Vortices subjected to non-axisymmetric strain z - unsteady asymptotic evolution H.K. Moffatt Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK 1. zyxwvu Introduction Much interest has been recently re-focused on the problem of concentrated vortices and their interactions. Much of this interest has been stimulated by the discovery of such structures in direct numerical simulations of turbulence (see, for example, Jimenez et a1 1993, and references therein). The relevance of stretched vortices to the problem of turbulence was first pointed out by Burgers (1948), and has recently been advocated by Moffatt, Kida & Ohkitani 1994 (hereafter MK0’94) who describe the situation in the following terms: “Vortices have often been described as the ‘sinews’ of fluid motion. Just z as sinews serve to connect a muscle with zyxw a bone or other structure, zy so the concentrated vortices of turbulence serve to connect large eddies of much weaker vorticity; and just as sinews can take the stress and strain of muscular effort, so the concentrated vortices can accommodate the stress associated with the low pressure in their cores and the strain imposed by relative motion of the eddies into which they must merge at their ends.” The particular problem addressed by MK0’94 was that of a vortex subjected to non-axisymmetric uniform strain U = (az I BY, zyxwv 72) (1.1) with cy + zyxwv p + y = zyxwv 0 , cy < /3 < 0 < y, for which a steady high-Reynolds-number asymptotic solution may be obtained in which the leading order vorticity distribution is simply = (O,O,wo(r)) (1.2) with r2 = z2 +- y2. The form of WO(T) is determined by a solvability condition at order RF1, where Rr = F/Y (1.3) www.moffatt.tc