The structure of the vortices in freely decaying two-dimensional turbulence

Abstract

The structure of a viscous two-dimensional vortex core in a imposed weak strain is analysed, in the same spirit as a similar analysis of strained columnar vortices (Moffatt, Kida & Ohkitani 1994). The analysis is recast in terms of a coordinate deformation, ensuring the uniform validity of the perturbation expansion up to the neighbourhood of a dividing streamline, beyond which it is not expected to work, and from where the exponentially weak vorticity is expected to be stripped to infinity. The orientation and ellipticity of the vorticity distribution of the cores is compared with the results of a numerical experiment in two-dimensional turbulence, and shown to agree. This is interpreted both as a confirmation of the theory and as an indication that the vortices of two-dimensional turbulence are sufficiently long-lived to be controlled by viscous diffusion, even at the relatively large Reynolds numbers of our simulation.