Nonlinear spatiotemporal instabilities in two-dimensional electroconvective flows

This work studies nonlinear spatiotemporal stability of two-dimensional electroconvection between two flat plates subjected to a through-flow, using numerical simulations and weakly analyses. We found that the traveling speeds leading trailing edges wave packet in regime are consistent with linear ones. derived for first time Ginzburg-Landau equation (GLE) an amplitude expansion method extending earlier Pham Suslov. GLE can predict absolute growth rate even when parameters away from critical conditions, outperforming multiple-scale method.