Facets and singularities

In recent months, in the conclusion of my research at Caltech, two papers have made it into the world. Although they’re pretty heavy on the maths and don’t feature very many illustrative figures, they both make a simple point: with an approximate model, you can show that a large class of shock waves starting off with smooth wobbles on their surface are guaranteed to develop sharp edges after some time which you can quantify. More precisely, there is a time when the shock geometry develops a singularity. Continue reading

Posted in Uncategorized | Leave a comment

The choice of magnetic fields in MHD implosions: Maximizing stabilization while retaining symmetry

Recently Physical Review Fluids published our paper Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field, which looks at our previous result that the RM instability can be suppressed in converging MHD flows (e.g. implosions) by an applied magnetic field, albeit with some caveats on the symmetry of the resulting flow, and takes the logical next step of asking whether maximizing the symmetry properties of the applied field also maximizes the symmetry of the implosion, and in particular whether doing so also retains suppression of the RM in a way comparable to the fields we tested earlier.

The study suggests that both these questions may be answered “yes” in the case of a particular field candidate which is octahedrally symmetric. Such a field could be formed by placing an array of six equally spaced electric current loops around the centre of the targeted implosion – this is similar to, but a more extreme form of, the “saddle” field considered in our earlier papers. It turns out that, for the simulations we performed here, the RM instability is suppressed at least comparably to the uniform-field case, which is the field otherwise best at RM-suppression, while retaining a much higher flow symmetry.

The results of the study is encouraging because it suggests that maximal RM suppression can be retained without having to compromise on the flow symmetry by the correct choice of an applied field, making the use of magnetic fields for RM stabilization in converging flow problems more plausible.

The article appeared in the following,

Mostert W., Pullin D.I., Wheatley V., and Samtaney R. (2017) Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field. Phys. Rev. Fluids2, 013701.

and may be downloaded here for personal use only. Copyright 2017 by The American Physical Society.

Posted in Uncategorized | Leave a comment