Order and disorder in two- and three-dimensional Bénard convection

Abstract

The character of transition from laminar to chaotic Rayleigh–Bénard convection in a fluid layer bounded by free-slip walls is studied numerically in two and three space dimensions. While the behaviour of finite-mode, limited-spatial-resolution dynamical systems may indicate the existence of two-dimensional chaotic solutions, we find that, this chaos is a product of inadequate spatial resolution. It is shown that as the order of a finite-mode model increases from three (the Lorenz model) to the full Boussinesq system, the degree of chaos increases irregularly at first and then abruptly decreases; no strong chaos is observed with sufficiently high resolution.