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The evolution of three-dimensional, cellular convective flows in a planehorizontal layer of a Boussinesq fluid heated from below is well studied. Herewe review results from the investigation of this system as well as a number ofrelated and novel numerical findings. We present theoretical results forpattern formation in Rayleigh-B\'enard convection with solving NS equationunder the Boussinesq approximation . System of equations were reduced to2-dimension form to simplify the analysis.The evolution of the flow agree withthe idea of the flow achieving an optimal form.

The selforganization phenomenon in Rayleigh-Benard convection: a hydrodynamics analysis