ON THE LOCAL TOPOLOGY EVOLUTION OF A HIGH-SYMMETRY FLOW

The local topology evolution of a high-symmetry, high resolution (effe ctive maximum resolution of 1024(3) grid points, maximum wave number o f 341) incompressible flow simulation having a Reynolds number (= 1/nu ) of 1000 is investigated. The Q-R invariants of the velocity gradient tensor A(ij), the enstrophy, Omega(ij)Omega(ij) and the mean-square s train rate SijSij are computed at an interval when the local maximum v orticity increases drastically. All the analysis of the computations a re done on the z = 0 plane, where the maximum vorticity and strain are located during the evolution. In the Q-R plane, most of the collocati on points evolve towards the lower right corner, a region where strain dominates over vorticity. The pressure Hessian tensor components are computed in the O planes, Points with very large strain and no vortici ty, which are located along the boundaries Separating oppositely signe d vortices, are found to have a diagonal pressure Hessian tenser. It i s discussed how such a Hessian tenser form can result in a singularity formation in strain (and Q invariant). Relevance of the results to tu rbulence is discussed. Results are compared to the predictions of a si ngular model by Leorat (Ph. D. thesis, Universite de Paris VII; pp. 12 5-129, 1975), Vieillefosse [J. Phys: 43, 837 (1982)], and Cantwell [Ph ys. Fluids A 5, 2008 (1999)]. (C) 1995 American Institute of Physics.