STRETCHED VORTICES - THE SINEWS OF TURBULENCE - LARGE-REYNOLDS-NUMBER ASYMPTOTICS

A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation GAMMA subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in epsilon = 1/R(GAMMA) where R(GAMMA) = GAMMA/nu. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(epsilon2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R(GAMMA) is large enough. The manner in which the theory may be extended to higher orders in epsilon is indicated. The results are discussed in relation to the high-vorticity regions (here described as 'sinews') observed in many direct numerical simulations of turbulence.