The interaction of two propagating vortex pairs is considered, each pair being initially
aligned along the positive principal axis of strain associated with the other. As a
preliminary, the action of accelerating strain on a Burgers vortex is considered and the
conditions for a finite-time singularity (or ‘blow-up’) are determined. The asymptotic
high Reynolds number behaviour of such a vortex under non-axisymmetric strain,
and the corresponding behaviour of a vortex pair, are described. This leads naturally
to consideration of the interaction of the two vortex pairs, and identifies a mechanism
by which blow-up may occur through self-similar evolution in an interaction zone
where scale decreases in proportion to
(t* − t)1/2, where t* is the
singularity time. The relevance of Leray scaling in this interaction zone is discussed.
On Stability of Blow-Up Solutions of the Burgers Vortex Type for the Navier–Stokes Equations with a Linear Strain
