Greenside, HS; Cross, MC, *Stability analysis of two-dimensional models of three-dimensional convection*,
Physical Review A, vol. 31 no. 4
(1985),
pp. 2492-2501 [doi] .
**Abstract:**

*Analytical and numerical methods are used to study the linear stability of spatially periodic solutions for various two-dimensional equations which model thermal convection in fluids. This analysis suggests new model equations that will be useful for investigating questions such as wave-number selection, pattern formation, and the onset of turbulence in large-aspect-ratio Rayleigh-Bénard systems. In particular, we construct a nonrelaxational model that has stability boundaries similar to those calculated for intermediate Prandtl-number fluids. © 1985 The American Physical Society.*