obtain optimal parameters. We discuss in detail the
simulation of nuclear quantum effects, and demonstrate that, by carefully
choosing parameters, one can successfully model strongly anharmonic solids such
as neon. For the reader's convenience, a library of thermostat parameters and
some demonstrative code can be downloaded from an on-line repository
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