865 research outputs found
Notes on aerodynamic forces on airship hulls
For a first approximation the air flow around the airship hull is assumed to obey the laws of perfect (i.e. free from viscosity) incompressible fluid. The flow is further assumed to be free from vortices (or rotational motion of the fluid). These assumptions lead to very great simplifications of the formulae used but necessarily imply an imperfect picture of the actual conditions. The value of the results depends therefore upon the magnitude of the forces produced by the disturbances in the flow caused by viscosity with the consequent production of vortices in the fluid. If these are small in comparison with the forces due to the assumed irrotational perfect fluid flow the results will give a good picture of the actual conditions of an airship in flight
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
Classical-path integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling
Simulations that couple different classical molecular models in an adaptive
way by changing the number of degrees of freedom on the fly, are available
within reasonably consistent theoretical frameworks. The same does not occur
when it comes to classical-quantum adaptivity. The main reason for this is the
difficulty in describing a continuous transition between the two different kind
of physical principles: probabilistic for the quantum and deterministic for the
classical. Here we report the basic principles of an algorithm that allows for
a continuous and smooth transition by employing the path integral description
of atoms.Comment: 8 pages 4 figure
Inertia Factors of Ellipsoids for Use in Airship Design
This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author
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
On the Geometry and Entropy of Non-Hamiltonian Phase Space
We analyze the equilibrium statistical mechanics of canonical, non-canonical
and non-Hamiltonian equations of motion by throwing light into the peculiar
geometric structure of phase space. Some fundamental issues regarding time
translation and phase space measure are clarified. In particular, we emphasize
that a phase space measure should be defined by means of the Jacobian of the
transformation between different types of coordinates since such a determinant
is different from zero in the non-canonical case even if the phase space
compressibility is null. Instead, the Jacobian determinant associated with
phase space flows is unity whenever non-canonical coordinates lead to a
vanishing compressibility, so that its use in order to define a measure may not
be always correct. To better illustrate this point, we derive a mathematical
condition for defining non-Hamiltonian phase space flows with zero
compressibility. The Jacobian determinant associated with time evolution in
phase space is altogether useful for analyzing time translation invariance. The
proper definition of a phase space measure is particularly important when
defining the entropy functional in the canonical, non-canonical, and
non-Hamiltonian cases. We show how the use of relative entropies can circumvent
some subtle problems that are encountered when dealing with continuous
probability distributions and phase space measures. Finally, a maximum
(relative) entropy principle is formulated for non-canonical and
non-Hamiltonian phase space flows.Comment: revised introductio
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
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