8,760 research outputs found
The Nonlinear Asymptotic Stage of the Rayleigh-Taylor Instability with Wide Bubbles and Narrowing Spikes
The potential flow of an incompressible inviscid heavy fluid over a light one
is considered. The integral version of the method of matched asymptotic
expansion is applied to the construction of the solution over long intervals of
time. The asymptotic solution describes the flow in which a bubble rises with
constant speed and the "tongue" is in free fall. The outer expansion is
stationary, but the inner one depends on time. It is shown that the solution
exists within the same range of Froude number obtained previously by
Vanden-Broeck (1984a,b). The Froude number and the solution depend on the
initial energy of the disturbance. At the top of the bubble, the derivative of
the free-surface curvature has a discontinuity when the Froude number is not
equal to 0.23. This makes it possible to identify the choice of the solution
obtained in a number of studies with the presence of an artificial numerical
surface tension. The first correction term in the neighborhood of the tongue is
obtained when large surface tension is included
Probing dynamical spacetimes with gravitational waves
This decade will see the first direct detections of gravitational waves by
observatories such as Advanced LIGO and Virgo. Among the prime sources are
coalescences of binary neutron stars and black holes, which are ideal probes of
dynamical spacetime. This will herald a new era in the empirical study of
gravitation. For the first time, we will have access to the genuinely
strong-field dynamics, where low-energy imprints of quantum gravity may well
show up. In addition, we will be able to search for effects which might only
make their presence known at large distance scales, such as the ones that
gravitational waves must traverse in going from source to observer. Finally,
coalescing binaries can be used as cosmic distance markers, to study the
large-scale structure and evolution of the Universe.
With the advanced detector era fast approaching, concrete data analysis
algorithms are being developed to look for deviations from general relativity
in signals from coalescing binaries, taking into account the noisy detector
output as well as the expectation that most sources will be near the threshold
of detectability. Similarly, several practical methods have been proposed to
use them for cosmology. We explain the state of the art, including the
obstacles that still need to be overcome in order to make optimal use of the
signals that will be detected. Although the emphasis will be on
second-generation observatories, we will also discuss some of the science that
could be done with future third-generation ground-based facilities such as
Einstein Telescope, as well as with space-based detectors.Comment: 38 pages, 9 figures. Book chapter for the Springer Handbook of
Spacetime (Springer Verlag, to appear in 2013
Large-amplitude capillary waves in electrified fluid sheets
Large-amplitude capillary waves on fluid sheets are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and non-conducting. Travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions found generalize the exact symmetric solutions of Kinnersley (1976) to include electric fields, for which no exact solutions have been found. Long-wave nonlinear waves are also constructed using asymptotic methods. The asymptotic solutions are compared with the full computations as the wavelength increases, and agreement is found to be excellent
Trapped waves between submerged obstacles
Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. In previous work involving a single obstacle (Dias & Vanden-Broeck 2002), new solutions called ‘generalized hydraulic falls’ were found. These solutions are characterized by a supercritical flow on one side of the obstacle and a train of waves on the other. However, in the case of a single submerged object, the generalized hydraulic falls are unphysical because the waves do not satisfy the radiation condition. In this paper new solutions for the flow past two obstacles of arbitrary shape are computed. These solutions are characterized by a train of waves ‘trapped’ between the obstacles. The generalized hydraulic falls are shown to describe locally the flow over one of the two obstacles when the distance between the two obstacles is large
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