Asymptotic behaviour of the Rayleigh--Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin & Williams\cite{clavin} for which we give a simplified demonstration. In particular we observe that the spike's curvature evolves like $t^3$ while the overshoot in acceleration shows a good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.Comment: 4 pages, 6 figure

Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(\eps',k)>0, where \eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and $k\gg 1$ the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion

Model Equation for the Dynamics of Wrinkled Shockwaves: Comparison with DNS and Experiments

International audienceA model equation for the dynamics and the geometry of the wrinkled front of shock waves, obtained for strong shocks in the Newtonian limit, is tested by comparison with direct numerical simulations and a shock tube experiment

A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears

Variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides an efficient tool for statistical speed analysis, as well as a fast and accurate method for speed computation. A variational principle based analysis is carried out on the ensemble of KPP speeds through spatially stationary random shear flows inside infinite channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speeds is proved to obey the quadratic law under certain shear moment conditions. Similarly, in the large rms amplitude regime, the enhancement follows the linear law. In particular, both laws hold for the Ornstein-Uhlenbeck process in case of two dimensional channels. An asymptotic ensemble averaged speed formula is derived in the small rms regime and is explicit in case of the Ornstein-Uhlenbeck process of the shear. Variational principle based computation agrees with these analytical findings, and allows further study on the speed enhancement distributions as well as the dependence of enhancement on the shear covariance. Direct simulations in the small rms regime suggest quadratic speed enhancement law for non-KPP nonlinearities.Comment: 28 pages, 14 figures update: fixed typos, refined estimates in section

Nonsteady condensation and evaporation waves

We study motion of a phase transition front at a constant temperature between stable and metastable states in fluids with the universal Van der Waals equation of state (which is valid sufficiently close to the fluid's critical point). We focus on a case of relatively large metastability and low viscosity, when it can be shown analytically that no steadily moving phase-transition front exists. Numerically simulating a system of the one-dimensional Navier-Stokes and continuity equations, we find that, in this case, the nonsteady phase-transition front emits acoustic shocks in forward and backward directions. Through this mechanism, the front drops its velocity and eventually comes to a halt. The acoustic shock wave may shuttle, bouncing elastically from the system's edge and strongly inelastically from the phase transition front. Nonsteady rarefaction shock waves appear in the shuttle process, despite the fact that the model does not admit steady rarefaction waves propagating between stationary states. If the viscosity is below a certain threshold, an instability sets in, driving the system into a turbulent state. This work was supported by the Japan Society for Promotion of Science.Comment: revtex text file and four eps files with figures. Physical Review Letters, in pres

The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs

The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities. We briefly review these instabilities and the corresponding flame acceleration. We discuss the conditions necessary for each of the currently proposed explosion mechanisms and the attendant uncertainties. A grid of critical masses for detonation in the range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and its sensitivity to composition explored. Prompt detonations are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. ``Active turbulent combustion'' and multi-point ignition are presented as two plausible ways of doing this. A deflagration that moves at the ``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if the front moves with the speed of the fastest floating bubbles. The relevance of the transition to the ``distributed burning regime'' is discussed for delayed detonations. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate mass elements, and warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

An Exploratory Study into the Factors Impeding Ethical Consumption

Although consumers are increasingly engaged with ethical factors when forming opinions about products and making purchase decisions, recent studies have highlighted significant differences between consumers’ intentions to consume ethically, and their actual purchase behaviour. This article contributes to an understanding of this “ethical purchasing gap” through a review of existing literature, and the inductive analysis of focus group discussions. A model is suggested which includes exogenous variables such as moral maturity and age which have been well covered in the literature, together with further impeding factors identified from the focus group discussions. For some consumers, inertia in purchasing behaviour was such that the decision-making process was devoid of ethical considerations. Several manifested their ethical views through post-purchase dissonance and retrospective feelings of guilt. Others displayed a reluctance to consume ethically due to personal constraints, a perceived negative impact on image or quality, or an outright negation of responsibility. Those who expressed a desire to consume ethically often seemed deterred by cynicism, which caused them to question the impact they, as an individual, could achieve. These findings enhance the understanding of ethical consumption decisions and provide a platform for future research in this area

Conservation efficiency and nutritive value of silages made from grass-red clover and multi-species swards compared with grass monocultures

peer reviewedBinary grass-clover and multi-species swards can increase herbage yields or facilitate reduced inputs of inorganic fertiliser nitrogen (N) compared with perennial ryegrass monocultures. However, the efficiency of the ensilage process and the nutritive value of silage produced from multi-species swards has not been documented. Replicate samples from grass-red clover binary mixture and multi-species mixture swards were ensiled in laboratory silos to assess the ensilability, fermentation characteristics, conservation losses and silage nutritive value compared with grass monocultures produced using inorganic N fertiliser. The results suggest that assessment of the ensilability and subsequent ensilage characteristics of binary and multi-species mixtures should be based on direct sampling from such mixtures rather than being predicted from values obtained from monocultures of constituent species. Under favourable ensiling conditions, unwilted binary mixtures and multi-species mixtures are satisfactorily preserved as silage, comparable to a perennial ryegrass monoculture receiving inorganic N fertiliser. However, when ensiled under more challenging crop conditions the mixtures exhibited a greater requirement for their preservation to be aided, compared with the perennial ryegrass monoculture. Despite the application of inorganic N reducing the legume content of multi-species mixture swards, it had relatively little effect on herbage ensilability or silage preservation. For all species treatments, silage nutritive values were primarily dependent on the pre-ensiling values, although herbage digestibility values declined during ensilage where the ensilage process was inefficient. The current study suggests that in order to be satisfactorily preserved as silage, binary grass-clover and multispecies swards have a greater requirement for an adequate rapid field wilt and/or effective preservative application compared with perennial ryegrass produced using inorganic fertiliser N