Wavelength Competition in Convective Systems

We investigate wavelength competition in two-dimensional pattern-forming systems with uniaxial anisotropy. A spatially periodic modulation of the external driving force leads to an interplay with the wave length of convection rolls which is similar to competing interactions between two equilibrium lattice constants in adsorption problems. For a class of anisotropic systems we find new types of stable patterns which are induced by such wavelength competition. These are the skewed varicose pattern, an undulatory pattern and an incommensurate undulatory pattern. Each of them seems observable in experiments on electroconvection and Rayleigh-Bénard convection in nematic liquid crystals.