Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source

Abstract

A model for convection induced by the selective absorption of radiation in a fluid layer is investigated. The concentration based internal heat source is modelled quadratically. A linear analysis and conditional nonlinear analysis are performed. Due to the presence of significantly large regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear. This lends much credence to the use of a linearly modelled internal heat source as used by Krishnamurti [Dyn. Atmos. Oceans 27 (1997) 367], within the constraints of the parameter ranges.