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-wave 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.