Induced defect nucleation and side-band instabilities in hexagons with rotation and mean flow

The combined effect of mean flow and rotation on hexagonal patterns is investigated using Ginzburg–Landau equations that include nonlinear gradient terms as well as the nonlocal coupling provided by the mean flow. Long- and short-wave side-band instabilities are determined. Due to the nonlinear gradient terms and enhanced by the mean flow, the penta–hepta defects can become unstable to the induced nucleation of dislocations in the defect-free amplitude, which can lead to the proliferation of penta–hepta defects and persistent spatio-temporal chaos. For individual penta–hepta defects the nonlinear gradient terms enhance climbing or gliding motion, depending on whether they break the chiral symmetry or not.