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Numerical simulation of the 2D fully hydrodynamic equations for the pure fluid in a rectangular channel with horizontal flow for Prandtl number Pr = 0.027 2 was conducted. Growth and spatiotemporal evolution of the 1L) traveling wave patterns in the Rayleigh-Benard convection of the pure fluid were investigated. It is found that the convective growth process can be divided into 3 stages: the development stage, the exponential growth stage and the periodic variation stage. Through analysis on the variation of the maximum vertical velocity field with time for different relative Rayleigh numbers Rar in the exponential growth stage, a formula of variation of linear growth rate γm was obtained with respect to Rar. Furthermore, the traveling wave convection periodicity and its dependence on the horizontal flow Reynolds number were revealed. [ABSTRACT FROM AUTHOR]