...–Bénard convection nonlinear spectral solution amplitude equations Lorenz model perturbation expansion mode selection The natural convection of a fluid layer heated from below or Rayleigh–Bénard convection has been extensively studied in the past, both experimentally [ 1–7 ] and theoretically...

.... The perturbation expansion method is employed with the prior assumption that eccentricity is very small compared with other dimensions. So eccentricity in nondimensional form is considered as the perturbation quantity. With respect to the origin, the outer surface is described as r s (θ) = r o  + e·f(θ) where e...