Acceleration-based classification and evolution of fluid flow structures in two-dimensional turbulence

Abstract

Zero acceleration points (ZAPs) and flow structures around them are studied in a direct numerical simulation of two-dimensional energy-cascading stationary homogeneous isotropic turbulence with an extended k(-5/3) energy spectrum. A well-defined classification of ZAPs in terms of the acceleration gradient tensor's (∇a) invariants emerges naturally as a result of well-defined properties of and relations between these invariants at ZAPs. About half of all ZAPs are anti-ZAPs [with det(∇a)<0 ] and the number of vortical and straining ZAPs [with det(∇a)>0 ] is about the same. Vortical and straining ZAPs are swept by the local fluid velocity to a good statistical approximation whereas anti-ZAPs, which are present in every vortical and straining ZAP's creation and destruction events, are not. The average lifetime of ZAPs seems to scale with the time scale of the smallest eddies in the turbulence, though ZAPs (in particular vortical ones) are able to survive up to a few integral time scales. Our ZAP classification can also be applied to extended flow regions and it turns out that vortical and straining regions are mediated by regions containing anti-ZAPs. A discussion of the length scales and sizes characterizing these regions and the distances between ZAPs is also given.