Generalized Lorenz models and their routes to chaos.II. Energy-conserving horizontal mode truncations

Many attempts have been made to extend 3D Lorenz model in higher dimension to describe 2D Rayleigh-Benard convection.3D Lorenz model was originally derived by taking into account only three Fourier modes.we make a novel attempt here to generalize this 3D model to higher dimensions by picking up the fourier modes in consistent way.In this paper we have derived a generalized Lorenz by selecting horizontal modes that conserve energy in the dissipationless limit and lead to the systems that have bounded solutions. An interesting result is that the lowest-order generalized Lorenz model, which satises these criteria, is a 5D model and that its route to chaos is the same as that observed in the original 3D Lorenz model.A rather interesting result is that the onset of fully developed chaos is at low Rayleigh ratio. I