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