Three-dimensional convection in an inclined layer heated from below

Abstract

Longitudinal rolls aligned with the component of gravity parallel to the layer represent the preferred mode of convection at onset for a wide range of parameters of the inclined layer problem. As the Rayleigh number is increased beyond the critical value the longitudinal rolls tend to become unstable with respect to the wavy instability. The three-dimensional convection flows evolving from this instability are studied in this paper by numerical computations. The main effect of the wavy distortions of the longitudinal rolls is a decrease of the heat transport. The stability of the steady three-dimensional convection flow with respect to disturbances with the same periodicity interval in the plane of the layer is also investigated. Various instabilities are found in dependence on the Prandtl number P and the angle γ of inclination and their evolution is studied in a few cases.