Collective structures in two-dimensional turbulence
Abstract: Although different from the three-dimensional case, two-dimensional turbulence is a plausible surrogate for some geophysical and stratified flows, and has served as a laboratory model for the analysis of high-dimensional nonlinear dynamical systems. Discouragingly, although theory correctly identifies important aspects of the flow, some predictions have turned out to be wrong in detail. The reason is that the flow organises into vortices that are too coherent to be treated by mean-field theory, but not permanent enough to be considered permanent ‘objects’. This talk deals with a further turn of the theoretical screw, showing that a subset of the vortices organise themselves into a collective superstructure (a ‘crystal’), that evolves more slowly than could be expected from the mean-field model. This object, whose evolution controls the flow, and whose formation is equivalent to the cascade of energy towards large scales, tends to minimise energy through mutual screening, but it is kept from reaching equilibrium by the occasional merging of like-signed vortices. This investigation stems from a computer search among random experiments for ‘things that have some effect on the flow evolution’. At least one of the candidates identified was interesting in the sense of not being trivially expected, but converting this ‘suggestion’ into a theory required human intervention using classical techniques. Part of the seminar will reflect on how long will computers stay limited to the role of suggesting research, and whether we can expect something else in future.
