We report experimental and theoretical results on the flexoelectric instability and crossover between flexoelectric domains and electroconvection in a hybrid aligned nematic MBBA under d.c. voltage. At threshold a spatially periodic flexoelectric deformation in the form of longitudinal domains (along the planar director) was observed. With increasing voltage the director deviation out of the initial plane becomes clearly detectable. Observations of tracers show that hydrodynamic flow develops inside the flexoelectric stripe pattern in the form of circular orbits perpendicular to the domain stripes. With further increasing d.c. voltage electroconvection sets in in the form of drifting oblique rolls inside the flexoelectric domains.

We investigate a number of complex patterns driven by the electroconvection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nematohydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasihomogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.

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