arXiv subjects
Publications and source records attributed to Paul Clavin.
The deflagration-to-detonation transition on the tip of an elongated flame in a tube is shown to be related to a dynamical saddle-node bifurcation of the inner flame structure leading to a runaway of the pressure in finite time. The comparison with the experiments shows a good agreement.
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.