The generation of vortices in high-resolution, two-dimensional decaying turbulence and the influence of initial conditions on the breaking of self-similarity

Abstract

The results of a very-high-resolution numerical integration of a two-dimensional turbulent flow is presented. The very long integration time allows a discussion of both the initial and the ultimate stage of the decay. It is established that the k−3 enstrophy inertial range is only obtained as a transient state of the system. For very long time the emergence of coherent vortices destroys the scale invariance and produces a rather steep spectrum. In addition, the long term behavior strongly depends on the initial conditions. For steep enough initial spectrum, a large-scale energy containing a range in which vortices are directly linked to the initial conditions separates from a small-scale range in which many coherent structures originate from inviscid instabilities. The results are compared with previous studies and the origin of self-similarity breaking in turbulent decay is discussed.