Professor Paolo Luchini (Universita` di Salerno): An Emergent Singularity in the Linear Response of a Turbulent Flow to Infinitesimal Perturbations
In a direct numerical simulation of turbulence aimed at explaining the formation of dunes in a channel with a wavy bottom, unexpected nontrivial behaviour was observed for waves much longer than the usually accepted DNS box size of 4 pi. In fact, the linear response of the mean velocity to an infinitesimal undulation of the bottom changes sign at a very long wavelength, and does so with a spectral response curve whose shape suggests a discontinuity in its derivative. The origin of this putative discontinuity, and its possible connection with transition to turbulence are presently unknown and deserve further investigation.