What is it about?
This adds to knowledge on the initial formation of Kelvin-Helmholtz instabilities in shear flow, in particular by verifying the nature of its genesis. It extends the work of Cowley, Baker and Tanveer (1999) by finding exact analytical solutions representing the formation of singularities in smooth initial data. Among other things, this solution demonstrates conclusively how many singularities form in the complex plane, their location and their local 3/2-power behaviour. It also generalises the scope of the initial data properties.
Featured Image
Why is it important?
Arguably it provides a firmer foundation for the initial genesis of singularities, being based on a broad-scope analytical solution rather than relying on a numerical solution in particular cases.
Perspectives
Essentially this paper confirms expected behaviour (by some authors at least), but the analytical solution provides opportunities for a more detailed analysis - and indeed theorems if later authors prefer.
Michael Page
Monash University
Read the Original
This page is a summary of: On the formation of small-time curvature singularities in vortex sheets, IMA Journal of Applied Mathematics, December 2017, Oxford University Press (OUP),
DOI: 10.1093/imamat/hxx041.
You can read the full text:
Contributors
The following have contributed to this page
