Study on frequency patterns of 2D square Rayleigh–Bénard convection filled with air

Abstract

Abstract In this paper, the coupled lattice Boltzmann BGK method (CLBGK) is applied to simulate the 2D enclosure Rayleigh–Benardconvection (RBC) filled with air at Rayleigh number Ra =7.5 × 104 ∼ 10 9. Based on these results, the pair of character frequencies with their corresponding oscillatory structures is achieved. The present study indicates that the time–dimensionless frequency (f*) of a specific oscillatory structure has a regular change with the increase of Ra. Three f* ∼ Ra trends are clearly confirmed respectively in laminar states, transitional states, and turbulent states, which can be summarized as f* ∼ Ra −1/6 in laminar and transitional states, and f* ∼ Ra 2∕7 in turbulent states, where the former one corresponds to the natural property of RBC and the latter one well matches the scale law of Nu ∼ Ra 2∕7 . With the guidance of these conclusions, a set of auxiliary RBC experiments are performed and obtain the similar f* ∼ Ra trends, which proves the reliability of LBM in the spectral research of RBC.