On the two-dimensional stability of the axisymmetric Burgers vortex

The stability of the axisymmetric Burgers vortex solution of the Navier–Stokes equations to two-dimensional perturbations is studied numerically up to Reynolds numbers, R=Gamma/2pinu, of order 104. No unstable eigenmodes for azimuthal mode numbers n=1,..., 10 are found in this range of Reynolds numbers. Increasing the Reynolds number has a stabilizing effect on the vortex

On velocity structure functions and the spherical vortex model for isotropic turbulence

We investigate a stochastic model for homogeneous, isotropic turbulence based on Hill's spherical vortex. This is an extension of the method of Synge and Lin [Trans. R. Soc. Can. 37, 45 (1943)], to the calculation of higher even-order velocity structure functions. Isotropic turbulence is represented by a homogeneous distribution of eddies, each modeled by a spherical vortex. The cascade process of eddy breakdown is incorporated into the statistical model through an average over an assumed log-normal distribution of vortex radii. We calculate the statistical properties of the model, in particular order-n velocity structure functions defined by rank-n tensors for the ensemble average of a set of incremental differences in velocity components. We define Di[centered ellipsis]s = , where denotes the ensemble average. Specifically Dij, Dijkl, and the longitudinal component of Dijklmn are calculated directly from the spherical vortex ensemble. Matching the longitudinal components of Dij and Dijkl with experimental results fixes two independent model parameters. The lateral and mixed components of Dijkl and the longitudinal component of Dijklmn are then model predictions

The velocity-scalar cross spectrum of stretched spiral vortices

The stretched-spiral vortex model is used to calculate the velocity-scalar cross spectrum for homogeneous, isotropic turbulence in the presence of a mean scalar gradient. The only nonzero component of the cospectrum is that contributed by the velocity component in the direction of the imposed scalar gradient while the quadrature spectrum is identically zero, in agreement with experiment. For the velocity field provided by the stretched-spiral vortex, the velocity-scalar spectrum can be divided into two additive components contributed by the velocity components along the vortex axis, and in the plane normal to this axis, respectively. For the axial velocity field, a new exact solution of the scalar convection-diffusion equation is found exhibiting scalar variation in the direction of the vortex tube axis. An asymptotic expression was found for the cospectrum contributed by this solution and the axial velocity, with the leading order term showing a k–5/3 range. This term is produced by the winding of the initial axial velocity field by the axisymmetric vortex core. The next order term gives a k–7/3 range, and arises from the lowest order effect of the nonaxisymmetric vorticity on the evolution of the axial velocity. Its coefficient can be of either sign or zero depending on the initial conditions. The contribution to the cospectrum from the velocity in the plane of the vortex is also calculated, but no universal high wave number asymptotic form is found. The integrals are evaluated numerically and it is found that the resulting cospectrum does not remain of one sign. Its form depends on the choice of the vortex core velocity profile and time cutoff in the spectral integrals. The one-dimensional cospectrum contributed by the axial velocity is compared with the experimental data of Mydlarski and Warhaft [J. Fluid Mech. 358, 135–175 (1998)]

Effect of Schmidt number on the velocity–scalar cospectrum in isotropic turbulence with a mean scalar gradient

We consider transport of a passive scalar by an isotropic turbulent velocity field in the presence of a mean scalar gradient. The velocity–scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shell-summed energy and scalar spectra. At high Schmidt number, this bound limits the possible contribution of the sub-Kolmogorov scales to the scalar flux. At low Schmidt number, we derive an asymptotic result for the cospectrum in the inertial–diffusive range, with a -11/3 power law wavenumber dependence, and a comparison is made with results from large-eddy simulation. The sparse direct-interaction perturbation (SDIP) is used to calculate the cospectrum for a range of Schmidt numbers. The Lumley scaling result is recovered in the inertial–convective range and the constant of proportionality was calculated. At high Schmidt numbers, the cospectrum is found to decay exponentially in the viscous–convective range, and at low Schmidt numbers, the -11/3 power law is observed in the inertial–diffusive range. Results are reported for the cospectrum from a direct numerical simulation at a Taylor Reynolds number of 265, and a comparison is made at Schmidt number order unity between theory, simulation and experiment

17 ways to say yes:Toward nuanced tone of voice in AAC and speech technology

People with complex communication needs who use speech-generating devices have very little expressive control over their tone of voice. Despite its importance in human interaction, the issue of tone of voice remains all but absent from AAC research and development however. In this paper, we describe three interdisciplinary projects, past, present and future: The critical design collection Six Speaking Chairs has provoked deeper discussion and inspired a social model of tone of voice; the speculative concept Speech Hedge illustrates challenges and opportunities in designing more expressive user interfaces; the pilot project Tonetable could enable participatory research and seed a research network around tone of voice. We speculate that more radical interactions might expand frontiers of AAC and disrupt speech technology as a whole

Discrete quantum gravity: a mechanism for selecting the value of fundamental constants

Smolin has put forward the proposal that the universe fine tunes the values of its physical constants through a Darwinian selection process. Every time a black hole forms, a new universe is developed inside it that has different values for its physical constants from the ones in its progenitor. The most likely universe is the one which maximizes the number of black holes. Here we present a concrete quantum gravity calculation based on a recently proposed consistent discretization of the Einstein equations that shows that fundamental physical constants change in a random fashion when tunneling through a singularity.Comment: 5 pages, RevTex, 4 figures, honorable mention in the 2003 Gravity Research Foundation Essays, to appear in Int. J. Mod. Phys.

Consistent discretizations: the Gowdy spacetimes

We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with local degrees of freedom. We show that the scheme can be correctly used to numerically evolve the space-times. We show that the resulting numerical schemes are convergent and preserve approximately the constraints as expected.Comment: 10 pages, 8 figure

On imploding cylindrical and spherical shock waves in a perfect gas

The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law result can then be interpreted as the leading-order, strong-shock approximation, valid near the origin at the implosion centre. We improve the Guderley solution by adding two further terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion, valid where the shock is still weak and very far from the origin, is also constructed. With an appropriate change of variables and using the exact shock-jump conditions, a numerical, characteristics-based solution is obtained describing the general shock motion from almost infinity to very close to the reflection point. Comparisons are made between the series expansions, the characteristics solution, and the results obtained using an Euler solver. These show that the addition of two terms to the Guderley solution significantly extends the range of validity of the strong-shock series expansion

Consistent discretization and loop quantum geometry

We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism constraint to reduce its space of solutions and the constraint is preserved exactly under the discrete evolution. One ends up with a theory that has as physical space what is usually considered the kinematical space of loop quantum geometry, given by diffeomorphism invariant spin networks endowed with appropriate rigorously defined diffeomorphism invariant measures and inner products. The dynamics can be implemented as a unitary transformation and the problem of time explicitly solved or at least reduced to as a numerical problem. We exhibit the technique explicitly in 2+1 dimensional gravity.Comment: 4 pages, Revtex, no figure

Building Realistic Mobility Models for Mobile Ad Hoc Networks

A mobile ad hoc network (MANET) is a self-configuring wireless network in which each node could act as a router, as well as a data source or sink. Its application areas include battlefields and vehicular and disaster areas. Many techniques applied to infrastructure-based networks are less effective in MANETs, with routing being a particular challenge. This paper presents a rigorous study into simulation techniques for evaluating routing solutions for MANETs with the aim of producing more realistic simulation models and thereby, more accurate protocol evaluations. MANET simulations require models that reflect the world in which the MANET is to operate. Much of the published research uses movement models, such as the random waypoint (RWP) model, with arbitrary world sizes and node counts. This paper presents a technique for developing more realistic simulation models to test and evaluate MANET protocols. The technique is animation, which is applied to a realistic scenario to produce a model that accurately reflects the size and shape of the world, node count, movement patterns, and time period over which the MANET may operate. The animation technique has been used to develop a battlefield model based on established military tactics. Trace data has been used to build a model of maritime movements in the Irish Sea. Similar world models have been built using the random waypoint movement model for comparison. All models have been built using the ns-2 simulator. These models have been used to compare the performance of three routing protocols: dynamic source routing (DSR), destination-sequenced distance-vector routing (DSDV), and ad hoc n-demand distance vector routing (AODV). The findings reveal that protocol performance is dependent on the model used. In particular, it is shown that RWP models do not reflect the performance of these protocols under realistic circumstances, and protocol selection is subject to the scenario to which it is applied. To conclude, it is possible to develop a range of techniques for modelling scenarios applicable to MANETs, and these simulation models could be utilised for the evaluation of routing protocols